On Stability And Robust H_∞ Of Stochastic Linear Time-delay System And The Stabilizability, Exact Observability Of Stochastic Linear Systems With Markovain Jumps

This thesis investigates the stability,robust H_∞control and robust H_∞filtering of a class of stochastic linear systems with multiple delays,and the stabilizability and exact observability of stochastic linear systems with Markovian jumps via a linear matrix inequality approach.Firstly,we investigate the stability of a class of stochastic linear systems with multiple delays.Using the Lyapunov function method,we present sufficient conditions for the exponential stability by means of a generalized differential Riccati equation and linear matrix inequalities.The method proposed is applied also to the problems of stabilization of linear time-invariant delay systems.Secondly,we deal with robust H_∞control and robust H_∞filtering of stochastic linear neutral time-delay systems.It is assumed that the systems are described in terms of It(?)'s stochastic differential equations,and exogenous disturbance is a stochastic process.A sufficient condition for controllability of robust H_∞is presented by linear matrix inequalities,and the robust H_∞filtering is constructed via solving a linear matrix inequality.Thirdly,we investigate the stabilizability and exact observability of stochastic linear systems with Markovian jumps and their applications.Using the operator spectrum technique,a necessary and sufficient condition for the stabilizability of stochastic systems with Markovian jumps is presented. Meanwhile,an unremovable spectrum and the stabilization with a given stabilizing degree is defined and discussed.Finally,a stochastic Popov-Belevith-Hautus Criterion for exact observability is given and as applications,we obtain a result on Lyapunov equations.