Author

# Guisheng Zhai

Other affiliations: Osaka Prefecture University, Kindai University, Wakayama University ...read more

Bio: Guisheng Zhai is an academic researcher from Shibaura Institute of Technology. The author has contributed to research in topics: Exponential stability & Control theory. The author has an hindex of 34, co-authored 270 publications receiving 5559 citations. Previous affiliations of Guisheng Zhai include Osaka Prefecture University & Kindai University.

##### Papers published on a yearly basis

##### Papers

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TL;DR: A class of switching laws is proposed so that the entire switched system is exponentially stable with a desired stability margin and it is shown quantitatively that, when norms of the perturbations are small, the solutions of the switched systems converge to the origin exponentially under the same switching laws.

Abstract: We study the stability properties of switched systems consisting of both Hurwitz stable and unstable linear time-invariant subsystems using an average dwell time approach. We propose a class of switching laws so that the entire switched system is exponentially stable with a desired stability margin. In the switching laws, the average dwell time is required to be sufficiently large, and the total activation time ratio between Hurwitz stable subsystems and unstable subsystems is required to be no less than a specified constant. We also apply the result to perturbed switched systems where nonlinear vanishing or non-vanishing norm-bounded perturbations exist in the subsystems, and we show quantitatively that, when norms of the perturbations are small, the solutions of the switched systems converge to the origin exponentially under the same switching laws.

593 citations

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TL;DR: This paper investigates the disturbance attenuation properties of time-controlled switched systems consisting of several linear time-invariant subsystems by using an average dwell time approach incorporated with a piecewise Lyapunov function and shows that if the total activation time of unstable subsystems is relatively small compared with that of the Hurwitz stable subsystems, then a reasonable weighted disturbance attenuations level is guaranteed.

Abstract: In this paper, we investigate the disturbance attenuation properties of time-controlled switched systems consisting of several linear time-invariant subsystems by using an average dwell time approach incorporated with a piecewise Lyapunov function. First, we show that when all subsystems are Hurwitz stable and achieve a disturbance attenuation level smaller than a positive scalar γ0, the switched system under an average dwell time scheme achieves a weighted disturbance attenuation level γ0, and the weighted disturbance attenuation approaches normal disturbance attenuation if the average dwell time is chosen sufficiently large. We extend this result to the case where not all subsystems are Hurwitz stable, by showing that in addition to the average dwell time scheme, if the total activation time of unstable subsystems is relatively small compared with that of the Hurwitz stable subsystems, then a reasonable weighted disturbance attenuation level is guaranteed. Finally, a discussion is made on the case for which nonlinear norm-bounded perturbations exist in the subsystems.

507 citations

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28 Jun 2000TL;DR: In this article, the authors study the stability properties of linear switched systems consisting of both Hurwitz stable and unstable subsystems using an average dwell time approach and derive a piecewise Lyapunov function for the switched system subjected to the switching law.

Abstract: We study the stability properties of linear switched systems consisting of both Hurwitz stable and unstable subsystems using an average dwell time approach. We show that if the average dwell time is chosen sufficiently large and the total activation time of unstable subsystems is relatively small compared with that of Hurwitz stable subsystems, then exponential stability of a desired degree is guaranteed. We also derive a piecewise Lyapunov function for the switched system subjected to the switching law and the average dwell time scheme under consideration, and we extend these results to the case for which nonlinear norm-bounded perturbations exist in the subsystems. We show that when the norms of the perturbations are small, we can modify the switching law appropriately to guarantee that the solutions of the switched system converge to the origin exponentially with large average dwell time.

284 citations

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TL;DR: In this article, the authors consider quadratic stabilizability via state feedback for both continuous-time and discrete-time switched linear systems that are composed of polytopic uncertain subsystems.

