Robust fault estimation and tolerant control for a class of discrete piecewise systems: An LMI approach

In this paper, we investigate the problem of fault estimation and tolerant control for a class of discrete piecewise systems. Firstly, a robust estimation observer is employed to estimate the fault, such that the corresponding estimation error system is asymptotically stable with a prescribed attenuation level as well as the robust performance of 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 fault estimation observer and tolerant controller are derived in terms of linear matrix inequalities (LMIs). Finally, a numerical example is given to demonstrate the effectiveness of our approach.