# Showing papers in "International Journal of Systems Science in 1984"

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TL;DR: The problems of input sensitivity, structure detection, model validation and input signal selection are discussed in the non-linear context.

Abstract: Least squares parameter estimation algorithms for non-linear systems are investigated based on a non-linear difference equation model. A modified extended least squares algorithm, an instrumental variable algorithm and a new suboptimal least squares algorithm are considered. The problems of input sensitivity, structure detection, model validation and input signal selection are also discussed in the non-linear context.

126 citations

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TL;DR: A model for choice within closed systems is extended to apply to open systems; and an unbiased version of Ulanowicz's ascendency, a purported index of the development of ecological communities, is given.

Abstract: Etiological networks are considered from the viewpoint of information theory. Rutledge et al.'a model for choice within closed systems is extended to apply to open systems; and an unbiased version of Ulanowicz's ascendency, a purported index of the development of ecological communities, is given. This information theoretical analysis is also applicable to flow networks arising as models of biological systems, economic systems, social systems, etc.

105 citations

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TL;DR: In this paper, an observability canonical form for non-linear time-variable systems, [xdot]=f(x,u,t), y=h(x and u, u, t), is introduced by analogy with the corresponding linear phase-variable forms.

Abstract: An observability canonical form for non-linear time-variable systems, [xdot]=f(x,u,t), y=h(x,u,t), is introduced by analogy with the corresponding linear phase-variable forms. The transformation into observability canonical form follows from the nonlinear observability map, whose jacobian must be assumed to be a regular matrix in the considered domains of state x, input u and time t. If this observability matrix can be inverted analytically or numerically, the transformation into the observability canonical coordinates can be achieved directly. As opposed to linear systems, the non-linear observability canonical form with input depends, additionally, on the time derivatives of the input. This restricts a practical implementation.

79 citations

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TL;DR: Four useful theorems are derived to determine optimum release times of a software system for operational use that minimize the total expected software cost with a scheduled software delivery time.

Abstract: Optimum release policies minimizing the total expected software cost with a scheduled software delivery time are discussed. Such cost considerations enable us to make a release decision as to when to transfer a software system from testing phase to operational phase. The underlying reliability model describing a software error occurrence phenomenon is a software reliability growth model based on a non-homogeneous Poisson process. It is assumed that the penalty cost functions due to delay for a scheduled software delivery time are proportional and exponential to time, respectively. We consider two cases; when the scheduled software delivery time is a constant and when it is a random variable with an arbitrary distribution. Four useful theorems are derived to determine optimum release times of a software system for operational use. Numerical examples are shown to illustrate the results.

69 citations

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TL;DR: In this paper, the authors present two easy-to-check criteria that test respectively the necessary condition for the asymptotic stability of linear time-varying systems and the sufficient condition for their instability.

Abstract: This paper presents two easy-to-check criteria that test respectively the necessary condition for the asymptotic stability and the sufficient condition for the instability of linear time-varying systems. A necessary and sufficient condition, defined in terms of the newly introduced concept of the mode-vectors is also given for stability of linear time-varying systems. An algorithm for finding the mode-vectors is presented. Several examples are given to illustrate the applications of the results in the paper.

43 citations

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TL;DR: In this paper, a new combination of Routh stability criterion and integral squared error (ISE) criterion approach is proposed for the linear model reduction of high-order dynamic systems, which consists of a two-step computational scheme, in the first step, the Routh approximation method is used to reduce the order of the denominator polynomial of the system transfer function.

Abstract: A new combination of Routh stability criterion and integral squared error (ISE) criterion approach is proposed for the linear model reduction of high-order dynamic systems. The method consists of a two-step computational scheme. In the first step, the Routh approximation method is used to reduce the order of the denominator polynomial of the system transfer function. In the second step, the Routh table is used to derive a set of optimal coefficients of the numerator polynomial of reduced model such that the ISE between the unit step responses of the original and simplified system is reduced to a minimum. The advantages of the proposed method are that it does not actually evaluate the system time response in the step of minimizing the ISE, and the reduced model is stable if the original system is stable.

33 citations

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TL;DR: This paper provides an algorithm for solving two-level convex optimization problems based on the subgradient formula for the upper level objective function which is not generally known to solve these problems.

Abstract: This paper provides an algorithm for solving two-level convex optimization problems. The algorithm is based on the subgradient formula for the upper level objective function which is not generally ...

30 citations

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TL;DR: In this paper, a new formulation for obtaining the optimal sale date and maintenance policy for a complex machine where failures are rectified through minimal repair and the salvage value is a random variable is proposed.

Abstract: In this paper, we propose a new formulation for obtaining the optimal sale date and maintenance policy for a complex machine where failures are rectified through minimal repair and the salvage value is a random variable. We incorporate two types of maintenance—one, continuous in time (for example, inspection, minor adjustments, repairs, etc.), and the other, discrete in time (such as overhaul). We give a complete characterization of the optimal solution.

