Conditions for the Stability of Switched Systems Containing Unstable Subsystems

This brief studies the stability of switched systems in which all the subsystems may be unstable. In addition, some of the switching behaviors of the systems are destabilizing. By using the piecewise Lyapunov function method and taking a tradeoff between the increasing scale and the decreasing scale...

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Bibliographic Details
Published in:IEEE transactions on circuits and systems. II, Express briefs Express briefs, 2019-04, Vol.66 (4), p.617-621
Main Authors: Wang, Yue-E, Karimi, Hamid Reza, Wu, Di
Format: Article
Language:English
Subjects:
Asymptotic stability
Circuit stability
destabilizing
Dwell time
Liapunov functions
Linear systems
Lyapunov function
Lyapunov methods
Nonlinear systems
Stability
Stability analysis
Subsystems
Switched nonlinear systems
Switched systems
Switches
Switching
unstable subsystems
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Summary:This brief studies the stability of switched systems in which all the subsystems may be unstable. In addition, some of the switching behaviors of the systems are destabilizing. By using the piecewise Lyapunov function method and taking a tradeoff between the increasing scale and the decreasing scale of the Lyapunov function at switching times, the maximum dwell time for admissible switching signals is obtained and the extended stability results for switched systems in a nonlinear setting are first derived. Then, based on the discretized Lyapunov function method, the switching stabilization problem for linear context is solved. By contrasting with the contributions available in the literature, we do not require that all the switching behaviors of the switching system under consideration are stabilizing. More specifically, even if all the subsystems governing the continuous dynamics are not stable and some of the switching behaviors are destabilizing, the stability of the switched system can still be retained. A numerical example is given to illustrate the validity of the proposed results.
ISSN:1549-7747
1558-3791
DOI:10.1109/TCSII.2018.2852766