Showing papers in "International Journal of Systems Science in 2009"
TL;DR: A new criterion based on linear matrix inequalities is established for checking the robust H 2 performance of the uncertain system and a sufficient condition for the existence of the state-feedback controllers is established such that the closed-loop system is quadratically mean square stable.
Abstract: This article deals with the robust H2 control problem for a class of Markovian jump linear systems with uncertain switching probabilities. The uncertainties under consideration appear both in the system parameters and in the mode transition rates. First, a new criterion based on linear matrix inequalities is established for checking the robust H2 performance of the uncertain system. Then, a sufficient condition for the existence of the state-feedback controllers is established such that the closed-loop system is quadratically mean square stable and has a certain level of robust H2 performance in terms of linear matrix inequalities with equality constraints. A globally convergent algorithm is also presented to construct such controllers effectively. Finally, an illustrative numerical example is used to demonstrate the developed theory.
145 citations
TL;DR: In this article, the formation control is investigated for a network of second-order dynamic agents with heterogeneous communication delays and a delay-dependent formation control algorithm is proposed to achieve the desired moving formation.
Abstract: In this article, the formation control is investigated for a network of second-order dynamic agents with heterogeneous communication delays. The desired stationary formation is achieved by introducing diverse self-delay for each agent. In addition, a delay-dependent formation control algorithm is proposed to achieve the desired moving formation. Based on the frequency-domain analysis and matrix theory, sufficient conditions are obtained for the multi-agent systems asymptotically converging to desired stationary and moving formations, respectively. Simulation results illustrate the correctness of the results.
122 citations
TL;DR: A decentralised information feedback mechanism is introduced to a group of mobile robots such that the robots asymptotically converge to a given moving formation if the graph is connected, then the convergence to the moving formation of the closed-loop system is guaranteed.
Abstract: In this article, a decentralised information feedback mechanism is introduced to a group of mobile robots such that the robots asymptotically converge to a given moving formation. It is assumed that the robots can exchange only position information according to a pre-specified communication graph. Each node represents a robot. Two robots are neighbours of each other if there is an edge between the two nodes. A feedback controller is performed for each robot by only using its own velocity information and the position information from its neighbours. It is proven that if the graph is connected, then the convergence to the moving formation of the closed-loop system is guaranteed. Several numerical simulations are presented to illustrate the results.
81 citations
TL;DR: It is shown that when cohesion rule is applied an equilibrium condition is reached in which all the UAVs settle at the same altitude on a circle of constant radius, and it is proved analytically that this equilibrium conditions is stable for all values of velocity and acceleration.
Abstract: In this article, several basic swarming laws for Unmanned Aerial Vehicles (UAVs) are developed for both two-dimensional (2D) plane and three-dimensional (3D) space. Effects of these basic laws on the group behaviour of swarms of UAVs are studied. It is shown that when cohesion rule is applied an equilibrium condition is reached in which all the UAVs settle at the same altitude on a circle of constant radius. It is also proved analytically that this equilibrium condition is stable for all values of velocity and acceleration. A decentralised autonomous decision-making approach that achieves collision avoidance without any central authority is also proposed in this article. Algorithms are developed with the help of these swarming laws for two types of collision avoidance, Group-wise and Individual, in 2D plane and 3D space. Effect of various parameters are studied on both types of collision avoidance schemes through extensive simulations.
75 citations
TL;DR: This article considers the robust H ∞ sliding mode control problem for a class of uncertain switched delay systems and proposes a single sliding surface such that the reduced-order equivalent sliding motion restricted to the sliding surface is completely invariant to all admissible uncertainties.
Abstract: This article considers the robust H∞ sliding mode control problem for a class of uncertain switched delay systems. A single sliding surface is constructed such that the reduced-order equivalent sliding motion restricted to the sliding surface is completely invariant to all admissible uncertainties. For cases of known delay and unknown delay, the existence conditions of the sliding surface are proposed, respectively. The corresponding hysteresis switching laws are designed such that the sliding motion is stabilisable with H∞ disturbance attenuation level γ. Furthermore, variable structure controllers are developed to drive the state of the switched system to reach the single sliding surface in finite time and remain on it thereafter. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design methods.
60 citations
TL;DR: This article is concerned with the problem of cost-guaranteed dynamic output feedback (DOF) control for a class of continuous-time linear switched system with both discrete and neutral delays, using the average dwell time approach and the piecewise Lyapunov function technique.
