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

Abstract

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.