Fault Tolerant Control for Singularly Perturbed Systems with Multiple Delays and Uncertainty

This paper studies the fault tolerant control problem of uncertain singularly perturbed systems with time-delay in both the control input and the state vector. Based on the Lyapunov stability theory and the relevant lemmas, the minimum upper bound of the performance index of the closed-loop system is obtained by using the free weight matrix, the piecewise analysis of the system with multiple-delay and the LMI method. According to the quadratic performance index of the system, the corresponding Lyapunov functional is constructed so that the sufficient criterion for satisfying the time-delay correlation is obtained. Finally, this paper gives a fault tolerant controller design scheme which satisfies the given conditions. In the last part of this paper, a numerical example is given to demonstrate the feasibility of the proposed method.