Dissipative Analysis For Singular Impulsive Discrete Systems With Time-delay

For the past few years, dissipativity problem is become a popular research incontrol theory. Dissipativity is widely applied in the system stability problem,impulsive control problem and robust control problem. Dissipativity is a veryimportant concept in control theory. And dissipative problem is researchedextensively. In practical problems, we need to use the impulsive delay singular system.But there have been very few results reported on dissipativity of singular impulsivediscrete time-delay systems, so this paper studies the dissipative problem for thesingular impulsive discrete time-delay system. And the main results summarized asfollows:（1）The background and significance of research dissipative problem areintroduced. Then for the impulsive delay systems, a brief introduction is given. At lastwe introduce the major work of this paper.（2）By the analysis of singular impulsive discrete time-delay system, thesufficient conditions for the system to be strict dissipative and admissible are given.Then the method of designing state feedback controller is presented, and thenumerical examples have been provided to demonstrate the effectiveness andapplicability of the proposed approach.（3）By using the methods of LMI, the sufficient conditions for the singularimpulsive discrete system with mixed time-varying delays to be strict dissipative andadmissible are given. Then the method of designing state feedback controller ispresented, and the numerical examples have been provided to demonstrate theeffectiveness and applicability of the proposed approach.（4）Summarize the major work and thoughts of this paper, then the future studiesare listed.