Abstract: This article is concerned with the problem of cost-guaranteed dynamic output feedback (DOF) control for a class of continuous-time linear switched system with both discrete and neutral delays. By using the average dwell time approach and the piecewise Lyapunov function technique, a sufficient condition is first proposed, in terms of a set of linear matrix inequalities (LMIs), to guarantee the exponential stability and a certain bound for the cost function of the closed-loop system, where the decay estimate is explicitly given to quantify the convergence rate. Then, the corresponding solvability conditions for a desired DOF controller under guaranteed cost are established by using the approach of linearising variable transforms. Since these obtained conditions are not all expressed by strict LMIs, the cone complementary linearisation method is exploited to cast them into sequential minimisation problems subject to LMI constraints, which can be easily solved numerically. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theory.
58 citations
TL;DR: The condition for stability of switched systems whose subsystems are stable are presented with dynamical dwell time approach, which is shown to be less conservative in switching law design than dwelling time approach.
Abstract: This article investigates the stability of a class of switched systems using dynamical dwell time approach. First, the condition for stability of switched systems whose subsystems are stable are presented with dynamical dwell time approach, which is shown to be less conservative in switching law design than dwell time approach. Then the proposed approach is extended to the switched systems with both stable and unstable subsystems. Finally, some numerical examples are given to illustrate the effectiveness of the proposed results.
56 citations
TL;DR: A deterministic inventory model for perishable items with stock-dependent selling rate is developed and a solution procedure is shown to find the optimal replenishment policy of the considered problem.
Abstract: This article develops a deterministic inventory model for perishable items with stock-dependent selling rate. In the model, the unsatisfied demand is partial backlogged and the backlogged demand rate is dependent on the negative inventory level during the stock-out period. Furthermore, a ceiling is imposed on the number of on-display stocks because too much inventory leaves a negative impression on the buyer and the amount of shelf space is limited. Next, the existence and uniqueness of the solution to the problem under two cases are examined, respectively. Then a solution procedure is shown to find the optimal replenishment policy of the considered problem. At last, two numerical examples and a real case study are presented to illustrate the application of the developed model.
56 citations
TL;DR: Improvements in the segmentation module, feature extraction module, and the classification module of a low-cost automated visual inspection (AVI) system for wood defect classification are presented and the use of computational intelligence techniques improved significantly the overall performance of the proposed automated visual inspectors for wood boards.
Abstract: This article presents improvements in the segmentation module, feature extraction module, and the classification module of a low-cost automated visual inspection (AVI) system for wood defect classification. One of the major drawbacks in the low-cost AVI system was the erroneous segmentation of clear wood regions as defects, which then introduces confusion in the classification module. To reduce this problem, we use the fuzzy min-max neural network for image segmentation (FMMIS). The FMMIS method grows boxes from a set of seed pixels, yielding ideally the minimum bounded rectangle for each defect present in the wood board image. Additional features with texture information are considered for the feature extraction module, and multi-class support vector machines are compared with multilayer perceptron neural networks in the classification module. Results using the FMMIS, additional features, and a pairwise classification support vector machine on a 550 test wood image set containing 11 defect categories show 91% of correct classification, which is significantly better than the original 75% of the low-cost AVI system. The use of computational intelligence techniques improved significantly the overall performance of the proposed automated visual inspection system for wood boards.
52 citations
TL;DR: The purpose of this study is to determine the optimal selling price and the length of replenishment cycle such that the total profit per unit time has a maximum value for the retailer.
Abstract: This article will formulate and solve an inventory system with non-instantaneous deteriorating items and price-sensitive demand. The purpose of this study is to determine the optimal selling price and the length of replenishment cycle such that the total profit per unit time has a maximum value for the retailer. We first establish a proper model for a mathematical formulation. Then we develop several theoretical results and provide the decision-maker with an algorithm to find the optimal solution. Finally, two numerical examples are provided to illustrate the solution procedure, and a sensitivity analysis of the optimal solution with respect to major parameters is carried out.
52 citations
TL;DR: Control quality enhancement is presented to show the control quality enhancement of this proposed fractional PIλDμ controller conception method compared to the PID controller conception using Ziegler–Nichols tuning method.
