The Guaranteed Cost Tolerant Control For Nonlinear Uncertain Switched Singular Systems With Time-Delay

The control system is affected by malfunctions caused by actuators,sensors and its own.To study the fault-tolerant system further,the idea of guaranteed cost fault-tolerant control is introduced,based on the original theory of control system.The basic idea of guaranteed cost-based fault-tolerant control is to design a state feedback controller for the system so that the closed-loop system is asymptotically stable and its performance index does not exceed a certain upper bound for all admissible uncertainties.This paper focuses on the design of fault-tolerant guaranteed cost controller for a class of nonlinear uncertain time-delay systems.The main contents are summarized as follows:(1)The research background and research actuality of the singular switched system,the research actuality of fault-tolerant control and guaranteed cost control and the theory of H_∞ fault-tolerant control are introduced.It is significant to study the guaranteed cost fault-tolerant control problem of nonlinear uncertain singular switched systems with time-delay.Secondly,some basic concepts of the singular switched systems,Lyapunov stability theory and linear matrix inequalities are introduced,and some lemmas are also discussed in this paper.(2)A class of nonlinear uncertain guaranteed cost fault tolerant control problems of singular switched systems,taking the situation with both state and input delays into account.When the actuator of the system fails,the problem of guaranteed cost fault-tolerant control of the system under the action of a specific switching rule is discussed.By means of Lyapunov function theory,LMIs method and convex combination technique,the sufficient conditions for closed-loop system to be asymptotically stable under the designed switching rule and upper bound of system performance index is given.The method of controller design is also given.By using the LMIs toolbox of Matlab,the numerical examples are programmed and the results are obtained,which verifies the feasibility of the method.(3)The guaranteed cost fault-tolerant control problem for a class of nonlinear uncertain singular switched systems with state delay is investigated.The sufficient conditions for the closed-loop system to be asymptotically stable with upper bound are given under arbitrary switching rules.Controller design method is also given.Finally,a numerical example is given and the feasibility of the method is verified by using LMI toolbox in Matlab.(4)The problem of guaranteed cost fault-tolerant control for a class of singular switched systems with time-varying delay is investigated.The system with time-varying delays in state is considered.The system with time-varying delays in state and input is also considered.The Lyapunov function theory and LMI technique are used to obtain the asymptotic stability of the closed-loop system under the condition of actuator failure.And a sufficient condition for the level γ of H_∞ interference suppression is given,and the method of controller design is given.Finally,a numerical example is given to demonstrate the feasibility of the method.