Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 68, Issue 10, Pages 6409-6416Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2023.3237492
Keywords
Switches; Switched systems; Stability analysis; Lyapunov methods; Asymptotic stability; Trajectory; Sufficient conditions; Contraction analysis; switched systems; mode-dependent average dwell time; stability analysis
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This article studies the contraction analysis of switched systems composed of contracting and noncontracting modes. It establishes the equivalence between the contraction of a switched system and the uniform global exponential stability of its variational system. Based on this equivalence, it provides sufficient conditions for a mode-dependent average dwell/leave-time based switching law to be contractive. Additionally, it derives linear matrix inequality (LMI) conditions to numerically validate the contraction property of nonlinear switched systems, including those with all noncontracting modes.
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.
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