Robust Control For Uncertain Stochastic Systems With Time-delays

Uncertainties and time-delays widely exist in various real systems while theimpactions caused by them can not be ignored such as the instability and dynamicperformance degradation. In order to design controllers with strong robustness,uncertainties and time-delays of the systems should be fully considered during theanalysis. Variable structure control (VSC) has fully robustness against some externaldisturbances and parameter uncertainties, so VSC is an effective robust controlapproach for systems with time-delays, uncertainties and external disturbance. Forthose good properties, VSC has received much attention from many researchers.The problems of robust control and VSC for some uncertain stochastic systemswith time-delays are studies in this thesis. The design of the robust controllers forsome different stochastic systems with time-delays and uncertainties are given here.The main contents are as follows:1. The development history and research situations about VSC and robust controlfor stochastic systems with uncertainties and time-delays are summarized. Also theproblems solved in this thesis are presented.2. The H control for Ito stochastic systems with Markovian switching hasbeen investigated. By means of linear matrix inequalities (LMIs), the suitable slidingsurfaces are given firstly. Then in order to guaranty the sliding motions on thespecified sliding surfaces are stochastically stable with disturbance attenuationlevel, two theorems are given by Lyapunov-Krasovskii functional. Finally, asimulation is provided to show the effectiveness and practicability of the proposedmethod.3. The robust stabilization for a class of uncertain discrete-time stochasticsystems with time-delays is investigated. Not only the nonlinearity and discreteness ofthe disturbed delays, but also the uncertainty of the parameters is concerned. Firstly, the sufficient conditions are given in this paper to guaranty the globallyasymptotically stable in the mean square sense and the stabilization of the system bymeans of LMIs. Secondly, the state controller is already designed here. Finally, anumerical example is provided to show the effectiveness of the given method.4. The H control for a class of uncertain discrete-time stochastic systems hasbeen discussed. The nonlinearity, discreteness of the disturbed delays and uncertaintyof the coefficient matrix are concerned. Firstly, a sufficient condition is given toguaranty the robustly mean-square exponentially stability with disturbance attenuation0by means of Lyapunov-Krasovskii functional method and LMIs technique.Secondly, the state feedback controller is designed for this system. Finally, anumerical example is provided to show the practicability of the presented method.