Stability And Fault-tolerant Control For Time-varying Descriptor Systems

The model of descriptor system has been widely used in electric power, petroleum,chemical industry, aviation, aerospace, nuclear energy, robot and other fields. With thedeeply research and the need of practical engineer problems, the scholars have transfertheir attention from traditional descriptor system to the time-varying descriptor system.This paper searched the stability and the fault-tolerant control for time-varying descriptorsystem which is extension from the time-invariant system to time-varying descriptorsystem.For the stability of the time-varying descriptor system, the paper discusses theproblem of stabilizability and stabilization. First of all, referring to the research statementof time-varying descriptor system, we do the extension to the stabilizability. The necessaryand sufficient conditions for stable are given using the theory of Lyapunov function andsolving Riccati equation. Then, in view of the problem of stabilization, the necessary andsufficient conditions of robust stabilization for a class of time-varying descriptor systemare obtained, and the normal from of the state feedback controller are described.It provides the theoretical basis for future research.For the robust fault-tolerant control of time-varying descriptor systems, this papermainly used the Lyapunov theory and LMI method. When there is no actuator failure, thepaper gives the necessary and sufficient condition for the robust stability of time-varyingdescriptor systems. When the actuator failure occurs, we discuss the problem from twoaspects when the state vector can be directly observed and state vector can not be totallyobserved. The dynamic observer is designed to gain the sufficient conditions for the robuststabilization. When the external interference occur, a sufficient condition for thestabilization is put out. In addition, this paper gives the measure for handling thetime-varying matrix which has the far value research.