Finite-Time Stochastic Stabilization And H_∞Control For Linear Singular Discrete Stochastic Systems

This thesis discusses the problems of finite-time stochastic stabilization and H∞control for singular linear discrete stochastic systems based on state feedback and output feedback. By using Schur Complement theory and cone complementary linearization algorithm, we respectively give a sufficient condi-tion based on state feedback and output feedback so that the close-loop system is finite-time stochastic stable and satisfies the H∞norm index.In chapter1, we simply introduce the research background of the problems of finite-time stochastic stabilization and H∞control for singular linear discrete stochastic systems. We give some main concepts, Schur Complement theory and cone complementary linearization algorithm, which we need in this paper. By doing this foundation work, we can proceed our paper steadily.In chapter2, we investigate the problems of finite-time stochastic sta-bilization and H∞control for singular linear discrete stochastic systems. We discuss two cases:state feedback and output feedback. By constructing a Lya-punov function, we respectively find a sufficient condition so that the close-loop system is finite-time stochastic stable and satisfies the H∞norm index. We prove it in detail. Furthermore, we discuss the limitation of this system and the room for improvement. Finally we give a numerical example to prove the effectiveness of our results.In chapter3, we investigate the problems of finite-time stochastic stabiliza-tion and H∞control for uncertain singular linear discrete stochastic systems. We discuss two cases:state feedback and output feedback, and respectively find a sufficient condition so that the close-loop system is finite-time stochastic stable and satisfies the H∞norm index.