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Journal of systems Science & Complexity 2013年第6期26卷 925-939页

作者： MU Xiaowu GAO Yang Department of Mathematics Zhengzhou University Graduate School of Beijing University Department of Mathematics Daqing Normal University Graduate School of the Harbin Institute of Technology

In this paper, global input-to-state stabilization with quantized feedback for discrete-time piecewise affine systems （PWA） with time delays are considered. Both feedback with time delays and feedback without time delays are considered. piecewise quadratic ISS-Lyapunov functions are adopted. Both Lyapunov-Razumikhin and Lyapunov-Krasovskii methods are adopted. The theorems for global input-to-state stabilization with quantized feedback of discrete PWA systems with time delays are

关键词： Discrete systems input-to-state stability piecewise affine systems quantized feedback stabilization.

LMI-based robust control of uncertain discrete-time piecewise affine systems

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控制理论与应用（英文版） 2010年第4期8卷 496-502页

作者： Zhiyuan LIU Yahui GAO Hong CHEN Department of Control Science and Engineering Harbin Institute of Technology Harbin Heilongjiang 150001 China Department of Control Science and Engineering Jilin University Changchun Jilin 130025 China

The main contribution of this paper is to present stability synthesis results for discrete-time piecewise affine （PWA） systems with polytopic time-varying uncertainties and for discrete-time PWA systems with norm-bounded uncertainties *** basic idea of the proposed approaches is to construct piecewise-quadratic （PWQ） Lyapunov functions to guarantee the stability of the closed-loop *** partition information of the PWA systems is taken into account and each polytopic operating region is outer approximated by an ellipsoid,then sufficient conditions for the robust stabilization are derived and expressed as a set of linear matrix inequalities （LMIs）.Two examples are given to illustrate the proposed theoretical results.

关键词： Discrete-time systems Linear matrix inequality piecewise affine systems piecewise Lyapunov function Robust control

Robust observer-based control for uncertain discrete-time piecewise affine systems

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控制理论与应用（英文版） 2012年第2期10卷 236-243页

作者： Yahui GAO 1 , Zhiyuan LIU 2 , Hong CHEN 3 1.AVIC (Aviation Industry Corporation of China) China Aviation Motor Control System Institute, Wuxi Jiangsu 214063, China 2.Department of Control Science and Engineering, Harbin Institute of Technology, Harbin Heilongjiang 150001, China 3.Department of Control Science and Engineering, Jilin University, Changchun Jilin 130025, China AVIC (Aviation Industry Corporation of China) China Aviation Motor Control System Institute Wuxi Jiangsu China Department of Control Science and Engineering Harbin Institute of Technology Harbin Heilongjiang China Department of Control Science and Engineering Jilin University Changchun Jilin China

The main contribution of this paper is to present a novel robust observer-based controller design method for discrete-time piecewise affine systems with norm-bounded uncertainties. The key ideas are to construct a piecewise quadratic Lyapunov function to guarantee the stability of the closed-loop systems, approximate polytopic operating regions by ellipsoids, and use the singular value decomposition technique to treat the constraint of matrix equality. It is shown that the suggested control method can be formulated as linear matrix inequalities that are numerically feasible with commer- cially available software. A numerical example is also given to verify the proposed approach.

关键词： piecewise affine systems Robust control Observer Linear matrix inequality

Nonsynchronized state estimation of uncertain discrete-time piecewise affine systems

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控制理论与应用（英文版） 2010年第3期8卷 286-292页

作者： Jianbin QIU Gang FENG Huijun GAO Space Control and Inertial Technology Research Center Harbin Institute of Technology Harbin Heilongjiang 150001 China Department of Manufacturing Engineering and Engineering Management City University of Hong Kong Hong Kong China

This paper investigates the problem of robust H-infinity state estimation for a class of uncertain discretetime piecewise affine systems where state space instead of measurable output space partitions are assumed so that the filter implementation may not be synchronized with plant state trajectory transitions. Based on a piecewise quadratic Lyapunov function combined with S-procedure and some matrix inequality convexifying techniques, two different approaches are developed to the robust filtering design for the underlying piecewise affine systems. It is shown that the filter gains can be obtained by solving a set of linear matrix inequalities （LMIs）. Finally, a simulation example is provided to illustrate the effectiveness of the proposed approaches.

关键词： piecewise affine systems State estimation Linear fractional uncertainties Linear matrix inequality

The Analysis of Global Input-to-state Stability for piecewise affine systems with Time-delay

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International Journal of Automation and computing 2012年第2期9卷 211-214页

作者： Xiao-Wu Mu Yang Gao Department of Mathematics Zhengzhou University Zhengzhou 450052 PRC Department of Mathematics Daqing Normal University Daqing 163712 PRC

In this paper, global input-to-state stability （ISS） for discrete-time piecewise affine systems with time-delay are considered piecewise quadratic ISS-Lyapunov functions are adopted. Both Lyapunov-Razumikhiu and Lyapunov-Krasovskii methods are used The theorems of Lyapunov-Razumikhin type and Lyapunov-Krasovskii type for piecewise affine systems with time-delay are shown respectively.

关键词： piecewise affine systems input-to-state stability time delays discrete systems Lyapunov function.

Non-Zenoness of piecewise affine dynamical systems and affine complementarity systems with inputs

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Control Theory and Technology 2014年第1期12卷 35-47页

作者： Le Quang THUAN Department of Mathematics Quy Nhon University 170 An Duong Vuongy Quy Nhon Binh Dinh Vietnam

In the context of continuous piecewise affine dynamical systems and affine complementarity systems with inputs, we study the existence of Zeno behavior, i.e., infinite number of mode transitions in a finite-length time interval, in this paper. The main result reveals that continuous piecewise affine dynamical systems with piecewise real-analytic inputs do not exhibit Zeno behavior. Applied the achieved result to affine complementarity systems with inputs, we also obtained a similar conclusion. A direct benefit of the main result is that one can apply smooth ordinary differential equations theory in a local manner for the analysis of continuous piecewise affine dynamical systems with inputs.

关键词： piecewise affine systems Zeno behavior Hybrid systems affine complementarity systems

On the Well-posedness of the PWM Control System

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Frontiers of Electrical and Electronic Engineering in China 2006年第1期1卷 105-110页

作者： FAN Qi-fu SHI Song-jiao Department of Automation Shanghai Jiaotong UniversityShanghai 200030China

One of the basic issues in the study of hybrid systems is the well-posedness(existence and uniqueness of solutions)problem of discontinuous dynamical *** paper addresses this problem for a class of piecewise affine discontinuous systems with affine inequalities such as systems with pulse-width modulator under the definition of Carathéodory solutions in terms of an analysis based on lexicographic inequalities and the smooth continuation property of ***,it is clear that when carrier signal h(t)=0,closed-loop pulse-width modulation(PWM)DC–DC converters are not well posed,and when some condition is satisfied,the closed-loop PWM DC–DC converters with a P controller are well posed.

关键词： piecewise affine systems hybrid systems discontinuous systems well-posedness lexicographic inequalities systems with pulse-width modulator

Delay-Independent Robust Stability of piecewise Afflne systems with Delay in State

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Delay-Independent Robust Stability of Piecewise Afflne Syste...