Robust simultaneous finite-time control and fault detection for uncertain linear switched systems with time-varying delay

This study deals with the problem of simultaneous finite-time control and fault detection for linear switched systems with state delay and parameter uncertainties. Delay is assumed to vary in an interval with a nonzero lower bound and specified range. Uncertainties are norm-bounded time-varying and exist in the matrix of the system. Based on average dwell time approach and using delay-dependent method, new sufficient conditions are given in terms of linear matrix inequalities to design a controller/detector unit. The detector is an observer and the controller is an observer-based controller. This problem is formulated as finite-time H optimisation problem and both finite-time stability and fault detection are considered through certain performance indexes. The effectiveness of the proposed method is verified by a numerical example.