Reliable And Finite-time Variable Structure Control For Singular Time-delay System

Singular time-delay systems have a wide range of applications in the objective world,they are found in practical areas such as power control,chemical process,aerospace industry,ocean exploration and economic control.With the development of modern control theory and technology,researchers have more and more in-depth explorations for singular time-delay system,from continuous-time singular time-delay system to discrete-time singular time-delay system,from constant delay to time-varying delay.Many kinds of control meth-ods have been adopted such as finite-time control and variable structure control.They have achieved fruitful results.By changing the system structure,the system performance can reach the expected requirements.The variable structure control has attracted increasing-ly attention from researchers as its high efficiency and practicability.Finite-time control problems focus on transient performance of the system.Fault-tolerant control can improve the security and reliability of the system significantly.Therefore,it is of certain practical significance and theoretical value to investigate finite-time variable structure control and fault-tolerant control for singular time-delay system.This paper mainly explore the problems of finite-time sliding-mode control for singu-lar time-delay system,and taken the faults in to consideration.By designing the proper switching function and sliding-mode controller,constructing the Lyapunov function,using the linear matrix inequality and convex optimization methods,we can realize the finite-time control and fault-tolerant control for singular time-delay system.The main contents of this paper are as follows:Firstly,the study of finite-time bounded is considered for continuous singular system with time-varying delay.By using the integral switching function,the corresponding sliding-mode controller can be obtained to make sure the system state trajectories are driven into the sliding surface in a short time interval.The sufficient conditions of finite-time bounded are given for the system in both reaching phase and sliding motion phase.The unknown parameters and the gain matrix of controller can be solved through the linear matrix inequality method.Secondly,the problem of finite-time sliding-mode control is investigated for singular Markov jump system with actuator fault;including singular stochastic finite-time bounded and singular stochastic_?finite-time bounded.The transition rates are partly known,with delay-dependent Lyapunov function and weak infinitesimal generator,sufficient criteria of stochastic finite-time stability are obtained for the system in the sense of expectation.Finally,the study of finite-time sliding-mode control is extended to discrete-time sin-gular Markov jump system with time-varying delay and sensor failure.By designing the discrete-time sliding-mode controller and novel Lyapunov function,using differential in-equalities,sufficient criteria have been obtained under the equivalent control law that the system is singular stochastic_?finite-time bounded.The controller gain matrices and_?performance are provided by using the linear matrix inequality approach.