Abstract: The proportional-integral-derivative (PID) controllers have remained, by far, the most commonly and practically used in all industrial feedback control applications; therefore, there is a continuous effort to improve the system control quality performances. More recently Podlubny has proposed the fractional PIλDμ controller, a generalisation of the classical PID controller, involving an integration action of order λ and differentiation action of order μ. Since then, many researchers have been interested in the use and tuning of this type of controller. In this article, a new conception method of this fractional PIλDμ controller is considered. The basic ideas of this new tuning method are based, in the first place, on the classical Ziegler-Nichols tuning method for setting the parameters of the fractional PIλDμ controller for λ = μ = 1, which means setting the parameters of the classical PID controller, and on the minimum integral squared error criterion by using the Hall-Sartorius method for setting the fractional integration action order λ and the fractional differentiation action order μ. Illustrative examples and simulation results are presented to show the control quality enhancement of this proposed fractional PIλDμ controller conception method compared to the PID controller conception using Ziegler-Nichols tuning method.
TL;DR: This article presents an algorithm based on the proposed learning automaton, called survival algorithm, for determination of the number of hidden units of three layers neural networks, which has been tested on a number of problems and shown through simulations that networks generated are near optimal.
Abstract: There is no method to determine the optimal topology for multi-layer neural networks for a given problem. Usually the designer selects a topology for the network and then trains it. Since determination of the optimal topology of neural networks belongs to class of NP-hard problems, most of the existing algorithms for determination of the topology are approximate. These algorithms could be classified into four main groups: pruning algorithms, constructive algorithms, hybrid algorithms and evolutionary algorithms. These algorithms can produce near optimal solutions. Most of these algorithms use hill-climbing method and may be stuck at local minima. In this article, we first introduce a learning automaton and study its behaviour and then present an algorithm based on the proposed learning automaton, called survival algorithm, for determination of the number of hidden units of three layers neural networks. The survival algorithm uses learning automata as a global search method to increase the probability of obtaining the optimal topology. The algorithm considers the problem of optimization of the topology of neural networks as object partitioning rather than searching or parameter optimization as in existing algorithms. In survival algorithm, the training begins with a large network, and then by adding and deleting hidden units, a near optimal topology will be obtained. The algorithm has been tested on a number of problems and shown through simulations that networks generated are near optimal.
TL;DR: In this work, a model of actuator faults is adopted such that both normal operation and partial actuator degradation are covered and a sufficient condition is derived such that the resultant sliding mode control system is asymptotically stable despite partial actuators degradation.
Abstract: This article is concerned with the design of sliding mode control for uncertain state-delayed systems with partial actuator degradation. In the systems under consideration, there are parameter uncertainties in their state matrices and possible variations in the output of the actuators. In this work, a model of actuator faults is adopted such that both normal operation and partial actuator degradation are covered. A sufficient condition is derived such that the resultant sliding mode control system is asymptotically stable despite partial actuator degradation. Furthermore, it is shown that when a couple of linear matrix inequalities are feasible, the design of the sliding mode controller can be easily obtained via convex optimisation.
TL;DR: The theoretical contribution of this article is to consider stochastic inflationary conditions with variable probability density functions over the time horizon, and the demand rate is dependent to the inflation rates.
Abstract: In the existing literature, inventory models under inflationary conditions are usually developed under the assumption of certain inflation rates and constant, time-varying or stock-dependent demand rate. In many real-life situations, the practical experiences reveal that the inflation is non-deterministic and a variable. Meanwhile, the demand rate can be related to the inflation rates. The theoretical contribution of this article is to consider stochastic inflationary conditions with variable probability density functions (pdfs) over the time horizon, and the demand rate is dependent to the inflation rates (any arbitrary pdfs can be used). The developed model, also, implicates to finite replenishment rate, finite time horizon and deteriorating items with shortages. The objective is minimisation of the expected present value of costs over the time horizon. The numerical example and case study have been provided for evaluation and validation of the theoretical results and some special cases of the model are discussed.
TL;DR: A new type of composite control scheme of disturbance-observer-based control and terminal sliding mode control for uncertain structural systems by integrating the disturbance observer with TSMC law so that the disturbance with the exogenous system can be estimated and compensated, and external excitation can be attenuated in finite time.
Abstract: A new type of composite control scheme of disturbance-observer-based control and terminal sliding mode control (TSMC) is proposed for uncertain structural systems. The disturbance are supposed to include two parts. One is generated by an exogenous system, which can represent the harmonic signals with modelling perturbations in structural system. The other part is external excitation in H2-norm context. The disturbance observers based on regional pole placement and D-stability theory are presented, which can be designed separately from the controller design. By integrating the disturbance observer with TSMC law, the disturbance with the exogenous system can be estimated and compensated, and external excitation can be attenuated in finite time. Finally, simulations for a four-degree-of-freedom building model excited by 1940 EI Centro earthquake excitation are given to demonstrate the effectiveness of the approach and compare the proposed results with the previous schemes with accuracy.
