The Study Of Some Robust Problems Of Uncertain Differential System With Delays

Uncertain time-delay differential system, i.e., differential system with time-delay and parameter uncertainty, is an effective tool to simulate related phenomena in the real world. With uncertain time-delay differential system more and more appearing in actual applica-tion, the research on it has attracted more and more researchers's attention. The study of robust problems of uncertain time-delay differential system is an important part of the research.In this thesis, some robust problems of uncertain differential system with delay were discussed and some results were obtained.The structure of this paper is as followsIn part 1, we introduced the preliminary knowledge which was necessary in this paper.In part 2, we mainly investigated the output feedback robust stability problem for uncertain systems with distributed and time-varying delays. Based on output dynamical feedback and the Lyapunov-Krasovskii functional, we obtained the delay-dependent robust stability conditions of the close-loop systems.In part 3, we discussed the problem of delay-dependent robust H∞control for un-certain singular systems with discrete and distributed delays. Robust delay-dependent stability criteria and a state-feedback control law, which guarantees the resultant closed-loop system is regular, impulse free and stable with H∞norm bound condition for all admissible uncertainties, were obtained.In part 4, we dealt with the robust H∞filtering problem for a class of uncertain linear singular stochastic systems with Markovian switching and mode-dependent time-varying delays. A sufficient condition on the existence of the desired robust exponential Hoo filter was given firstly. After that, an explicit expression of the desired filter parameters was characterized.