Construction of Time-Varying ISS-Lyapunov Functions for Impulsive Systems

Patrick  Bachmann; Saeed Ahmed

doi:10.1016/j.ifacol.2023.02.001

Construction of Time-Varying ISS-Lyapunov Functions for Impulsive Systems

Patrick Bachmann^*
, Saeed Ahmed^*

^*Corresponding author for this work

Discrete Technology and Production Automation

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

3 Citations (Scopus)

134 Downloads (Pure)

Abstract

Time-varying ISS-Lyapunov functions for impulsive systems provide a necessary and sufficient condition for ISS. This property makes them a more powerful tool for stability analysis than classical candidate ISS-Lyapunov functions providing only a sufficient ISS condition. Moreover, time-varying ISS-Lyapunov functions cover systems with simultaneous instability in continuous and discrete dynamics for which candidate ISS-Lyapunov functions remain inconclusive. The present paper links these two concepts by suggesting a method of constructing time-varying ISS-Lyapunov functions from candidate ISS-Lyapunov functions, thereby effectively combining the ease of construction of candidate ISS-Lyapunov functions with the guaranteed existence of time-varying ISS-Lyapunov functions.

Original language	English
Pages (from-to)	1-6
Number of pages	6
Journal	IFAC-PapersOnLine
Volume	56
Issue number	1
DOIs	https://doi.org/10.1016/j.ifacol.2023.02.001
Publication status	Published - 2023

Access to Document

10.1016/j.ifacol.2023.02.001Licence: CC BY-NC-ND

Construction of Time-Varying ISS-Lyapunov Functions for Impulsive SystemsFinal publisher's version, 468 KBLicence: CC BY-NC-ND

Handle.net

Persistent link

Cite this

@article{93cf82307d084c6181630216fe0af574,

title = "Construction of Time-Varying ISS-Lyapunov Functions for Impulsive Systems",

abstract = "Time-varying ISS-Lyapunov functions for impulsive systems provide a necessary and sufficient condition for ISS. This property makes them a more powerful tool for stability analysis than classical candidate ISS-Lyapunov functions providing only a sufficient ISS condition. Moreover, time-varying ISS-Lyapunov functions cover systems with simultaneous instability in continuous and discrete dynamics for which candidate ISS-Lyapunov functions remain inconclusive. The present paper links these two concepts by suggesting a method of constructing time-varying ISS-Lyapunov functions from candidate ISS-Lyapunov functions, thereby effectively combining the ease of construction of candidate ISS-Lyapunov functions with the guaranteed existence of time-varying ISS-Lyapunov functions.",

author = "Patrick Bachmann and Saeed Ahmed",

year = "2023",

doi = "10.1016/j.ifacol.2023.02.001",

language = "English",

volume = "56",

pages = "1--6",

journal = "IFAC-PapersOnLine",

issn = "2405-8963",

publisher = "Elsevier",

number = "1",

}

TY - JOUR

T1 - Construction of Time-Varying ISS-Lyapunov Functions for Impulsive Systems

AU - Bachmann, Patrick

AU - Ahmed, Saeed

PY - 2023

Y1 - 2023

N2 - Time-varying ISS-Lyapunov functions for impulsive systems provide a necessary and sufficient condition for ISS. This property makes them a more powerful tool for stability analysis than classical candidate ISS-Lyapunov functions providing only a sufficient ISS condition. Moreover, time-varying ISS-Lyapunov functions cover systems with simultaneous instability in continuous and discrete dynamics for which candidate ISS-Lyapunov functions remain inconclusive. The present paper links these two concepts by suggesting a method of constructing time-varying ISS-Lyapunov functions from candidate ISS-Lyapunov functions, thereby effectively combining the ease of construction of candidate ISS-Lyapunov functions with the guaranteed existence of time-varying ISS-Lyapunov functions.

AB - Time-varying ISS-Lyapunov functions for impulsive systems provide a necessary and sufficient condition for ISS. This property makes them a more powerful tool for stability analysis than classical candidate ISS-Lyapunov functions providing only a sufficient ISS condition. Moreover, time-varying ISS-Lyapunov functions cover systems with simultaneous instability in continuous and discrete dynamics for which candidate ISS-Lyapunov functions remain inconclusive. The present paper links these two concepts by suggesting a method of constructing time-varying ISS-Lyapunov functions from candidate ISS-Lyapunov functions, thereby effectively combining the ease of construction of candidate ISS-Lyapunov functions with the guaranteed existence of time-varying ISS-Lyapunov functions.

U2 - 10.1016/j.ifacol.2023.02.001

DO - 10.1016/j.ifacol.2023.02.001

M3 - Article

SN - 2405-8963

VL - 56

SP - 1

EP - 6

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

IS - 1

ER -

Construction of Time-Varying ISS-Lyapunov Functions for Impulsive Systems

Abstract

Access to Document

Handle.net

Fingerprint

Cite this