26 citations

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TL;DR: It is shown that an aperiodic discrete-continuous sampling system may be modelled by a difference equation matrix which may be used in the same way as in the case of periodic discrete systems, which allows the computation of the outputs as finite combinations of previous inputs and outputs.

Abstract: It is 8hown that an aperiodic discrete-continuous sampling system may be modelled by a difference equation matrix which may be used in the same way as in the case of periodic discrete systems. This fact allows the computation of the outputs as finite combinations of previous inputs and outputs. This is accomplished using a finite set of time-varying parameters, which are dependent on the parameters of the continuous transfer matrix and on a finite set of sampling periods equal to the order of the system state, and thus avoids impulse response methods and state variable measurements.

23 citations

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TL;DR: In this article, a matrix sign function in conjunction with a geometric approach is utilized to construct a block modal matrix and a (scalar) modal matrices of a system map, so that the system map can be block diagonalized and block triangularized.

Abstract: A matrix sign function in conjunction with a geometric approach is utilized to construct a block modal matrix and a (scalar) modal matrix of a system map, so that the system map can be block-diagonalized and block-triangularized, and that the Riccati-type problems can be solved.

20 citations

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TL;DR: In this paper, the Laguerre polynomial function is modified with an additional parameter and is applied to solve integral equations, where the dependent variables in the integral equation are assumed to be expressed by a modified Laguersomial series and a recursive computational algorithm is employed to calculate the expansion coefficients.

Abstract: The Laguerre polynomial function is modified with an additional parameter and is applied to solve integral equations. First, the convolution of two modified Laguerre polynomials is developed. The dependent variables in the integral equation are assumed to be expressed by a modified Laguerre polynomial series. A set of algebraic equations is obtained from the integral equation. A recursive computational algorithm is employed to calculate the expansion coefficients. Examples are given, the results obtained from the modified Laguerre polynomials being much better than from the conventional Laguerre polynomials.

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TL;DR: In this paper, the authors discuss stochastic modelling of a multiprocessor system from the viewpoints of both the performance and reliability, and introduce some new performance/reliability measures in which they take account of the incoming jobs.

Abstract: A multi-processor system is one of the most advanced computer systems because of its high performance and reliability. We discuss stochastic modelling of a multiprocessor system from the viewpoints of both the performance and reliability. The existing reliability measures such as the availability and the mean time between failures (MTBF) are not adequate to evaluate such a system since they do not take account of the demand of the jobs or transactions. We introduce some new performance/reliability measures in which we take account of the incoming jobs. Analysis by the extended Markov renewal processes enables us to formulate stochastic modelling of the multi-processor system. Both the exact and approximate formulae are given for the existing and new performance/reliability measures. Numerical examples assure that the approximate formulae are sufficiently precise. The other numerical examples show that the multi-processor system is better than the single-processor system having equivalent performance with ...

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TL;DR: In this article, two-dimensional Laguerre polynomials are used for estimating the parameters of linear distributed systems and algorithms for formulating the algebraic equations to estimate unknown parameters are recursive and suitable for on-line implementation.

Abstract: Two-dimensional Laguerre polynomials are used for estimating the parameters of linear distributed systems. The algorithms for formulating the algebraic equations to estimate unknown parameters are recursive and suitable for on-line implementation. Appropriate examples are included to illustrate the algorithm.

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TL;DR: An extension of dynamic programming models to include goal objectives is described, and illustrative examples are provided.

Abstract: An extension of dynamic programming models to include goal objectives is described, and illustrative examples are provided.

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TL;DR: In this paper, the conditions for the control law and for a hyperplane are determined so that a stable sliding mode is obtained, and an approximation is presented which simplifies the determination of an admissible sliding hyperplane.

Abstract: Single variable control systems of variable structure are analysed. The conditions for the control law and for a hyperplane are determined so that a stable sliding mode is obtained. No restrictions are placed on the linear state variable representation and it is not necessary to switch all of the states. An approximation is presented which simplifies the determination of an admissible sliding hyperplane.

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TL;DR: Structural properties for balanced minimal realizations of scalar transfer functions are used to formulate a realization algorithm when the transfer function has simple poles.

Abstract: Structural properties for balanced minimal realizations of scalar transfer functions are used to formulate a realization algorithm when the transfer function has simple poles.

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Ghent University

^{1}TL;DR: In this paper, the stability properties of systems described by the linear differential difference equation [xdot](t) = Ax(t) + Bx(t − t) are studied.

