A Matrosov Theorem for Hybrid Systems With Memory

In this article, stability problems are investigated for hybrid systems with memory, which are developed to model hybrid systems affected by time delays. A nested Matrosov functional theorem is proposed to guarantee uniform asymptotic stability for time-varying hybrid systems with memory. Specifical...

Full description

Saved in:
Bibliographic Details
Published in:IEEE transactions on automatic control 2021-10, Vol.66 (10), p.4918-4925
Main Authors: Liu, Kun-Zhi, Wang, Xue-Fang, Teel, Andrew R., Sun, Xi-Ming, Liu, Jun
Format: Article
Language:English
Subjects:
Asymptotic properties
Asymptotic stability
Delay systems
Delays
Hybrid systems
Lyapunov methods
Matrosov's theorem
Stability
Stability criteria
System effectiveness
Theorems
Time-domain analysis
Time-varying systems
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this article, stability problems are investigated for hybrid systems with memory, which are developed to model hybrid systems affected by time delays. A nested Matrosov functional theorem is proposed to guarantee uniform asymptotic stability for time-varying hybrid systems with memory. Specifically, with a weak Lyapunov functional whose derivative in the flow set and whose difference in the jump set are negative semidefinite, if there exist some Matrosov functionals that satisfy nested conditions, uniform asymptotic stability can be asserted. The proposed result benefits from the concept of generalized solutions developed for hybrid systems with memory. Finally, an example is given to show the effectiveness of the result.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2020.3042482