TL;DR: A software reliability growth model based on stochastic differential equations is proposed in order to consider the active state of the open source project and it is shown that the proposed model can assist improvement of quality for OSS systems developed under theopen source project.
Abstract: A new distributed software development paradigm typified by such open source project will evolve at a rapid pace in the future. Especially, open source software (OSS) which serve as key components of critical infrastructures in the social life are still ever-expanding now. We propose a software reliability growth model based on stochastic differential equations in order to consider the active state of the open source project. Especially, we assume that the software failure intensity depends on the time, and the software fault-reporting phenomena on the bug-tracking system keeps an irregular state. Moreover, it has been necessary to manage the software development process in terms of reliability, development effort and version-upgrade time. We find the optimal version-upgrade time based on the total expected software maintenance effort. We show that the proposed model can assist improvement of quality for OSS systems developed under the open source project.
TL;DR: A new finite time position synchronised control approach for parallel manipulators is proposed using a fast terminal sliding mode (TSM) that can guarantee position error and synchronisation error converge to zero in a finite time simultaneously without requiring the explicit using system dynamic model.
Abstract: A new finite time position synchronised control approach for parallel manipulators is proposed using a fast terminal sliding mode (TSM). By developing a novel synchronisation and coupling position error, a non-singular fast TSM is proposed in coupling position error space. The proposed controller can guarantee position error and synchronisation error converge to zero in a finite time simultaneously without requiring the explicit using system dynamic model. The corresponding stability analysis is presented to lay a foundation for theoretical understanding to the underlying issues as well as safe operation for real systems. An illustrative example is demonstrated in support of the effectiveness of the proposed approach.
TL;DR: An inventory model under a situation in which the supplier provides the purchaser with a permissible delay of payments is developed and an easy-to-use algorithm is provided to find the optimal solution.
Abstract: This article develops an inventory model under a situation in which the supplier provides the purchaser with a permissible delay of payments. Shortages are not allowed and the effect of the inflation rate, deterioration rate and delay in payment are discussed as well. As a result, in this article, we establish a mathematical model to determine the optimal payment period and replenishment cycle. Using Taylor series approximation, we characterise the optimal solution and provide an easy-to-use algorithm to find the optimal solution. Finally, the proposed models are illustrated through numerical examples and the sensitivity analysis is reported.
TL;DR: The optimal production for an inventory control system of deteriorating multi-items where items are either complementary and/or substitute is formulated with a resource constraint and the results are presented both in tabular form and graphically.
Abstract: The optimal production for an inventory control system of deteriorating multi-items where items are either complementary and/or substitute is formulated with a resource constraint. Here, the production function is unknown and considered as a control variable. Also, the deterioration rates of the items are either stock dependent or constant. The demand is stock dependent, shortages are not allowed and deteriorated items are salvaged. The total profit, which consists of the sales proceeds, production cost, inventory holding cost, salvage value, is formulated as a Pontryagin's Optimal Control problem for both steady and transient states and evaluated using Taylor's theorem, generalised reduced gradient technique and optimal control theory satisfying the Generalised Legendre conditions. The model is formulated in general form for n-items, and in particular, is illustrated with three items for some numerical data. The optimum results are presented both in tabular form and graphically.
TL;DR: An iterative learning control approach is proposed for a class of sampled-data non-linear systems over network communication channels which satisfies a global Lipschitz condition and the convergence property of this approach is proven.
Abstract: In this article, an iterative learning control approach is proposed for a class of sampled-data non-linear systems over network communication channels. The effects of constant time delays and stochastic packet loss are discussed and demonstrated by simulation results. The focus of this article is to study the remote control problems when the environment is periodic or repeatable over iterations in a fixed finite interval. Because of the existence of time delays and packet loss in input and output signal transmissions, it is not trivial to accomplish the remote stabilisation task of any system. Moreover, to track a desired trajectory through a remote controller is even more difficult. Previous cycle-based learning method is incorporated into the network-based control for a class of non-linear systems which satisfies a global Lipschitz condition. The convergence property of this approach is proven. Furthermore, the convergence in the iteration domain is also discussed when there exists packet loss in both transmission channels of the system. Finally, one single-link rigid robot is given as an example to show the effectiveness of the proposed approach.
