Observer Design And Fault-tolerant Control For Singular Bilinear Systems

Singular bilinear system is a kind of singular nonlinear system which is most close to the singular linear system, and singular bilinear system models widely exist in the practical lives. Hence researching on singular bilinear system is of great theoretical significance and practical application importance. So far, the studying for singular bilinear system theory is still on the initial and developmental stage, the results of research for singular bilinear system with delays and uncertainties are stills less.This paper focuses on the problems of state observation and observer-based fault-tolerant control for singular bilinear system. The main contents are summarized as follows:1. The singular state observer for singular bilinear system is designed and the sufficient conditions of existence of the singular state observer are given by the theory of Lyapunov stabilization. Two methods for devising the observer gain matrix L are proposed. One method obtains the matrix L by pole's configuration, and the other method uses a change of variable on the control inputs and LMI technology.2. The singular state observer is designed for time-delay singular bilinear system and the sufficient conditions are gained to verify for existence of the singular state observer based on Lyapunov-Krasovskii function and LMI method. The singular state observer is designed for time-delay stochastic singular bilinear system which its stochastic disturbance is a standard wiener process. Criterion for error system being mean-square stable is presented in terms of Lyapunov-Krasovskii function, It o formula and LMI method.3. The problem of robust H∞state estimation is discussed for time-delay singular bilinear system with uncertainties. Delay-dependent singular state observer and delay-independent singular state observer are designed for singular bilinear system with time-delays and allowable parameter uncertainties. The results obtained involve two singular algebraic Riccati inequalities. 4. The problem of fault-tolerant control for time-delay singular bilinear system is studied. As actuator failures exist in system, a method of designing observer-based feedback controller against actuator failures is presented in terms of generalized algebraic Riccati inequations; As sensor failures exist in system, based on singular algebraic Riccati inequalities and H∞control theory, the observer-based integrity controller designed can guarantee the resultant closed-loop system as well as in the event of sensor failures are admissible and keep certain H∞norm performance in the normal condition.