The Robust Control For Singular Time-delay Systems Subject To Actuator Saturation

The performance of a system depends on the uncertainties, time-delay and nonlinearsaturation in the system, and the fact that they are the major cause of instability and poorperformance of dynamic systems. Therefore, the research for the stability of uncertaintime-delay systems subject to actuator saturations has important theoretical and practicalsignificance. Uncertain time-delay singular system subject to actuator saturations is a classof uncertain time-delay system subject to actuator saturations broader than others, whichhas attracted many domestic and foreign scholars to research, and the conclusions of manynormal linear systems has been successively promoted.This dissertation studies the problem of delay-dependent exponential stability, staticoutput feedback control and memory feedback control for uncertain time-delay singularsystem subject to actuator saturations by constructing appropriate Lyapunov-Krasovskiifunctional, combining with free-weighting matrix methods and some new integralinequalities. Then the problem of memory feedback control for uncertain time-delaysingular Markov jump system subject to actuator saturations is discussed. The main worksare as follows:Firstly, the main background is introduced in this paper. The background for theuncertain time-delay singular system subject to actuator saturations is introduced, anddiscuss the recent develop for the corresponding topic.Secondly, for the uncertain time-delay singular system subject to actuator saturations,by referencing the linear matrix inequality methods, integral inequality and convexcombination approach, the problem of exponential stability and static output feedbackcontroller design is discussed. Numerical examples demonstrate the promoted method isfeasible and has less conservativeness, which has fully explained that the method hastheoretical significance.Thirdly, the problem of delay-dependent robust H exponential stability andmemory feedback stabilization of uncertain time-delay singular systems with saturatingactuators are considered. By using linear matrix inequality methods, free-weightingmatrices and integral inequality, a sufficient condition which guarantees that the uncertain time-delay singular systems with actuator saturation are regular, impulse free andexponential stable with H performance is given. Then, the design method of H static output feedback controller and the estimation of stability region are given by solvinga convex optimization problem. At the same time, some numerical examples are providedto demonstrate the effectiveness of the proposed results.Finally, the problem of delay-dependent H robust exponential stability andmemory state feedback stabilization of time-delay singular Markov jump systems withsaturating actuators is investigated. According to Lyapunov functional theory and weakinfinitesimal generator, a new delay-dependent criterion which guarantees that thestochastic systems are regular, impulse free and exponential stable is given. Then, thememory feedback controller is designed, which can make the closed system robuststability and satisfy the H performance. Some numerical examples are provided todemonstrate the effectiveness and merit of the proposed results.