Showing papers by "Long Wang published in 2002"
TL;DR: This paper investigates the number of switchings and design of switching sequences for controllability of switched linear systems and establishes a new constructive approach to designing switching sequences that coincides with the controllable subspace of switchedlinear systems.
Abstract: In this paper, the controllability of a switched linear system, which is a collection of linear time-invariant systems along with some maps for "switching" among them, is addressed. First, a controllable state set is defined as a basic tool to discuss the controllability condition. Next, it is proved that the controllability of a multi-input system is equivalent to that of a single-input system. Finally, a sufficient and necessary condition for controllability of third-order systems is presented. According to the proof of this criterion, we state a conjecture on the controllability condition of n-dimensional systems. A numeric example is given to illustrate the result.
167 citations
08 May 2002
TL;DR: In this paper, the controllability of switched linear systems with time-delay has been studied and a necessary and sufficient condition has been established for the system to be controllable.
Abstract: We study the controllability of switched linear systems. First, the concept of controllable state set is introduced as the basic tool for evaluating the controllability. We then prove that, for a switched linear system, there exists a basic switching sequence such that the controllable state set of this basic switching sequence is equal to the controllable state set of the system. Hence, the controllability can be realized by using only one switching sequence. This striking fact reveals some intrinsic properties of switched linear systems, and is the most fundamental starting point for further development. Based on this fact, a necessary and sufficient condition for controllability of switched linear systems is established. Furthermore, these results are extended to switched linear systems with time-delay. A geometric criterion for controllability of switched time-delay systems is established as well. Illustrative examples are provided.
54 citations
01 May 2002-Materials Science and Engineering A-structural Materials Properties Microstructure and Processing
TL;DR: In this paper, the combined effect of Al-3wt.%Ti-4.%B and Al-10.%Sr on Al-Si-Cu alloy has been investigated.
Abstract: The combined effect of Al–3wt.%Ti–4wt.%B and Al–10wt.%Sr on Al–Si–Cu alloy has been investigated. Equiaxed dendritic grain of 100–120 μm was obtained with holding time of at least 240 min through addition of more than 0.020% Ti and 0.026% B, though the laminar morphology of eutectic Si kept unaltered. Eutectic Si was completely modified for more than 240 min through addition of Al–10wt.%Sr which also had some benefit on the refinement of primary α-Al. The combined addition of both Al–3wt.%Ti–4wt.%B and Al–10wt.%Sr led to shorter working time of modification and slightly coarser grain size. The above results are mainly due to the formation of SrB6 through the reaction between Al–10wt.%Sr and Al–3wt.%Ti–4wt.%B. It was found that satisfactory grain refinement and modification could be attained by suitable addition of both Al–3wt.%Ti–4wt.%B and Al–10wt.%Sr in spite of the formation of SrB6.
42 citations
10 Dec 2002
TL;DR: In this article, a geometric algorithm with order reduction for robust strictly positive real (SPR) synthesis is presented, where the synthesis problem is transformed to finding a feasible solution in ellipses with two variables.
Abstract: A new geometric algorithm with order reduction for robust strictly positive real (SPR) synthesis is presented. By searching from the boundary of the region of the weak strict positive realness (WSPR) of a polynomial, we can find the intersection of the WSPR regions of the polynomial family. Then the synthesis problem can be transformed to finding a feasible solution in ellipses with two variables, thus the problem becomes simpler and easy to solve, and the computational burden has been significantly reduced. Moreover, the derived conditions are necessary and sufficient for robust SPR synthesis of low-order polynomial segments (n/spl les/5) or interval polynomials (n/spl les/4). The algorithm is computationally efficient for some types of polynomial sets, such as segments, intervals and polytopes with arbitrary order. Illustrative examples are provided.
12 citations
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TL;DR: This paper gives a necessary and sufficient condition for robust D-stability of polytopic polynomial matrices.
Abstract: This paper gives a necessary and sufficient condition for robust D-stability of Polytopic Polynomial Matrices. Edge theorem is extended to multi-input-multi-output case.
8 citations
TL;DR: Componentwise estimates of (global) exponential convergence are obtained for a class of neural networks with multiple delays by Lyapunov method for delay differential equations, which shows explicitly the effect of time delays on exponential decay rate of the networks.
