Fault-Tolerant Control for Markovian Jump Delay Systems with an Adaptive Observer Approach

This paper investigates the problem of fault estimation and fault-tolerant control for a class of Markovian jump systems with mode-dependent interval time-varying delay and Lipschitz nonlinearities. In this paper, a new adaptive fault observer is designed to solve the problem of fault estimation. The proposed observer can estimate the states and faults simultaneously, whether faults are of time-varying or constant characterization. Based on the fault estimation, a fault-tolerant controller is designed to stabilize the closed-loop system. Sufficient conditions for the existence of the observer gain and fault-tolerant controller gain are got by a set of linear matrix inequalities. Finally, a numerical example is presented to illustrate the effectiveness of the proposed fault-tolerant control method.