Finite-Time Stability Analysis And Controller Design Of Nonlinear Systems Based On LMI Theory

It is well known that most of the existing results related to system stability focus on Lyapunov asymptotic stability,which is defined in infinite time interval.Therefore,it describes the steady-state performance of the system,but it cannot represent the transient behavior of the system.In some practical applications,the transient behavior is required,but the asymptotic stability of the system does not satisfy the demand.In the 1950s,Peter Dorato,a professor of the University of New Mexico,introduced the concept of short-time stability,original the concept of finite-time stability,and discussed the system behavior in a fixed time interval.Subsequently,it attracted more and more attention and was applied in many fields,such as network communication,robot control and ATM network control and so on.This paper mainly discusses the finite-time stability and the controller design of nonlinear systems.In Chapter 1,we introduced the background of this article,the structure of the thesis and some important lemmas of this paper.In Chapter 2,by constructing an appropriated multiple Lyapunov-Krasovskii functional,employing ADT method,and free-weighting matrix method,some sufficient conditions are derived to guar-antee the finite-time stability of the addressed uncertain switched delayed neu-ral networks of neutral type.Meanwhile,the finite-time stabilization conditions are proposed for the concerned neural networks via designing the state feedback controller.Finally,two examples with its simulation are proposed to show the effectiveness of our proposed theoretical results.In Chapter 3,by constructing Lyapunov-Krasovskii functional and employing Cauchy matrix inequality and sin-gular analysis technique used in the recent literature,some new sufficient condition-s for finite-time stability have been derived in terms of linear matrix inequalities(LMIs).In addition,the controller for nonlinear system is designed and then some sufficient conditions of the finite-time stabilization are obtained.Finally,two ex-amples with its numerical simulation were provided to show the effectiveness of the proposed method.