Control Of Non-Linear Stochastic T-S Fuzzy Systems With Time Delay

As an efficient approach of modeling nonlinear systems, Takagi-Sugeno (T-S) fuzzy model which has polytopic local structure, is often utilized in the stability analysis and controller design. When the parameters of a T-S fuzzy system are perturbed with random noises, the system turns to be a stochastic fuzzy system. Essentially, it is a nonlinear stochastic differential system. If the state evolution of the stochastic fuzzy system depends on its previous states, then we need to introduce a time delay term in the system, and hence formulate the system as a stochastic fuzzy system with time delay, which are a class of nonlinear stochastic differential systems and the topic of this dissertation.First of all, we work on the mean-square stabilization issue of stochastic fuzzy system with time delay. We define the analytical formulation of the system in Ito sense, and prove the existence and uniqueness of solution to the formulation. Then, the exponential mean square stability conditions of the closed-loop system with time delay are derived from Lyapunov approach of nonlinear stochastic differential systems with time delay. The fuzzy controller of the system is proposed by means of the parallel distributed compensation (PDC) technique, by which, the local state feedback compensators are configured for every local linear systems, and the overall fuzzy controller is composed of these local compensators. Therefore, we obtain the sufficient conditions for stabilizing the stochastic fuzzy systems with time delay. Furthermore, by Schur's lemma we transform these sufficient conditions into the format of linear matrix inequality(LMI) which could be solved readily by Matlab LMI toolbox. An illustration example shows that the proposed method in the dissertation could stabilize nonlinear stochastic differential systems with time delay which are difficult to be stabilized by the methods in the literature.Secondly, we do some research on the robust stabilization issue for uncertain stochastic fuzzy system with time delay. In this part, we obtain some sufficient conditions of robust stability of the stochastic fuzzy system with time delay for a set of permissible uncertainties. The sufficient conditions are reduced to LMIs by using several matrix inequalities. The robust state feedback controller can be designed based on the LMIs. A simulation example is given to show the application of the robust state feedback controller.Thirdly, we consider robust H_∞control problem of uncertain stochastic fuzzy systems with time-delay. Compared with the systems in the former parts, the system includes exogenous disturbances and is no longer a closed-loop one. Therefore, the main concern is how to guarantee disturbance attenuation while stabilizing the system. We propose an LMI design procedure for the robust H_∞control problem. The numerical example demonstrates the effectiveness of the proposed method.Finally, we summarize the conclusions of the study, and put forward some problems which worth to be investigated further. The results in the dissertation are somewhat conservative, since the stability conditions don't depend on the length of the time delay, and the design of state feedback controller depends on the existence of a common positive matrix for all local systems. Less conservative methods, such as delay-dependent stability conditions, are expected in the future.