| The discrete-time singular system is a class of singular systems broader than others.With the development of computer science, discrete-time becomes more and moreimportant in many aspects of our real life. For example, traffic control,telecommunications, network control system, chemical reactions, power transducers andso on. The combination of discrete-time singular with others have been paid more andmore attention. The hot areas of robust H_∞control problem and finite-time boundedresearch on discrete-time systems have important theory significances and practical value.This dissertation studies the problem of H_∞control for discrete-time singularsystems by constructing appropriate Lyapunov-Krasovskii function, combining with newdifference inequality, singular value theory and linear matrix inequality (LMI) approach.The main works are as follows:Firstly, the delay-depended robust stability theory of uncertain discrete-time wasconcerned based on the LMI methods and the obtained condition was proved to beeffective by the Matlab tool box.Secondly, the problem of non-fragile H_∞control for discrete-time singular systemswith state-delay is dealt with. By constructing appropriate generalized Lyapunov-Krasovskii function, using Schur-complement Lemma and a new integral inequality, thena sufficient condition is given to guarantees the resultant closed-loop system is regular,impulse free, and stable with a H_∞norm bound constraint.Thirdly, the Finite-time control problem for discrete-time singular systems withactuator saturation is considered. Based on Lyapunov-Krasovskii stability theory, thedesign method of finite-time controller is given by the LMI method and the singular valuetheory.Finally, the problem of finite-time H_∞control problem for a class of discrete-timeswitched singular systems with delays subject to input saturation is investigated. Based onLMI approach and the singular value theory, sufficient conditions for the existence offinite-time H_∞control law are obtained. |
PDF Full Text Request