Analysis, Control And Filter Design Of Time - Delay Dynamic System

In natural science and social science,time delay often appears and it is the main reason of instability and oscillation. As a result, the study of time-delay dynamic systems has been gained considerable attention. For the stability analysis and synthesis of time-delay dynamic systems, Lyapunov functional method has been one of the powerful tools. Because this method is simple and clear and can be used to obtain tractable linear matrix inequality(LMI) conditions, it has received widespread application. Based on the current research findings for time-delay dynamic systems, this thesis will utilize Lyapunov stability theory, complete Lyapunov functional method, fuzzy line-integral Lyapunov functional approach and various inequalities to systematically investigate the stability analysis and synthesis problem of several classes of time-delay dynamic systems, and develop new delay-dependent stability criteria, control design scheme and filter design scheme. The main results of this thesis are as follows:1. The problems of stability analysis and stabilization of linear time-delay systems are studied. In the stability analysis, first, via complete Lyapunov functional and the recently developed reciprocally convex inequality, new delay-dependent stability criteria are provided. Then, by constructing new augmented complete Lyapunov functional, introducing appropriate integral terms to give more freedom in choosing matrix variables, and applying the inequalities technique, new less conservative stability criteria are further derived. Based on the criteria, the state feedback controller is designed. The obtained result is applicable for systems that are stabilizable with delay in an interval but unstabilizable outside the interval. Compared with the existing results, the advantages of the obtained stability and stabilization criteria lie in less conservatism and wider application.2. The problems of the stability analysis and control design of T-S fuzzy systems with time delay are investigated. First, for a T-S fuzzy system with constant delay, by choosing the fuzzy line-integral Lyapunov functional and using a recently developed Wirtinger-based integral inequality, less conservative conditions in terms of LMIs are derived, then an effective state feedback controller is developed. The proposed design scheme is less complex. Next, for T-S fuzzy systems with input time-varying delay, by combining Lyapunov functional method and the reciprocally convex inequality, new less conservative conditions for the existence of the dynamic output feedback H∞ controllers are given. The obtained control design scheme involves less decision variables and serves a wider class of systems than the existing results.3. For two classes of time-delay dynamic systems, the problems of H∞ filtering design are considered. First, for nonlinear systems with time-varying delay through T-S fuzzy models, by constructing new augmented fuzzy line-integral Lyapunov functional and the reciprocally convex inequality, a new sufficient condition for the existence of the fuzzy H∞ filter design is established. Next, for nonlinear interconnected systems with time-varying delay through T-S fuzzy models, based on the same approaches, a delay-dependent decentralized H∞ filter is designed by guaranteeing the asymptotic stability and a prescribed H∞ performance index for the overall filter error system. A new sufficient condition for the existence of such a filter is established. For two classes of systems, the proposed methods can produce better H∞ performance index and involve less decision variables than the existing ones in the literature.4. The stability problem for delayed complex-valued recurrent neural networks is investigated. In the stability analysis, the assumptions of the complex-valued activation functions are relaxed. Then by separating complex-valued neural networks into real and imaginary parts, forming an equivalent real-valued system, constructing appropriate Lyapunov functional and applying homeomorphism theory, a sufficient condition to ascertain the existence, uniqueness, and globally asymptotical stability of the equilibrium point of complex-valued systems is provided in terms of LMI. Moreover, the obtained result not only improves but also generalizes the existing ones.