Lyapunov small-gain theorems for networks of not necessarily ISS hybrid systems

Andrii Mironchenko; Guosong Yang; Daniel Liberzon

doi:10.1016/j.automatica.2017.10.020

Lyapunov small-gain theorems for networks of not necessarily ISS hybrid systems

Andrii Mironchenko
, Guosong Yang
, Daniel Liberzon

Research output: Contribution to journal › Article › peer-review

Abstract

We prove a novel Lyapunov-based small-gain theorem for networks composed of n≥2 hybrid subsystems which are not necessarily input-to-state stable. This result unifies and extends several small-gain theorems for hybrid and impulsive systems proposed in the last few years. We also show how average dwell-time (ADT) clocks and reverse ADT clocks can be used to modify the ISS Lyapunov functions for subsystems and to enlarge the applicability of the derived small-gain theorems.

Original language	English (US)
Pages (from-to)	10-20
Number of pages	11
Journal	Automatica
Volume	88
DOIs	https://doi.org/10.1016/j.automatica.2017.10.020
State	Published - Feb 2018

Keywords

Hybrid systems
Input-to-state stability
Small-gain theorems

ASJC Scopus subject areas

Control and Systems Engineering
Electrical and Electronic Engineering

Online availability

10.1016/j.automatica.2017.10.020

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title = "Lyapunov small-gain theorems for networks of not necessarily ISS hybrid systems",

abstract = "We prove a novel Lyapunov-based small-gain theorem for networks composed of n≥2 hybrid subsystems which are not necessarily input-to-state stable. This result unifies and extends several small-gain theorems for hybrid and impulsive systems proposed in the last few years. We also show how average dwell-time (ADT) clocks and reverse ADT clocks can be used to modify the ISS Lyapunov functions for subsystems and to enlarge the applicability of the derived small-gain theorems.",

keywords = "Hybrid systems, Input-to-state stability, Small-gain theorems",

author = "Andrii Mironchenko and Guosong Yang and Daniel Liberzon",

note = "The work of A. Mironchenko was supported by the German Research Foundation (DFG) grant Wi 1458/13-1 . The work of G. Yang and D. Liberzon was supported by the NSF grants CNS-1217811 and ECCS-1231196 . The material in this paper was partially presented at the 21st International Symposium on Mathematical Theory of Networks and Systems, July 7\textbackslash{}u201311, 2014, Groningen, Netherlands. This paper was recommended for publication in revised form by Associate Editor Ricardo Sanfelice under the direction of Editor Christos G. Cassandras.",

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doi = "10.1016/j.automatica.2017.10.020",

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AU - Yang, Guosong

AU - Liberzon, Daniel

N1 - The work of A. Mironchenko was supported by the German Research Foundation (DFG) grant Wi 1458/13-1 . The work of G. Yang and D. Liberzon was supported by the NSF grants CNS-1217811 and ECCS-1231196 . The material in this paper was partially presented at the 21st International Symposium on Mathematical Theory of Networks and Systems, July 7\u201311, 2014, Groningen, Netherlands. This paper was recommended for publication in revised form by Associate Editor Ricardo Sanfelice under the direction of Editor Christos G. Cassandras.

PY - 2018/2

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N2 - We prove a novel Lyapunov-based small-gain theorem for networks composed of n≥2 hybrid subsystems which are not necessarily input-to-state stable. This result unifies and extends several small-gain theorems for hybrid and impulsive systems proposed in the last few years. We also show how average dwell-time (ADT) clocks and reverse ADT clocks can be used to modify the ISS Lyapunov functions for subsystems and to enlarge the applicability of the derived small-gain theorems.

AB - We prove a novel Lyapunov-based small-gain theorem for networks composed of n≥2 hybrid subsystems which are not necessarily input-to-state stable. This result unifies and extends several small-gain theorems for hybrid and impulsive systems proposed in the last few years. We also show how average dwell-time (ADT) clocks and reverse ADT clocks can be used to modify the ISS Lyapunov functions for subsystems and to enlarge the applicability of the derived small-gain theorems.

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KW - Input-to-state stability

KW - Small-gain theorems

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JO - Automatica

JF - Automatica

ER -

Lyapunov small-gain theorems for networks of not necessarily ISS hybrid systems

Abstract

Keywords

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