Analysis And Synthesis Of Stochastic Singular Systems With Time Delays Based On LMI Techniques

As a new frontier topic in system science,the analysis and research of stochastic singular systems are very challenging.In recent years,more and more scholars have studied stochastic singular systems and obtained many meaningful results.However,the research on stochastic singular systems with time-delays is rare,and time-delays will cause the instability of the systems,which bring great difficulties to the research process.This thesis takes the analysis technique of stochastic singular systems and the theory of stochastic stability as the basic idea,and uses some mathematical techniques,such as constructing Lyapunov-Krasovskii functional,by using some methods such as free weighting matrix technique,Jensen inequality and linear matrix inequality to study the stability and related performance design of parameter deterministic stochastic singular systems with state time-delays.Furthermore,the stability and related problems of parameter uncertain stochastic singular systems with state time-delays are analyzed.The main research work of this thesis includes the following aspects:Firstly,the stability and H performance of stochastic singular systems with deterministic time-varying delays are studied.In this thesis,a suitable Lyapunov-Krasovskii functional is constructed.by using the auxiliary vector function,the free weighting matrix technique and Jensen inequality,the stochastic admissibility criterion of stochastic singular systems with time-varying delays in the sense of mean square is proposed.Secondly,a state feedback controller is designed.By using the dual equation to simplify the calculation,it is obtained that the corresponding closed-loop system is regular,impulse-free,stochastically stable in the sense of mean square and has H performance index ?.A simulation example shows the correctness and effectiveness of the proposed method.Secondly,the dissipative performance of stochastic singular systems with time-varying delays with parameter uncertainties is studied.For uncertain stochastic singular systems,by constructing an appropriate Lyapunov-Krasovskii functional,using the improved free weighting matrix technique and Jensen inequality,under the condition that the system satisfies regularity and no impulse,a criterion of stochastic stability in the sense of mean square is proposed.A state feedback controller is designed,which can make the system stochastically admissible in the sense of mean square and strictly dissipative.Finally,we propose an example to prove the proposed problem by simulation,and prove the correctness and effectiveness of the proposed method.