Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 6

Publications

6 Robust Quadratic Stabilization of Uncertain Impulsive Switched Systems

Authors: Xiuyong Ding, Shouming Zhong, Xiu Liu

Abstract:

This paper focuses on the quadratic stabilization problem for a class of uncertain impulsive switched systems. The uncertainty is assumed to be norm-bounded and enters both the state and the input matrices. Based on the Lyapunov methods, some results on robust stabilization and quadratic stabilization for the impulsive switched system are obtained. A stabilizing state feedback control law realizing the robust stabilization of the closed-loop system is constructed.

Keywords: Switched Systems, Robust Stabilization, Impulsive systems, quadratic stabilization

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5 On General Stability for Switched Positive Linear Systems with Bounded Time-varying Delays

Authors: Xiuyong Ding, Shouming Zhong, Xiu Liu

Abstract:

This paper focuses on the problem of a common linear copositive Lyapunov function(CLCLF) existence for discrete-time switched positive linear systems(SPLSs) with bounded time-varying delays. In particular, applying system matrices, a special class of matrices are constructed in an appropriate manner. Our results reveal that the existence of a common copositive Lyapunov function can be related to the Schur stability of such matrices. A simple example is provided to illustrate the implication of our results.

Keywords: Switched Systems, delays, Common linear co-positive Lyapunov functions, positive systems

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4 Stability of a Special Class of Switched Positive Systems

Authors: Xiuyong Ding, Lan Shu, Xiu Liu

Abstract:

This paper is concerned with the existence of a linear copositive Lyapunov function(LCLF) for a special class of switched positive linear systems(SPLSs) composed of continuousand discrete-time subsystems. Firstly, by using system matrices, we construct a special kind of matrices in appropriate manner. Secondly, our results reveal that the Hurwitz stability of these matrices is equivalent to the existence of a common LCLF for arbitrary finite sets composed of continuous- and discrete-time positive linear timeinvariant( LTI) systems. Finally, a simple example is provided to illustrate the implication of our results.

Keywords: Switched Systems, positive systems, Linear co-positive Lyapunov functions

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3 Controller Synthesis of Switched Positive Systems with Bounded Time-Varying Delays

Authors: Xiuyong Ding, Xinhui Wang

Abstract:

This paper addresses the controller synthesis problem of discrete-time switched positive systems with bounded time-varying delays. Based on the switched copositive Lyapunov function approach, some necessary and sufficient conditions for the existence of state-feedback controller are presented as a set of linear programming and linear matrix inequality problems, hence easy to be verified. Another advantage is that the state-feedback law is independent on time-varying delays and initial conditions. A numerical example is provided to illustrate the effectiveness and feasibility of the developed controller.

Keywords: Stabilization, Switched Systems, time-varying delays, Switched copositive Lyapunov functions, positive linear systems

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2 Stability Analysis of Linear Switched Systems with Mixed Delays

Authors: Xiuyong Ding, Lan Shu

Abstract:

This paper addresses the stability of the switched systems with discrete and distributed time delays. By applying Lyapunov functional and function method, we show that, if the norm of system matrices Bi is small enough, the asymptotic stability is always achieved. Finally, a example is provided to verify technically feasibility and operability of the developed results.

Keywords: Stability, lyapunov function, delays, lyapunov functional, Switched system

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1 New Delay-dependent Stability Conditions for Neutral Systems with Nonlinear Perturbations

Authors: Xiuyong Ding, Shouming Zhong, Lianglin Xiong

Abstract:

In this paper, the problem of asymptotical stability of neutral systems with nonlinear perturbations is investigated. Based on a class of novel augment Lyapunov functionals which contain freeweighting matrices, some new delay-dependent asymptotical stability criteria are formulated in terms of linear matrix inequalities (LMIs) by using new inequality analysis technique. Numerical examples are given to demonstrate the derived condition are much less conservative than those given in the literature.

Keywords: linear matrix inequality (LMI), asymptotical stability, nonlinear perturbation, Neutral system, delay-dependent

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