Analysis of different Lyapunov function constructions for interconnected hybrid systems

Guosong Yang; Daniel Liberzon; Andrii Mironchenko

doi:10.1109/CDC.2016.7798312

Analysis of different Lyapunov function constructions for interconnected hybrid systems

Guosong Yang, Daniel Liberzon, Andrii Mironchenko

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

This paper studies stability of interconnections of hybrid dynamical systems, in the general scenario that the continuous or discrete dynamics of subsystems may have destabilizing effects. We analyze two existing methods of constructing Lyapunov functions for the interconnection based on candidate ISS Lyapunov functions for subsystems, small-gain conditions, and auxiliary timers modeling restrictions on jump frequency in terms of average dwell-time and reverse average dwell-time. We compare their feasibility and limitations for different types of subsystem dynamics, and examine a case that the combination of them is needed to establish global asymptotic stability.

Original language	English (US)
Title of host publication	2016 IEEE 55th Conference on Decision and Control, CDC 2016
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	465-470
Number of pages	6
ISBN (Electronic)	9781509018376
DOIs	https://doi.org/10.1109/CDC.2016.7798312
State	Published - Dec 27 2016
Event	55th IEEE Conference on Decision and Control, CDC 2016 - Las Vegas, United States Duration: Dec 12 2016 → Dec 14 2016

Publication series

Name	2016 IEEE 55th Conference on Decision and Control, CDC 2016

Other

Other	55th IEEE Conference on Decision and Control, CDC 2016
Country/Territory	United States
City	Las Vegas
Period	12/12/16 → 12/14/16

ASJC Scopus subject areas

Artificial Intelligence
Decision Sciences (miscellaneous)
Control and Optimization

Online availability

10.1109/CDC.2016.7798312

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Yang, G., Liberzon, D., & Mironchenko, A. (2016). Analysis of different Lyapunov function constructions for interconnected hybrid systems. In 2016 IEEE 55th Conference on Decision and Control, CDC 2016 (pp. 465-470). Article 7798312 (2016 IEEE 55th Conference on Decision and Control, CDC 2016). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2016.7798312

Analysis of different Lyapunov function constructions for interconnected hybrid systems. / Yang, Guosong; Liberzon, Daniel; Mironchenko, Andrii.
2016 IEEE 55th Conference on Decision and Control, CDC 2016. Institute of Electrical and Electronics Engineers Inc., 2016. p. 465-470 7798312 (2016 IEEE 55th Conference on Decision and Control, CDC 2016).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Yang, G, Liberzon, D & Mironchenko, A 2016, Analysis of different Lyapunov function constructions for interconnected hybrid systems. in 2016 IEEE 55th Conference on Decision and Control, CDC 2016., 7798312, 2016 IEEE 55th Conference on Decision and Control, CDC 2016, Institute of Electrical and Electronics Engineers Inc., pp. 465-470, 55th IEEE Conference on Decision and Control, CDC 2016, Las Vegas, United States, 12/12/16. https://doi.org/10.1109/CDC.2016.7798312

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AB - This paper studies stability of interconnections of hybrid dynamical systems, in the general scenario that the continuous or discrete dynamics of subsystems may have destabilizing effects. We analyze two existing methods of constructing Lyapunov functions for the interconnection based on candidate ISS Lyapunov functions for subsystems, small-gain conditions, and auxiliary timers modeling restrictions on jump frequency in terms of average dwell-time and reverse average dwell-time. We compare their feasibility and limitations for different types of subsystem dynamics, and examine a case that the combination of them is needed to establish global asymptotic stability.

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Analysis of different Lyapunov function constructions for interconnected hybrid systems

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