New stability criteria of switched systems with unstable modes under a weighted ADT scheme

Two concepts of the weighted average dwell time (WADT) and the fast weighted average dwell time (FWADT) are introduced for continuous-time switched systems. The stability problems for a switched system with WADT and FWADT are investigated under a class of ergodic switching signals. The relationship between the ADT/mode-dependent ADT schemes and the WADT scheme is also discussed, which shows that the classic schemes are included in the new one under some conditions. The proposed switching law based on the (F)WADT scheme is more flexible and has a larger feasible region than the existing results. Finally, two numerical examples with some comparisons among several schemes are included to illustrate the validity and superiority of the developed techniques.