Fuzzy Control Of T-S Discrete-Time Fuzzy Systems With Actuator Saturation

The system analysis and control synthesis of nonlinear systems is a major subject of control theory. T-S fuzzy approach is an effective method of studying nonlinear system. Since Tanaka and Sugeno firstly put forward the T-S Fuzzy modeling approach in 1985, the system analysis and control synthesis of T-S fuzzy systems have been extensively studied. In the past few years, the stability analysis and control design of nonlinear systems with actuator saturation have been receiving increasing attention.In this thesis, in view of the T-S fuzzy representation of nonlinear discrete-time systems, we study the fuzzy control synthesis problem of T-S discrete-time systems with actuator saturation.In Chapter One, the development of control theory and the existing conclusions of nonlinear systems with actuator saturation are briefly reviewed, then the main results of this thesis are introduced.In Chapter Two, considering the T-S discrete-time fuzzy systems with actuator saturation, a criterion of asympotic stability of the closed-loop fuzzy systems is established. Based on the criterion, the problem of designing fuzzy controllers to stabilisize the closed-loop fuzzy systems and estimating the domain of attraction is obtained by solving some LMIs. We also extend the result to the case whose saturation parameters are not 1. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.In Chapter Three, considering the T-S discrete-time fuzzy systems with actuator saturation, the linear qudratic(LQ) fuzzy control problem of T-S discrete-time fuzzy systems with actuator saturation is studied. By using qudratic Lyapunov stability theory and parallel distributed compensation(PDC) scheme, the asympotic stability conditions and an upper bound of qudratic performance of T-S discrete-time fuzzy systems arc given. Based on these,the design method of LQ fuzzy controllers to stabilisize the closed-loop fuzzy systems is proposed. For two different, optimization problems, the corresponding feasible procedures in LMI frameworks arc presented. Finally, we use a numerical example to illustrate the effectiveness of the proposed method.