TL;DR: To further enhance the performance of job completion time prediction and internal due date assignment in a wafer fab, a fuzzy-neural knowledge-based system is constructed in this study.
Abstract: To further enhance the performance of job completion time prediction and internal due date assignment in a wafer fab, a fuzzy-neural knowledge-based system is constructed in this study. In the constructed system, multiple experts construct their own fuzzy multiple linear regression models from various viewpoints to predict the completion/cycle time of a job. Each fuzzy multiple linear regression model can be converted into an equivalent non-linear programming problem to be solved. Subsequently, a two-step aggregation mechanism is applied. At the first step, fuzzy intersection is applied to aggregate the fuzzy completion time forecasts into a polygon-shaped fuzzy number, in order to improve the precision of completion time forecasting. The polygon-shaped fuzzy number contains the actual value, and its upper bound determines the internal due date of the job. After that, a back propagation network is constructed to defuzzify the polygon-shaped fuzzy number and to generate a representative/crisp value, so as to enhance the accuracy. A practical example is used to evaluate the effectiveness of the proposed methodology. According to experimental results, the proposed methodology improved both the precision and accuracy of job cycle time prediction by 16 and 21%, respectively.
TL;DR: A new algorithm is firstly introduced to reduce the computation of mode-dependent redundancy relation parameter matrices to solve problems of parity space-based fault detection for a class of discrete-time linear Markovian jump systems.
Abstract: This article deals with problems of parity space-based fault detection for a class of discrete-time linear Markovian jump systems. A new algorithm is firstly introduced to reduce the computation of mode-dependent redundancy relation parameter matrices. Different from the case of linear time invariant systems, the parity space-based residual generator for a Markovian jump system cannot be designed off-line because it depends on the history of system modes in the last finite steps. In order to overcome this difficulty, a finite set of parity matrices is pre-designed applying a unified approach to linear time invariant systems. Then the on-line residual generation can be easily implemented. Moreover, the problem of residual evaluation is also considered which includes the determination of a residual evaluation function and a threshold. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.
TL;DR: The aim of this article is to establish Razumikhin-type theorems on asymptotic stability of stochastic retarded systems, which is a generalisation of the result obtained by Mao, and generalised exponential stability is considered for better estimate of Lyapunov exponent of time-variant systems.
Abstract: The Razumikhin-type theorems have been well developed and are very effective for the stability of deterministic retarded dynamic systems. Chang (1984) studied the Razumikhin-type stability conditions for stochastic retarded functional differential equations (SRFDEs). But the stability is not in a global sense. Recently, by utilising the Razumikhin-type argument, Mao (1997a) provided some useful criteria for exponential stability of stochastic retarded functional differential equations. However, the important general asymptotic stability has not been considered. The aim of this article is to establish Razumikhin-type theorems on asymptotic stability of stochastic retarded systems, which is a generalisation of the result obtained by Mao. Moreover, generalised exponential stability is considered for better estimate of Lyapunov exponent of time-variant systems. In the conclusion, this article is to show the underlying principle of the Razumikhin-type theorems on stability of stochastic retarded functional differential equations. With this idea, it is not difficult to apply Razumikhin-type techniques to stochastic retarded systems.
TL;DR: A general proportional–integral (PI) law for updating the fuzzy parameters is proposed and boundedness of the error signals is shown through Lyapunov's direct method.
Abstract: In this article, the direct adaptive fuzzy control problem is investigated for a class of general non-linear systems with zero dynamics. The direct adaptive fuzzy controller is developed based on a unified observer which is used to estimate the time derivatives of the output. The corrective term of the proposed observer involves a well-defined design function which is shown to be satisfied by the commonly used high-gain-based observers, namely for the usual high-gain observers and the sliding-mode observers together with their implementable versions. By using a general error function, and without resorting to the famous strictly positive real condition or the filtering of the observation error, a general proportional-integral (PI) law for updating the fuzzy parameters is proposed. Ultimately boundedness of the error signals is shown through Lyapunov's direct method. Theoretical results are illustrated through two simulation examples.
TL;DR: An age-replacement model with minimal repair based on a cumulative repair cost limit and random lead time for replacement delivery and a general cost model is developed for the average cost per unit time based on the stochastic behavior of the assumed system.