Abstract: Stability properties of systems described by the linear differential difference equation [xdot](t) = Ax(t) + Bx(t − t) are studied. If the system x(t) = Bx(t − t) is stable enough and the term Ax(t) is ‘ small ’ enough, then the above differential difference systems may be proved to be stable. Based on this intuition, several stability criteria are derived. Studies are first carried out for systems without the term Ax(t) and then the results are extended to cover more general cases. The criteria are expressed in terms of the locations of the eigenvalues of the matrix B in the complex plane.

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TL;DR: In this paper, conditions for the complete separation of slow and fast subsystems are given, which are obtained by applying the slow-and fast subcontrollers to the corresponding subsystems, and also, the composite control, when being applied to the original system, will place the eigenvalues sufficiently close to the desired locations.

Abstract: Output feedback design of discrete-time decentralized systems with slow and fast modes is considered. Conditions for the complete separation of slow and fast subsystems are given. The slow and fast subsystem outputs, which are obtained by applying the slow and fast subcontrollers to the corresponding subsystems, will be shown to approximate those of the original system. Also, the composite control, when being applied to the original system, will place the eigenvalues sufficiently close to the desired locations.

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TL;DR: This paper discusses the application of discrete Chebyshev polynomial expansion to reduce the order of a linear time-invariant discrete system described by 2-transfer function.

Abstract: This paper discusses the application of discrete Chebyshev polynomial expansion to reduce the order of a linear time-invariant discrete system described by 2-transfer function. Two approaches are used to obtain the reduced models. One uses discrete Chebyshev spectrum matching to determine both the coefficients of the denominator and numerator of the reduced model. The other uses stable reduction methods to determine the coefficients of the denominator and discrete Chebyshev spectrum matching to determine the coefficients of the numerator. The latter has the advantage that the reduced model is stable provided the original model is stable.

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TL;DR: In this article, a deterministic optimal control theory is used to find the time dependent optimal service rate in an 5-server, finite capacity (N), markovian queue (M/M/S/A), where Chapman-Kolmogorov differential equations are used as the state equations of the control problem with N + 1 state variables and one control variable.

Abstract: In this paper, deterministic optimal control theory is used to find the time dependent optimal service rate in an 5-server, finite capacity (N), markovian queue (M/M/S/A). Chapman-Kolmogorov differential equations are used as the state equations of the control problem with N +1 state variables and one control variable. The objective to be minimized is the cost of waiting customers plus the cost of service over a specified time interval. A final time penalty cost of deviations from a desired expected queue length is also included in the objective. Optimal dynamic service rate is found by using Pontryagin's minimum principle which gives rise to a two point boundary value problem and is solved numerically by applying the Newton-Raphson boundary iteration. An example illustrates the results.

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TL;DR: In this paper, the state space model for 2D filters originally proposed by Attasi (1976) is re-examined and a necessary and sufficient condition for the Attasi statespace model to be minimal is shown.

Abstract: In this paper the state space model for 2D filters originally proposed by Attasi (1976) is re-examined. A necessary and sufficient condition for the Attasi state space model to be minimal is shown. A canonic form is developed for this state space model. The canonic form is then used to provide a computationally beneficial technique for realizing the Attasi state space model from 2D filter pulse response data.

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TL;DR: This model is analogous to the two-dimensional model of Kung, and in the pure recursive and non-recursive cases has lower dimensionality than the corresponding model of Galkowski, which was derived for first-order M -dimensional transfer functions.

Abstract: A procedure is presented for deriving a canonical state-space model of the Roesser type for linear discrete single-input single-output systems of three dimensions, starting from their transfer function representation. This model is analogous to the two-dimensional model of Kung (1977), and in the pure recursive and non-recursive cases has lower dimensionality than the corresponding model of Galkowski, which was derived for first-order M -dimensional transfer functions. The present model can be written down by simple inspection of the coefficients of the given transfer function model. Two examples are given which were tested by simulating both the transfer function and the state-space models.

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TL;DR: In this paper, a new set of operational matrices for delay and advance via Walsh functions is introduced, along with the well known operational matrix for integration, which reduce the calculus of a large class of delay (or advance) systems to an algebra approximate in the sense of least squares.

Abstract: This paper introduces a new set of operational matrices for delay and advance via Walsh functions. These matrices, along with the well known operational matrix for integration, reduce the calculus of a large class of delay (or advance) systems to an algebra approximate in the sense of least squares. Some useful properties and applications of the proposed matrices are discussed. In particular, a method of integrating delay differential equations is extensively illustrated. With the single term Walsh series method (Prasada Rao et at. 1980) the computation becomes very simple. In addition to the piecewise constant solutions, discrete solutions can also be computed. Some features of the paper are : (i) a technique to include carry over effects ; and (ii) an analysis of the error and stability of computations. Several illustrative examples are included and the results are compared with those obtained by certain conventional methods.

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TL;DR: In this paper, the problem of determining decentralized control for linear, time-invariant interconnected systems with quadratic performance measures is treated as one of constrained optimization under structural control restrictions.

