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Stability and l 2 ‐gain of discrete‐time switched systems with unstable modes
Author(s) -
Wang ZiMing,
Wei Airong,
Zhao Xudong,
Li Fan
Publication year - 2019
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.4778
Subject(s) - dwell time , control theory (sociology) , discrete time and continuous time , stability (learning theory) , lyapunov function , mathematics , exponential stability , high gain antenna , computer science , control (management) , physics , nonlinear system , medicine , clinical psychology , statistics , quantum mechanics , artificial intelligence , machine learning , optics
Summary 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 systems with 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.