Delay-Dependent Stability Analysis And Control Of Nonlinear Time-Delay Systems

With development of science, technology and productivity, the controlled plants have been becoming so increasingly complex that there exist highly various nonlinear sections, uncertainties and time delay in practical systems. It has profound significance to investigate the stability analyse and synthesis problem of nonlinear time delay systems. However, there is until now no sufficient and efficient methods to solve this class of problems. Firstly, the stability analyse of qusi-nonlinear delay systems is considered. Based on linear delay systems, the relation of the system states, the delay states and the derivative of the delay, and their effect to the stability is considered, then delay-dependent stability problem is studied to result in less conservatism. As we know T-S fuzzy model is capable of approximating nonlinear system significantly, and being analyzed easily for us. T-S fuzzy control method has been the hotspots in the investigation of nonlinear systems. Since there are such advantages above, The way to the stability analyse and control problems of nonlinear time delay systems via T-S fuzzy model is effective. Secondly, the stability analyse of continuous T-S fuzzy system with time-vary delay is investigated. The effect resulting from system states, delay states and the derivative of delay to the stability are considered. By Leibniz-Newton formula, and some free matrices with appropriate dimension, a zero term is constructed, and used in the stability analyse. Consequently the term is useful to reduce the conservatism. As is indicated in the study, indicates, the limit to the derivative of delay can be canceled. Finally, a class of discrete T-S fuzzy uncertain systems with time delays are studied. Based on Lyapunov-Krasovskii(L-K) approach, the sufficient stability conditions are proposed, and then a fuzzy controller is designed via parallel distribute compensation technique as to stabilize the plant. The closed-loop system is asymptotically stable with the guaranteed cost performance. In addition, a generalized dynamic output feedback controller is introduced. With the controller, the closed-loop system is asymptotically stable with the guaranteed cost performance.