Research On Robust Stability And Stabilization For Two Classes Of Stochastic Systems With Polytopic-type

There are some uncertain random factors in real system. When random uncertainty is modeled as stochastic processes, the stochastic systems can de-scribe actual engineering systems more really and more accurately. Nonlinear and time-delay of system are commonly encountered in real systems. Time-delay is frequently a source of instability or oscillation. The existence of time-delay in control systems increases the difficulty of theoretical analysis and engineering application. On the other hand, the controlled systems are often impacted by parameter error, unmodeled dynamics and uncertain external disturbances. The system model has uncertainties. Therefore, it is great importance in theoretical and practical application to research into robust stability and control of nonlin-ear uncertain stochastic systems. By using stochastic Lyapunov stability theory, model transform and free-weighting matrix method, and by means of Ito differen-tial formula, Schur complement lemma, linear matrix inequality, some important lemmas and inequalities, we study the robust stabilization and control of non-linear uncertain stochastic systems. The main contents of this dissertationg are summarized as follow:1. In Chapter 2, the robust stability problem for nonlinear time-varying delay stochastic system with polytopic-type uncertainties is discussed. Since nonlinear term, distributed delay and discrete delay term in uncertain systems, the model becomes more general and the upper bound of derivative of the delay term needn’t less than 1. Based on parameter-dependent Lyapunov-Krasovskii functional and free-weighting matrix method, some delay-dependent and parameter-dependent stability conditions are presented in terms of linear matrix inequalities.2. In Chapter 3, the parameter-dependent state feedback control problem for stochastic delay-varying system with polytopic-type uncertainties is discussed. Some examples show that many systems can’t be stabilization by fixed gain matrix(parameter-independent controller), but can be stabilization by parameter-dependent controller. Based on parameter-dependent Lyapunov-Krasovskii func- tional and free-weighting matrix method, some delay-dependent and parameter-dependent stabilization conditions are presented in terms of linear matrix inequal-ities. Since the number of free-weighting matrices is reduced when introducing free-weighting matrix, the given parameter-dependent controller is easier to im-plement.3. In Chapter 4, the non-fragile stabilization problem for stochastic delay-varying systems with polytopic-type uncertainties is discussed, and the perturbed matrix in the actual implemented controller is assumed satisfying polytopic-type uncertainties(a sort of more natural description). By using parameter-dependent Lyapunov-Krasovskii functional method and free-weighting matrix method, the product terms for Lyapunov matrix and system matrix are separated. Then a non-fragile robust exponential stabilization condition for stochastic delay-varying systems with polytopic-type uncertainties is proposed in terms of linear matrix inequalities. The non-fragile state feedback controller can be obtained by solving LMI.Finally, the main results of the dissertation are concluded, and the issues of future investigation are proposed.