Observer-based L2 gain control for switched linear systems with time-delay in detection of switching signal

Using average dwell time approach, this paper investigates the observer-based L₂ gain control problem of switched linear systems with time-delay in detection of switching signal. The feedback mechanism considered is off-line type. First, estimates on the generalized matrix norm and the state transition matrix are established, respectively (Lemmas 2-3 in Section 2). Then, based on these estimations, under the assumption that each subsystem is controllable and observable, we prove that there exists an observer-based switched state feedback controller such that the corresponding closed-loop switched system has an L₂ gain less than gamma for any switching signal with average dwell time greater than a given constant. Finally, an example is given to illustrate our results.