On Contraction Analysis of Switched Systems With Mixed Contracting-Noncontracting Modes via Mode-Dependent Average Dwell Time

This article studies contraction analysis of switched systems that are composed of a mixture of contracting and noncontracting modes. The first result pertains to the equivalence of the contraction of a switched system and the uniform global exponential stability of its variational system. Based on this equivalence property, sufficient conditions for a mode-dependent average dwell/leave-time based switching law to be contractive are established. Correspondingly, linear matrix inequality (LMI) conditions are derived that allow for numerical validation of contraction property of nonlinear switched systems, which include those with all noncontracting modes.