Design of Adaptive Observer for Time-Varying Delay System Based on Delay-Dependent Stability and H Infinity Tracking Performance

Based on the adaptive observer, this paper is concerned with the problem of robust fault identification for system whose time-varying delay is in a range. Not only can this adaptive observer estimate system state, but also does it identify the fault. The H_infin tracking performance criteria is proposed to analyse the design methods and stable conditions of adaptive observer, which is then transformed to the optimal problem restrict by linear matrix inequalities (LMIs). A method is used to estimate the upper bound of the derivative of Lyapunov functional without ignoring some useful terms and the introduction of additional terms into the proposed Lyapunov functional, which take into account the range of delay. A numerical example is given to demonstrate the effectiveness and the benefits of the proposed method.