Stability Analysis of Switched Systems under Φ-Dependent Average Dwell Time Approach

Abstract

The concept of the Φ-dependent average dwell time (Φ DADT) is presented for both continuous-time and discrete-time switched systems. Some new stability criteria for switched systems are obtained under the Φ DADT approach, which depends on the choice of the classification function Φ. The relationships among the classic ADT approach, the mode-dependent ADT approach and the proposed one are also discussed, which shows that those existing approaches can be unified to the new one. More concretely, stability results based on ADT/MDADT schemes can be regarded as some special cases of our results with specific functions Φ. The obtained switching design by the new approach is more flexible and practical. At last, a numerical example with some comparisons among the differences in the selection of Φ is included to explain the validity and advantages of the new technique.