Abstract
This paper deals with the fault detection observer design problem for switched system with all modes unstable. First, the error system model is presented. With the consideration of the instability caused by the unobservable condition of , a switching signal is obtained via average dwell time method and discretised Lyapunov function. By means of linear matrix inequalities, sufficient conditions pledging exponential stability and performance are proposed. Through transferring the observer design problem into performance analysis, proper observer gain is obtained via solving these LMIs. In the end, the validity of the proposed Luenberger observer is verified by an example.
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