NDLI: Discovering multiple Lyapunov functions for switched hybrid systems with global exponential stability

Content Provider	IEEE Xplore Digital Library
Author	Lu, Junjie She, Zhikun Xue, Bai
Copyright Year	2015
Description	Author affiliation: Centre for High Performance Embedded Systems, Nanyang Technological University, Singapore (Xue, Bai) \|\| School of Mathematics and Systems Science, Beihang University, Beijing, China (Lu, Junjie) \|\| SKLSDE, LMIB and School of Mathematics and Systems Science, Beihang University, Beijing, China (She, Zhikun)
Abstract	We in this paper analyze the global exponential stability of switched hybrid systems, whose subsystems have polynomial vector fields, by discovering multiple Lyapunov functions in quadratic forms. We start with an algebraizable sufficient condition for the existence of quadratic multiple Lyapunov functions. Then, since different discrete modes are considered, we apply real root classification together with a projection operator to under-approximate this sufficient condition step by step, arriving at a set of semi-algebraic sets which only involve the coefficients of the pre-assumed multiple Lyapunov function. Afterwards, we compute a sample point in the corresponding semi-algebraic set for the coefficients, resulting in a multiple Lyapunov function. Finally, we test our approach on some examples using a prototypical implementation. These computation results show the applicability and promise of our approach. Especially, our present approach can further be extended for discovering multiple homogeneous Lyapunov functions of even degree.
Starting Page	4252
Ending Page	4259
File Size	195067
Page Count	8
File Format	PDF
e-ISBN	9781479978861
DOI	10.1109/CDC.2015.7402882
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-12-15
Publisher Place	Japan
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Switches Lyapunov methods Control theory Stability Asymptotic stability Switched systems Trajectory
Content Type	Text
Resource Type	Article

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