Paper Info
Title
Input-to-state stability of impulsive and switching hybrid systems with time-delay
Abstract
This paper investigates input-to-state stability (ISS) and integral input-to-state stability (iISS) of impulsive and switching hybrid systems with time-delay, using the method of multiple Lyapunov-Krasovskii functionals. It is shown that, even if all the subsystems governing the continuous dynamics, in the absence of impulses, are not ISS/iISS, impulses can successfully stabilize the system in the ISS/iISS sense, provided that there are no overly long intervals between impulses, i.e., the impulsive and switching signal satisfies a dwell-time upper bound condition. Moreover, these impulsive ISS/iISS stabilization results can be applied to systems with arbitrarily large time-delays. Conversely, in the case when all the subsystems governing the continuous dynamics are ISS/iISS in the absence of impulses, the ISS/iISS properties can be retained if the impulses and switching do not occur too frequently, i.e., the impulsive and switching signal satisfies a dwell-time lower bound condition. Several illustrative examples are presented, with their numerical simulations, to demonstrate the main results.
Year
DOI
Venue
2011
10.1016/j.automatica.2011.01.061
Automatica
Keywords
Field
DocType
Hybrid system,Impulsive system,Switched system,Time-delay system,Multiple Lyapunov–Krasovskii functionals,Impulsive stabilization,Input-to-state stability (ISS),Integral input-to-state stability (iISS)
Lyapunov function,Switching signal,Control theory,Upper and lower bounds,Pulse response,Stopping time,Hybrid system,Arbitrarily large,Mathematics
Journal
Volume
Issue
ISSN
47
5
Automatica
Citations 
PageRank 
References 
85
2.95
16
Authors
3
Name
Order
Citations
PageRank
Jun Liu121520.63
Xinzhi Liu21318106.23
Wei-Chau Xie327612.07