Observer-based Scheme for Fault Estimation and Robust Tolerant Control: An LMI Approach

In this paper, we investigate the problem of fault estimation and robust fault tolerant control for a class of discrete time piecewise systems. Firstly, a robust fault estimation observer is employed to estimate the fault, such that the estimation error system is asymptotically stable with a prescribed attenuation level and robust performance of the fault estimation is minimized. Then, according to the estimate of fault, the piecewise static output feedback fault tolerant controller is proposed, such that it stabilizes the closed-loop system and provides an upper bound on the robust performance of the faulty system. Sufficient conditions for the existence of robust fault estimation observer and fault tolerant controller are derived in terms of linear matrix inequalities (LMIs), which can be solved using the convex optimization techniques. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach.