Fault Tolerant Control for Uncertain Time-Delay Systems with a Trajectory Tracking Approach

This paper studies the problem of fault tolerant control by trajectory tracking for a class of linear constant time-delay systems. The aim is to design a control law by considering the fault detected by the observer to make the faulty system track the reference model even if faults occur. By considering two kinds of actuator faults, one constant and another time-varying, the corresponding proportional integral observers and active FTC control laws are designed, respectively. State tracking error, state estimation error, output estimation error, and fault estimation error are combined into a descriptor system. Based on Lyapunov-Krasovskii functional approach stability problems of the descriptor system are easily solved in terms of the Linear Matrix Inequalities (LMI). Finally, a numerical example is considered to prove the effectiveness in both cases.