Abstract: Componentwise estimates of (global) exponential convergence are obtained for a class of neural networks with multiple delays by com- parison method for delay differential equations. The method is simple and straightforward and does not resort to any Lyapunov functional. The main result shows explicitly the effect of time delays on exponential decay rate of the networks and is hence of practical interest in designing a fast and stable neural network. Compared with some existing results for stability of the Hopfield network model and delayed cellular neural network model via Lyapunov method, the present results can provide further detailed charac- terization of the convergence behavior for the systems under the same or similar conditions.
7 citations
TL;DR: A new numerical method based on Genetic Algorithm for robust Strictly Positive Real (SPR) synthesis is presented that works well in coefficient space of continuous-time systems and is computationally efficient for some types of polynomial families.
5 citations
TL;DR: In this article, the stability of interval polynomials with respect to the Ωθ region was studied and an analysis on how to generate the finite set whose stability implies robust stability of the entire family was given.
3 citations
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TL;DR: In this article, the authors used the complete discrimination system for polynomials to study the number of positive solutions in a polynomial integral equation and showed that there are infinitely many positive solutions for the integral equation in the case of small √ n.
Abstract: By using the complete discrimination system for polynomials, we study the number of positive solutions in {\small $C[0,1]$} to the integral equation {\small $\phi (x)=\int_0^1k(x,y)\phi ^n(y)dy$}, where {\small $k(x,y)=\phi_1(x)\phi_1(y)+\phi_2(x)\phi_2(y), \phi_i(x)>0, \phi_i(y)>0, 0
3 citations
TL;DR: In this paper, it is shown that the m-dimensional system state can be almost decoupled by similarity transformations if the system matrices generate a solvable Lie algebra, and the solvability condition is checked directly from the system matrix.
2 citations
26 Aug 2002
TL;DR: In this paper, the frequency response of uncertain systems using Kharitonov stability theory on the first order complex polynomial set was studied and it was shown that the minimal real part of the response at any fixed frequency is attained at some prescribed vertex transfer functions.
Abstract: We study the frequency response of uncertain systems using Kharitonov stability theory on the first order complex polynomial set. For an interval transfer function, we show that the minimal real part of the frequency response at any fixed frequency is attained at some prescribed vertex transfer functions.
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TL;DR: In this article, the authors provide some simple and efficient criteria to judge the robustness of two families of polynomials, i.e., an interval multilinear polynomial matrix family and a polytopic matrix family.
Abstract: The focal point of this paper is to provide some simple and efficient criteria to judge the ${\cal D}$-stability of two families of polynomials, i.e., an interval multilinear polynomial matrix family and a polytopic polynomial family. Taking advantage of the uncertain parameter information, we analyze these two classes of uncertain models and give some LMI conditions for the robust stability of the two families. Two examples illustrate the effectiveness of our results.
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TL;DR: In this paper, some Kharitonov-like robust Hurwitz stability criteria are established for a class of complex polynomial families with nonlinearly correlated perturbations.
Abstract: Some Kharitonov-like robust Hurwitz stability criteria are established for a class of complex polynomial families with nonlinearly correlated perturbations. These results are extended to the polynomial matrix case and non-interval D-stability case. Applications of these results in testing of robust strict positive realness of real and complex interval transfer function families are also presented.
Journal Article•
TL;DR: In this paper, some Kharitonov-like robust Hurwitz stability properties for complex polynomial families with nonlinearly correlated perturbations are established for a class of real and complex interval transfer function families.
Abstract: Some Kharitonov-like robust Hurwitz stability crite- ria are established for a class of complex polynomial families with nonlinearly correlated perturbations. These results are extended to the polynomial matrix case and non-interval D-stability case. Ap- plications of these results in testing of robust strict positive realness of real and complex interval transfer function families are also pre- sented.
TL;DR: In this article, the robustness of multivariable systems with parametric uncertainties was studied and an illustrative example is presented, and a multivariability version of Edge Theorem was established.
Abstract: : This paper studies robustness of multivariable systems with parametric uncertainties, and establishes a multivariable version of Edge Theorem. An illustrative example is presented.
TL;DR: From this viewpoint, the robust performance problem is reconsidered and a numerical example is given to show the efficiency of the result.
