Stability Analysis And Controller Design Of Some T-S Fuzzy Systems

Compared with classical control systems, fuzzy control systems have the following two unmatched advantages. First, it can be easy to realize effectively human control strategies and experience in many applications. Second, it can achieve better control performance in the absence of the mathematic model for the controlled system. In the control area, fuzzy systems are used as a nonlinear function approximation tool. In 1985, both Takagi and Sugeno proposed the Takagi-Sugeno (T-S) fuzzy model, which brings far-reaching impact for fuzzy control theory and its application, and makes stability analysis of fuzzy systems to a new theoretical height. Now, some results have been applied into practical systems. An advantage of a T-S fuzzy model is that it can fully use Lyapunov stability theory to analyze stability of systems and design controller, and a systematic method is provided to study the problem of stability of nonlinear systems and controller design by T-S fuzzy modelling for nonlinear systems.When phenomenons like time-delay, input saturation and uncertainty exist in T-S fuzzy systems, the existence of these phenomenons can often greatly deteriorate the performance of the systems, and even drive the systems to be unstable. In this dissertation, for T-S fuzzy systems subject to time-delay, input saturation or uncertainty, stability conditions and fuzzy controllers design are correspondingly established using the Lyapunov-Krasovskii approach. At the same time, a novel algorithm for fuzzy model identification is proposed. The main research works in the dissertation can be described as follows:In chapter 1, a brief review of the principle of T-S fuzzy systems and the design method for fuzzy controller are first presented. Then, the present research situation of stability analysis of T-S fuzzy systems is summarized. Finally, the main research contents of this dissertation are provided.In chapter 2, T-S fuzzy model construction is first proposed, and the modelling error between a fuzzy model and its corresponding nonlinear system is characterized by a 2-norm uncertainty structure. Then, for T-S fuzzy system with input-delay, a reduced system is obtained by applying the reduction method. A fuzzy controller to stabilizethe reduced system is also designed using the concept of parallel distributed compensation. Based on Lyapunov-Krasovskii functional approach, a sufficient condition for stabilizing the fuzzy system is presented in the form of linear matrix inequalities.In chapter 3, by constructing appropriate Lyapunov-Krasovskii functional, sufficient conditions for robust stabilization of T-S fuzzy system with time-varying input-delay are given in the form of linear matrix inequalities. The fuzzy controller design does not have to require that the time-derivative of time-varying input delay must be smaller than one.In chapter 4, a sufficient condition for stability of time-delay T-S fuzzy systems subject to actuator saturation is first provided, and the problem of estimating the domain of attraction is also formulated. Based on the stability condition, the robust stability of uncertain time-delay T-S fuzzy systems subject to actuator saturation is discussed, and the state feedback gain that maximizes the domain of attraction is designed.In chapter 5, a problem of determing stability domain of time-delay T-S fuzzy systems with input saturation is discussed. The stability domain may be enlarged by applying a fuzzy anti-windup compensator to the considered system. For T-S fuzzy systems with delayed state and saturating input, delay-independent and delay-dependent, stability conditions are correspondingly established using Lyapunov-Krasovskii approach. Finally, a numerical algorithm in the form of linear matrix inequalities is provided to compute an anti-windup gain in order to maximize an estimate of the domain of stability associated to it.In chapter 6, for a class of discrete-time T-S fuzzy systems subject to input saturation, a more general Lyapunov function, i.e, a new fuzzy Lyapunov function, is presented. A sufficient condition that ensures the stability of the origin of the system is derived, and the domain of attraction may be enlarged by applying a fuzzy anti-windup compensator to the considered system. This new method avoids being difficult to seek for a public positive matrix P satisfying all fuzzy rules of this system. Moreover, an iterative optimization algorithm for obtaining the anti-windup compensator gain is given.In chapter 7, fuzzy associative memories with perfect recall are constructed, and novel on-line learning algorithms adapting the weights of its interconnections based onmin-implication composition are incorporated into this neural network when the solution set of the fuzzy relation equation is non-empty. These weight matrices are actually the least solution matrix and all maximal solution matrices of the min-implication fuzzy relation equation, respectively. The complete solution set of min-implication fuzzy relation equation can be determined by the maximal solution set of this equation.Finally, some concluding remarks are given, and the future research works are pointed out.