Abstract: In this paper, we consider quadratic stabilizability via state feedback for both continuous-time and discrete-time switched linear systems that are composed of polytopic uncertain subsystems By state feedback, we mean that the switchings among subsystems are dependent on system states For continuous-time switched linear systems, we show that if there exists a common positive definite matrix for stability of all convex combinations of the extreme points which belong to different subsystem matrices, then the switched system is quadratically stabilizable via state feedback For discrete-time switched linear systems, we derive a quadratic stabilizability condition expressed as matrix inequalities with respect to a family of non-negative scalars and a common positive definite matrix For both continuous-time and discrete-time switched systems, we propose the switching rules by using the obtained common positive definite matrix

257 citations

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08 May 2002TL;DR: In this article, the authors investigated the stability of a time-controlled switched system consisting of several linear discrete-time subsystems and showed that the system is exponentially stable if the average dwell time is chosen sufficiently large and the total activation time ratio between Schur stable and unstable subsystems is not smaller than a specified constant.

Abstract: We investigate some qualitative properties for time-controlled switched systems consisting of several linear discrete-time subsystems. First, we study exponential stability of the switched system with commutation property, stable combination and average dwell time. When all subsystem matrices are commutative pairwise and there exists a stable combination of unstable subsystem matrices, we propose a class of stabilizing switching laws where Schur stable subsystems are activated arbitrarily while unstable ones are activated in sequence with their duration time periods satisfying a specified ratio. For more general switched system whose subsystem matrices are not commutative pairwise, we show that the switched system is exponentially stable if the average dwell time is chosen sufficiently large and the total, activation time ratio between Schur stable and unstable subsystems is not smaller than a specified constant. Secondly, we use an average dwell time approach incorporated with a piecewise Lyapunov function to study the /spl Lscr//sub 2/ gain of the switched system.

195 citations

##### Cited by

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05 Mar 2007TL;DR: This work reviews several recent results on estimation, analysis, and controller synthesis for NCSs, and addresses channel limitations in terms of packet-rates, sampling, network delay, and packet dropouts.

Abstract: Networked control systems (NCSs) are spatially distributed systems for which the communication between sensors, actuators, and controllers is supported by a shared communication network. We review several recent results on estimation, analysis, and controller synthesis for NCSs. The results surveyed address channel limitations in terms of packet-rates, sampling, network delay, and packet dropouts. The results are presented in a tutorial fashion, comparing alternative methodologies

3,748 citations

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2,618 citations

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TL;DR: This paper focuses on the stability analysis for switched linear systems under arbitrary switching, and highlights necessary and sufficient conditions for asymptotic stability.

Abstract: During the past several years, there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems. This paper aims to briefly survey recent results in this field. First, the stability analysis for switched systems is reviewed. We focus on the stability analysis for switched linear systems under arbitrary switching, and we highlight necessary and sufficient conditions for asymptotic stability. After a brief review of the stability analysis under restricted switching and the multiple Lyapunov function theory, the switching stabilization problem is studied, and a variety of switching stabilization methods found in the literature are outlined. Then the switching stabilizability problem is investigated, that is under what condition it is possible to stabilize a switched system by properly designing switching control laws. Note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature. A necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here.

2,470 citations

01 Jan 2005

TL;DR: In this paper, a number of quantized feedback design problems for linear systems were studied and the authors showed that the classical sector bound approach is non-conservative for studying these design problems.

Abstract: This paper studies a number of quantized feedback design problems for linear systems. We consider the case where quantizers are static (memoryless). The common aim of these design problems is to stabilize the given system or to achieve certain performance with the coarsest quantization density. Our main discovery is that the classical sector bound approach is nonconservative for studying these design problems. Consequently, we are able to convert many quantized feedback design problems to well-known robust control problems with sector bound uncertainties. In particular, we derive the coarsest quantization densities for stabilization for multiple-input-multiple-output systems in both state feedback and output feedback cases; and we also derive conditions for quantized feedback control for quadratic cost and H/sub /spl infin// performances.

1,292 citations

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TL;DR: A new analysis method for H"~ performance of NCSs is provided by introducing some slack matrix variables and employing the information of the lower bound of the network-induced delay.

Abstract: This paper is concerned with the design of robust H"~ controllers for uncertain networked control systems (NCSs) with the effects of both the network-induced delay and data dropout taken into consideration. A new analysis method for H"~ performance of NCSs is provided by introducing some slack matrix variables and employing the information of the lower bound of the network-induced delay. The designed H"~ controller is of memoryless type, which can be obtained by solving a set of linear matrix inequalities. Numerical examples and simulation results are given finally to illustrate the effectiveness of the method.

1,057 citations