Abstract: The problem of determining decentralized control for linear, time-invariant interconnected systems with quadratic performance measures is considered. The problem is treated as one of constrained optimization under structural control restrictions. An iterative block-diagonalization procedure is developed whereby a local minimum is attained ; the overall system stability is guaranteed at each iteration and the computational burden is greatly reduced in comparison with that required by existing methods.

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TL;DR: In this article, sensitivity analysis and robust regression are applied to the problem of measuring the performance of investment portfolios and the sensitivity of systematic risk estimates is gauged via the deletion of outliers from the data set.

Abstract: The novel statistical techniques of sensitivity analysis and robust regression are applied to the problem of measuring the performance of investment portfolios. The sensitivity of systematic risk estimates is gauged via the deletion of outliers from the data set. The robust regression procedure of least absolute residuals is employed to derive new estimates of Jensen's measure of investment performance.

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TL;DR: In this paper, a regulator problem for a distributed parameter system with constant disturbances is investigated, where the goal is to determine a feedback control law which stabilizes and regulates the system.

Abstract: This paper investigates a regulator problem for a distributed parameter system with constant disturbances. The regulator problem considered here is to determine a feedback control law which stabilizes and regulates the system. From a practical point of view, a design procedure is proposed for a regulator which can be realized in finite-dimensional theories and techniques for an infinite-dimensional system. In the design procedure it is necessary to construct a state observer in order to estimate the system state from observations. Explicit sufficient conditions are presented for the convergence of the schemes and the theory is applied to a parabolic distributed parameter system with more general types of inputs and outputs, given in suitable Hilbert spaces.

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TL;DR: In this paper, a general left invertibility problem (GL1P) is given in the frequency domain as follows: for a given system S, does there exist some linear system S* such that R(S* ) R (S) = R(s' ) where R(R, R, S' ) and R (R,R, S* ) are the transfer function matrices of S, S', S' and S respectively?

Abstract: A general left invertibility problem (GL1P) is given in the frequency domain as follows. Let S' be a fixed linear system. For a given system S,does there exist some linear system S* such that R(S* ) R(S) = R(S' ) where R(S), R(S' ) and R(S* ) are the transfer function matrices of S, S'and S respectively? This paper considers the GLIP in the framework of the mathematical systems theory. The notion of S'-invertibility is formalized in the framework. The necessary and sufficient conditions of the S'-invertibility are given for the class of output controllable and weakly causal basic linear systems. The conditions are presented both on the input response level and on the system behaviour (input and output relation) level. Furthermore the meaning of S' -invertibility is considered in terms of the information of an input. In order to reveal the significance of our results, the main theorem is applied to A-invertibility and IL invertibility. These problems are generalizations of the standard L-integral invertibi...

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TL;DR: In this article, the authors considered linear shift-invariant discrete-time systems satisfying the two time-scale properties and provided conditions for a complete separation of slow and fast subsystems.

Abstract: Linear shift-invariant discrete-time systems satisfying the two time-scale property are considered. Conditions for a complete separation of slow and fast subsystems are given. The composite controller will be formed from the slow and fast subsystem controllers. The slow and fast subsystem trajectories will be obtained and they will be shown to approximate those of the original system. Conditions for existence of the solutions of the subsystem regulator problems will also be given

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TL;DR: In this article, the stability analysis of non-linear and/or large-scale discrete-time dynamical systems by using vector positive definite functions for the construction of a positive upper aggregated system whose stability properties imply analogous properties for the system being studied is presented.

Abstract: This paper deals with the stability analysis of non-linear and/or large-scale discrete-time dynamical systems by using vector positive definite functions for the construction of a positive upper aggregated system whose stability properties imply analogous properties for the system being studied. In the first part of the paper a rigorous foundation of the approach is presented. The second part is concerned with the stability analysis of non-linear positive discrete-time dynamical systems. Two examples are given to illustrate the application of the results.

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TL;DR: In this paper, a semi-markovian state-space model for two and three sequentially tested components is presented and analyzed, and suitable availability indices for the systems are derived and computer results are obtained.

Abstract: This paper develops state-space models for unavailability analysis of protective systems where the components are tested sequentially rather than simultaneously (normally known as ‘ block ’ testing). The components are subject to revealed failures. Failures and repairs are assumed to follow exponential density functions. Components are sequentially tested after a fixed testing interval. This leaves some measure of protection from the system during the testing operation. The random process generated by the failure-repair testing actions is not Markov due to the testing operation. The process, nevertheless, contains enough properties of a Markov process that it could be described by a semi-Markov process. In this paper, semi-markovian state-space models for systems of two and three sequentially tested components are presented and analysed. Suitable availability indices for the systems are derived and computer results are obtained.