H∞ integrated fault estimation and fault tolerant control of discrete-time piecewise linear systems

In this paper we consider the problem of fault estimation and accommodation for discrete time piecewise linear systems. A robust fault estimator is designed to estimate the fault such that the estimation error converges to zero and H_∞ performance of the fault estimation is minimized. Then, the estimate of fault is used to compensate for the effect of the fault. Hence, using the estimate of fault, a fault tolerant controller using a piecewise linear static output feedback is designed such that it stabilizes the system and provides an upper bound on the H_∞ performance of the faulty system. Sufficient conditions for the existence of robust fault estimator and fault tolerant controller are derived in terms of linear matrix inequalities. Upper bounds on the H_∞ performance can be minimized by solving convex optimization problems with linear matrix inequality constraints. The efficiency of the method is demonstrated by means of a numerical example.