Lyapunov small-gain theorems for not necessarily ISS hybrid systems

Title data

Mironchenko, Andrii ; Yang, Guosong ; Liberzon, Daniel:
Lyapunov small-gain theorems for not necessarily ISS hybrid systems.
In: Proceedings of 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014). - Groningen, The Netherlands : University of Groningen Press , 2014 . - pp. 1001-1008
ISBN 978-90-367-6321-9

Official URL:

Abstract in another language

We prove a novel Lyapunov-based small-gain theorem for interconnections of n hybrid systems, 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. Also we show how the average dwell-time (ADT) clocks and reverse ADT clocks can be used to modify the Lyapunov functions for subsystems and to enlarge the applicability of derived small-gain theorems.

Further data

Item Type:	Article in a book
Refereed:	Yes
Keywords:	dwell-time; hybrid systems; impulsive systems; ISS; Lyapunov methods
Subject classification:	Mathematics Subject Classification Code: 34A38 93D09 93D05
Institutions of the University:	Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) Profile Fields > Advanced Fields > Nonlinear Dynamics
Result of work at the UBT:	No
DDC Subjects:	500 Science > 510 Mathematics
Date Deposited:	11 Mar 2025 09:58
Last Modified:	11 Mar 2025 09:58
URI:	https://eref.uni-bayreuth.de/id/eprint/92716