Abstract: In this article, we consider an age-replacement model with minimal repair based on a cumulative repair cost limit and random lead time for replacement delivery A cumulative repair cost limit policy uses information about a system's entire repair cost history to decide whether the system is repaired or replaced; a random lead time models delay in delivery of a replacement once it is ordered A general cost model is developed for the average cost per unit time based on the stochastic behaviour of the assumed system, reflecting the costs of both storing a spare and of system downtime The minimum-cost policy time is derived, its existence and uniqueness is shown, and structural properties are presented Various special cases are included Because the framework and analysis are general, the proposed model extends several existing results Finally, a numerical example is provided for illustration
TL;DR: This article proposes a linearisation strategy to formulate the FMOMBFP problem in which extra binary variable is not required, and achieves the highest membership value of each fuzzy goal defined for the fractional objective function.
Abstract: Fuzzy multiple objective fractional programming (FMOFP) is an important technique for solving many real-world problems involving the nature of vagueness, imprecision and/or random. Following the idea of binary behaviour of fuzzy programming (Chang 2007), there may exist a situation where a decision-maker would like to make a decision on FMOFP involving the achievement of fuzzy goals, in which some of them may meet the behaviour of fuzzy programming (i.e. level achieved) or the behaviour of binary programming (i.e. completely not achieved). This is turned into a fuzzy multiple objective mixed binary fractional programming (FMOMBFP) problem. However, to the best of our knowledge, this problem is not well formulated by mathematical programming. Therefore, this article proposes a linearisation strategy to formulate the FMOMBFP problem in which extra binary variable is not required. In addition, achieving the highest membership value of each fuzzy goal defined for the fractional objective function, the proposed method can alleviate the computational difficulties when solving the FMOMBFP problem. To demonstrate the usefulness of the proposed method, a real-world case is also included.
TL;DR: New criteria for exponential robust stability of switched stochastic delay systems with non-linear uncertainties are derived in terms of linear matrix inequalities and average dwell-time conditions.
Abstract: This article considers the robust exponential stability of uncertain switched stochastic systems with time-delay. Both almost sure (sample) stability and stability in mean square are investigated. Based on Lyapunov functional methods and linear matrix inequality techniques, new criteria for exponential robust stability of switched stochastic delay systems with non-linear uncertainties are derived in terms of linear matrix inequalities and average dwell-time conditions. Numerical examples are also given to illustrate the results.
TL;DR: This study investigates a marketing and production problem that uses price, warranty length and production rate as simultaneous dynamic decision variables and establishes a model-driven Decision Support System that provides a graphical user interface for overcoming the complexity of the analytical process.
Abstract: This study investigates a marketing and production problem that uses price, warranty length and production rate as simultaneous dynamic decision variables. Furthermore, this study was conducted under a policy of free replacement of defective items; and under conditions where demand was dynamic and dependent on price, warranty and cumulative sales. A continuous profit maximisation model was formulated, which first considers the expected warranty cost per item. Then, it considers the steps for dynamic optimisation, which eventually derive the optimal price, warranty length and production rate. Discretisation was then applied to the profit maximisation model and a digital computer was used to identify the optimal control paths, obtaining a finite solution that is a set of real numbers for practical application. A model-driven Decision Support System is finally established, which provides a graphical user interface for overcoming the complexity of the analytical process. Subsequently, the proposed system was tested and the analytical solution was verified using several demand functions for additive lifetime distributions, thereby demonstrating the system's effectiveness.
TL;DR: A mathematical model which generalises several known deterministic Economic Order Quantity inventory systems with partial backlogging and considers purchasing cost, holding cost, shortage costs and replenishment cost is presented.
Abstract: We present a mathematical model which generalises several known deterministic Economic Order Quantity (EOQ) inventory systems with partial backlogging. This inventory model considers purchasing cost, holding cost, shortage costs and replenishment cost. Shortage costs (backorder cost and lost sales cost) are both made up of a fixed cost and a variable cost which depends on the length of the waiting time for the next replenishment. The optimal policy is characterised through a sequential optimisation procedure. To illustrate the model, numerical examples and sensitivity results are given.
TL;DR: A sufficient condition on the minimum dwell time that guarantees the stability of switched linear systems is given and an explicit relation in view of stability is obtained between the family of the involved subsytems and the set of admissible switching signals.
Abstract: In this article, a sufficient condition on the minimum dwell time that guarantees the stability of switched linear systems is given. The proposed method interprets the stability of switched linear systems through the distance between the eigenvector sets of subsystem matrices. Thus, an explicit relation in view of stability is obtained between the family of the involved subsytems and the set of admissible switching signals.