Finite-time Control For A Class Of Nonlinear Systems

In the study of control theory, people often focus on the Lyapunov stability theory, while in practical engineering applications, especially for those systems which operates transient and response quickly, the usual Lyapunov stability theory can not achieve the desired control performance, sometimes the external disturbances and uncertainties may lead to some bad results, such as overshot is too large or reaction is too slow, therefore it is particularly important to study the finite-time stability theory at times. This paper is based on the concept of finite-time stability, combining with the Lyapunov-Krasovskii function and linear matrix inequalities (LMIs) , the finite-time control of nonlinear systems described by the T-S fuzzy model is studied, and some new theoretical results are obtained. This topic includes the followings:1) The basic theories are reviewed. The background of this study is presented, and the course of development and research status of T-S fuzzy model and finite-time control theory are recalled; the basic theory on T-S fuzzy model, finite-time stability, finite-time boundedness as well as the linear matrix inequalities and some common key lemma are introduced.2) The finite-time stabilization problem of the nonlinear systems described by T-S fuzzy model is studied. Respectively, for the general situation and uncertain case with time-delay, the finite-time stabilization problems of the fuzzy nonlinear systems are studied.3) The finite-time H∞control of nonlinear systems described by T-S fuzzy model is studied, and respectively for the uncertain system with stationary and time-varying time-delay, the design of the H∞filter is given.4) Based on the above study, for the fuzzy Markov jump uncertain system, the finite-time control is studied, and the design of the stabilization controller via state feedback is given.