Optimal fault diagnosis for systems with time-delay based on Lyapunov functional

Facing to the time-delay systems with actuator faults and sensor faults whose dynamic characteristics are known but the initial states and the initial times are unknown, the approach of fault diagnosis is studied. A kind of design scheme of fault diagnoser is proposed based on duality principle and Lyapunov functional. Firstly, the design problem of the observer for fault diagnosis is translated into the state feedback problem of optimal control by duality principle. Then the optimal fault diagnoser is designed to diagnose the fault and to cater the quadratic performance index, and the stability of the optimal fault diagnoser is proven by Lyapunov functional. Finally, a numerical example is given. Simulation results show the feasibility and validity of the proposed scheme.