| Since the 1960s, stochastic systems have received much attention as stochas-tic modeling has come to play an important role in many branches of Science and engineering applications. A great number of results on stochastic systems have been presented and various approaches have been proposed. Control of stochastic systems is a research topic of both practical and theoretical im-portance, which has received much attention [8,9]. Many results related to stochastic systems have been reported in the literature. For instance,an optimal stochastic linear-quadratic control problem was investigated by a stochastic al-gebraic Riccati equation approach in infinite-time horizon in [12], where the diffusion term in dynamics depends on both the state and the control variables. The robust H∞control problem for different types of discrete stochastic system was studied in [6]and [14], respectively,where a linear matrix inequality(LMI) approach was developed to solve the problem. The H∞-type theory was con-sidered for continuous-time stochastic systems via dynamic output feedback controllers in[7], where a version of bounded real lemma for stochastic systems has been developed.The corresponding results on discrete-time stochastic sys-tem can be found in[15].Stochastic H2/H∞control with state-dependent noise was investigated for Ito differential systems in [16] via the Riccati inequality technique. A controller set of a class of nonlinear stochastic control systems was characterized by using optimal control theory of diffusion processes in[10], while H∞controllers was constructed for a class of nonlinear stochastic time-delay systems in [17]. Delay-dependent stability in the mean-square sense has been studied for stochastic systems with time-varying delays,Markovian switching and nonlinearities in article [18]. Basic theory and applications can be found in the book by Meyn and Sweedie [22] on Markov chains evolving in discrete time and on general state spaces.Stability and stabilization of stochastic systems have been studied exten-sively by many researchers.The problems of absolute stabilization and minimax control were investigated in [11] in the context. Characterizations of stabil-ity radii of a stable linear stochastic Ito system with respect to structured multi-perturbations were presented in [13]. Four types of definitions of expo-nentials stability in the mean square are discussed for a more general class of discrete-time linear stochastic systems in [19], and they are equivalent for the system considered in this paper. In order to investigated stability and stabiliza-tion,the spectrum concept and spectrum assignment problem were proposed in [20]; these are similar to the pole concept and pole placement of deterministic systems. It was demonstrated in [20] that a stochastic system is stabilizable if and only if there exists a state feedback controller such that the spectrum of the close-loop system belongs to the open left-hand side complex plane. There-fore, the concept of spectrum proposed in [20] is efficient in dealing with the stabilization problem for stochastic systems.As shown in [21], the spectrum of a stochastic system cannot be assigned arbitrarily even if it reduces to a con-trollable deterministic system.However,we can consider the problem of putting the spectrum of a stochastic system in the open left-hand side complex plane of one line.For this purpose,the concept of"stabilizing degree" was proposed in [21]. It is worth mentioning that for the deterministic case,which is due to the adoption of the concept of spectrum given by [20].In this paper, we are concerned with the exponential stabilization for linear stochastic systems. It is known that stochastic stability plays a crucial role, which is an essential assumption in many physical problems. In [12], an optimal stochastic linear-quadratic control problem was studied in the infinite time horizon. To analyze the stochastic algebraic Riccati equation(SARE)which arises from such a problem, LMIs were applied whose feasibility was shown to be equivalent to the solvability of the SARE.Stability and exact observability have been analyzed via spectral techniques for stochastic systems in [20]. It is well known that ti is very useful in practice to design a controller such that closed-loop systems can converge as fast as it can,that is, with optimal decay rate.This problem has been solved for linear systems without stochastic terms, related results about linear stochastic system have been discussed in article [1].Base on the research about linear stochastic system, in this paper,we investigated uncertain stochastic linear continuous-time system with convex polytopic uncertainties. For instanc(?),the optimal decay rate,stability, robust stability,stabilization,robust stabilization.And we design state feedback con-troller and output feedback controller.What's more, we discussed robust H∞stability. This paper is organized as follows.Chapter 1 presents some necessary preliminaries,and describe the prob-lem studied in this paper. In Chapter 2 the robust stabilization with decay rate constraints is studied. Using convex optimization method and LMI ap-proach,an optimal state feedback controller is designed, which insures that the close-loop system is robustly stochastically stable with maximal decay rate. Chapter 3 considered output feedback controller. Chapter 4 discusses the ro-bust H∞control problem with maximal decay rate. |
PDF Full Text Request