Piecewise structure of Lyapunov functions and densely checked decrease conditions for hybrid systems

We propose a class of locally Lipschitz functions with piecewise structure for use as Lyapunov functions for hybrid dynamical systems. Subject to some regularity of the dynamics, we show that Lyapunov inequalities can be checked only on a dense set and thus we avoid checking them at points of nondif...

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Published inMathematics of control, signals, and systems Vol. 33; no. 1; pp. 123 - 149
Main Authors Della Rossa, Matteo, Goebel, Rafal, Tanwani, Aneel, Zaccarian, Luca
Format Journal Article
LanguageEnglish
Published London Springer London 01.03.2021
Springer Nature B.V
Springer Verlag
Subjects
Automatic
Communications Engineering
Control
Dynamical Systems
Engineering Sciences
Hybrid systems
Liapunov functions
Mathematics
Mathematics and Statistics
Mechatronics
Networks
Original Article
Robotics
Systems Theory
Hybrid systems
Densely checked conditions
Lyapunov analysis
Piecewise differentiable functions
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Summary:We propose a class of locally Lipschitz functions with piecewise structure for use as Lyapunov functions for hybrid dynamical systems. Subject to some regularity of the dynamics, we show that Lyapunov inequalities can be checked only on a dense set and thus we avoid checking them at points of nondifferentiability of the Lyapunov function. Connections to other classes of locally Lipschitz or piecewise regular functions are also discussed, and applications to hybrid dynamical systems are included.
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ISSN:0932-4194
1435-568X
DOI:10.1007/s00498-020-00273-9