Stabilisability of switched linear systems with time-varying delay in the detection of switching signals

Exponential stabilisability of switched linear systems with time-varying delay in the detection of switching signals is investigated via state feedback by average dwell time approach incorporated with multiple Lyapunov function techniques. The feedback mechanism considered is of off-line type. Sufficient conditions for exponential stabilisability are established for three cases: some subsystems are stabilisable, all subsystems are stabilisable and all subsystems are controllable. Our results complement and generalise the results of Xie and Wang (2005) and Ji et al. (2007).