Optimal Fault-tolerant Control For Time-varying Descriptor Systems

Descriptor system,also known as generalized state space system,singular system or differential algebraic system,can more accurately describe many real dynamic systems.With the development of research and the need for reality,the research of descriptor time-varying system theory has been paid more attention.In the actual control systems,there are usually a series of unavoidable problems,therefore,fault tolerant control is very important for the system.The problem of fault-tolerant control is investigated for a class of parameters uncertain time-varying descriptor systems with nonlinear time-varying perturbation,especially,when the system is in fault.First,the nonlinear perturbation in the system is linearized under the assumption that the perturbation satisfies the Lipschitz condition.Then,a fault model is established for the faults in the system,and sufficient conditions for generalized quadratic stability and robust stability of the system are determined by constructing a Lyapunov equation.Finally,a state-feedback fault-tolerant controller is obtained under the condition of stability of the system.In this way,a fault-tolerant control is achieved for the fault system.This dissertation also investigates the problem of optimal fault-tolerant control for a class of descriptor time-varying systems with nonlinear input.Based on the Lyapunov stability theorem,the sufficient conditions of the stability are obtained when the system is normal and ineffective.Furthermore,the fault-tolerant control of the systems are carried out in two cases,and the state feedback fault-tolerant controller is obtained to satisfy the quadratic performance index and reach the minimum value in order to achieve the optimal fault-tolerant control.