Dissipative And Admissible Analysis Of Generalized Time-delay System

Time delay often exists in various dynamic systems,and it is considered to be the main reason of oscillation,poor performance and instability.Different from normal state-space systems,descriptor systems can describe the structure of real systems more precisely and are widely used in biology,economics,network control,astronautics,and constrained mechanics.The dissipative theory plays an important role in analyzing the stability of the system,and its essence is that there is an energy supply function,so that the energy supply rate of the system is always greater than the energy loss.Therefore,it is of great theoretical and practical significance to study the dissipativity and admissibility of descriptor timedelay systems.However,there is still a certain conservativeness for the analytical problems of dissipativity and admissibility of descriptor time-delay systems.Based on the existing research results,this thesis mainly uses the asymmetric L-K functional method to study the dissipativity and admissibility analysis problem of descriptor time-delay systems,and obtains the less conservativeness results.The main contents of this thesis are as follows:(1)We study the problems of dissipativity and admissibility analysis of descriptor time-delay systems.First,an augmented asymmetric Lyapunov-Krasovskii(L-K)functional is constructed.Next,Jensen inequality and Wirtinger inequality are used to estimate the L-K functional,and the overall positive definite conditions of the L-K functional are obtained,in which the restricted matrices in L-K functional are not required to be positive definite,and the restrictions on these matrices are relaxed.Subsequently,the derivative of the L-K functional is bounded by using integral inequality techniques,and the strict(7)Q,S,R(8)-γ-dissipative and admissible conditions for the systems are given in terms of strict linear matrix inequalities(LMIs).Finally,the effectiveness and superiority of the proposed method are verified by numerical simulation.(2)We study the problems of dissipativity and admissibility analysis of T-S fuzzy descriptor time-delay systems.First,constructing an augmented asymmetric L-K functional.Then,combining with the integral inequality technique,the positive definite conditions for the L-K functional and more compact upper bounds for its derivative are obtained.Thereby,the improved dissipative and admissible criteria of the corresponding systems are obtained,which reduce the conservatism compared with the previous results.