Abstract: In this paper, a new viewpoint of H X control in frequency domain is presented. From this viewpoint, the robust performance problem is reconsidered. A numerical example is given to show the efficiency of the result.
Journal Article•
TL;DR: In this paper, the authors studied the number of positive solutions in C[0, 1] to the integral equation and showed that when n = 1, either there does not exist, or there exist infinitely many positive solutions, when n greater than or equal to 2, there exist at least 1, at most n + 1 positive solutions.
Abstract: By using the complete discrimination system for polynomials, we study the number of positive solutions in C[0,1] to the integral equation phi(x) = integral(0)(1) k(x,y) phi(n)(y)dy, where k(x,y) = phi(1)(x)phi(1)(y) + phi(2)(x)phi(2)(y),phi(i)(x) > 0, phi(i)(y) > 0,0 < x, y < 1, i = 1, 2, are continuous functions on [0, 1], n is a positive integer. We prove the following results: when n = 1, either there does not exist, or there exist infinitely many positive solutions in C[0, 1]; when n greater than or equal to 2, there exist at least 1, at most n + 1 positive solutions in C[0, 1]. Necessary and sufficient conditions are derived for the cases: 1) n = 1, there exist positive solutions; 2) n greater than or equal to 2, there exist exactly m (m epsilon {1, 2,..., n + 1}) positive solutions. Our results generalize the ones existing in the literature, and their usefulness is shown by examples.
08 May 2002
TL;DR: In this article, the authors proposed several special kinds of matrices, which transform directly the space of the coefficients of a stable polynomial into a bounded domain without destroying the stability.
Abstract: Simultaneous stabilization is an open problem in the design of robust controllers. Based on the stability preserving maps (SPM), genetic algorithms (GA) are applied to solving the problems of simultaneous stabilization of a set of SISO plants. The paper proposes several special kinds of matrices, which transform directly the space of the coefficients of a stable polynomial into a bounded domain without destroying the stability. The corresponding polynomial converted is suitable for processing in GAs. Hence, the simultaneous stabilization problem can be solved effectively by using GAs. Some illustrative examples are presented and related topics are discussed. Our examples show that while the simultaneous stabilization problem is generally NP-hard or rationally undecidable, in most cases, it can be tackled numerically by some optimization algorithms. Thus, simultaneously stabilizing controllers can be found accordingly.
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TL;DR: For any two $n$-$th$ order polynomials $a(s)$ and $b(s),$ the Hurwitz stability of their convex combination is necessary and sufficient for the existence of a polynomial $c(s)/a(S)$ such that $c (s)/b(S), and the combination of these polynomorphisms are both strictly positive real.
Abstract: For any two $n$-$th$ order polynomials $a(s)$ and $b(s),$ the Hurwitz stability of their convex combination is necessary and sufficient for the existence of a polynomial $c(s)$ such that $c(s)/a(s)$ and $c(s)/b(s)$ are both strictly positive real.
27 Oct 2002
TL;DR: In this article, the controllability and stabilizability of a class of hybrid dynamic systems (HDSs) is discussed and the necessary and sufficient conditions for stabilisation are established.
Abstract: Many practical engineering problems can be modelled as such a class of hybrid dynamic systems (HDSs), where N plants are controlled by a central controller in sharing time manner. These plants are described by differential equations and the controller works according to the mechanism of discrete event. This paper discuss the controllability and stabilizability of this class of hybrid dynamic systems. First, we define the controllability of this class of HDSs and establish the necessary and sufficient condition for controllability. Furthermore, we define the stabilizability of this class of HDSs and establish the necessary and sufficient condition for stabilizability as well.
06 Oct 2002
TL;DR: It is pointed out that the controllability of linear descriptor systems with multiple time-delays in control is independent of the size of the time-Delays.
Abstract: AbstmctThis paper studies the controllability of linear descriptor systems with multiple time-delays in control. Several controllability concepts are investigated. First, necessary and sufficient criteria for the controllability of the canonical system are established. Then, equivalent criteria for that of the general system are given. Finally, it is pointed out that the controllability is independent of the size of the time-delays. Kewordscontrollability, descriptor systems, singular systems, time-delay.