Stabilizability of Time-Varying Switched Systems Based on Piecewise Continuous Scalar Functions

Inspired by the idea of multiple Lyapunov functions (\mathtt {MLFs}), we use piecewise continuous scalar functions to investigate the stabilizability of time-varying switched systems. Starting with time-varying switched linear systems, we first combine the idea of \mathtt {MLFs} with the existence o...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2019-06, Vol.64 (6), p.2637-2644
Main Authors: Lu, Junjie, She, Zhikun, Feng, Weijie, Ge, Shuzhi Sam
Format: Article
Language:English
Subjects:
Asymptotic properties
Asymptotic stability
Continuity (mathematics)
Liapunov functions
Linear systems
Nonlinear systems
Piecewise continuous scalar functions
Stability analysis
stabilizability
Switched systems
Switches
time-varying systems
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Summary:Inspired by the idea of multiple Lyapunov functions (\mathtt {MLFs}), we use piecewise continuous scalar functions to investigate the stabilizability of time-varying switched systems. Starting with time-varying switched linear systems, we first combine the idea of \mathtt {MLFs} with the existence of asymptotically (exponentially, uniformly exponentially) stable functions to provide necessary and sufficient conditions for their asymptotic (exponential, uniform exponential) stabilizability. Compared to traditional differential Lyapunov inequalities, we release the requirement on negative definiteness of the derivatives of \mathtt {MLFs}. Successively, the above results are extended to time-varying switched nonlinear systems. Then, two illustrative examples are given to show the applicability of our theoretical results. In the end, we consider the computation issue of our current results for a special class of nonautonomous switched systems, i.e., rational nonautonomous switched systems.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2018.2867933