Title of Paper:Stability and l(2)-gain of discrete-time switched systems with unstable modes

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Date of Publication:2020-01-25

Journal:INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL

Included Journals:EI、SCIE

Volume:30

Issue:2

Page Number:567-586

ISSN No.:1049-8923

Key Words:multiple discontinuous Lyapunov functions; slow/fast mode-dependent average dwell time; stability; switched system; l(2)-gain

Abstract:This paper addresses stability and l(2)-gain for discrete-time switched systems with unstable modes based on slow/fast mode-dependent average dwell time (MDADT) switching strategies. Firstly, by employing a class of multiple discontinuous Lyapunov functions (MDLFs) and developing a kind of alternative switching signals, the sufficient conditions on stability are established for the system without external disturbances under a slow/fast MDADT switching scheme with a tighter bounds on the dwell time. Furthermore, by defining indicator functions and exploring the features of slow/fast MDADT switching, the weighted l(2)-gain conditions are achieved for the system with external disturbances. Particularly, the criteria of stability and l(2)-gain are also established for the corresponding discrete-time switched linear systemswith unstable modes via the MDLFs method and the slow/fast MDADT switching strategy. Finally, two numerical examples are presented to illustrate the advantages of the proposed methods.