Study Of The Quadratic Guaranteed Cost Control,State Feedback H_∞ Control And Stability Of Stochastic Systems

Based on the knowledge of stochastic differential equation,the stochasticprocess and the stochastic control, this article studies quadratic guaranteedcost control and output feedback H_∞control of uncertain stochastic systems,the H_∞control of nonlinear stochastic systems and the stability of stochasticsystems with time-delay, and some useful results are obtained.There are five chapters:In the first chapter: the development history,the research object andcontents of stochastic control are introduced.In Chapter Two: we introduce basic mathematics knowledge that used in thisarticle: the existence and uniqueness condition of the solution; Linear matrixinequality.In Chapter Three: quadratic guaranteed cost control and output feedback H_∞control of uncertain stochastic systems, the quadratic guaranteed cost controland output feedback H_∞control under both parametric and stochasticuncertainties are studied. It is assumed that the uncertain parameter is normbounded, the exogenous disturbance is stochastic uncertainty. We give thedefinition of quadratic guaranteed cost control of uncertain stochastic systems,and prove that the state feedback law u(t)=Kx(t)can enable the system to achievequadratic stability and the cost function to be bounded via the linear matrixinequality. We give relationship between quadratic guaranteed cost control andquadratic stabilizable. Meanwhile, a sufficient condition is obtained for theexistence of output feedback control.Chapter Four is about the stability of nonlinear systems and H_∞controlproblem of a class of nonlinear stochastic systems, where linear part can beseparated from the nonlinear counterpart, and the design of H_∞controller isdeveloped via the linear matrix inequality.Chapter Five is about the stability of polytopic uncertain time-delaystochastic systems, where the parameters of the system are not exactly given,which are known to reside in a given polytope. We give a very effective sufficientcondition that enables the system to be globally asymptotically stable via linearmatrix inequality, which can be solved via the Matlab control toolbox directly.