The University of Southampton
University of Southampton Institutional Repository

Stability analysis of 2D Roesser systems via vector Lyapunov functions

Stability analysis of 2D Roesser systems via vector Lyapunov functions
Stability analysis of 2D Roesser systems via vector Lyapunov functions
The paper gives new results that contribute to the development of a stability theory for 2D nonlinear discrete and differential systems described by a state-space model of the Roesser form using an extension of Lyapunov’s method. One of the main difficulties in using such an approach is that the full derivative or its discrete counterpart along the trajectories cannot be obtained without explicitly finding the solution of the system under consideration. This has led to the use of a vector Lyapunov function and its divergence or its discrete counterpart along the system trajectories. Using this approach, new conditions for asymptotic stability are derived in terms of the properties of two vector Lyapunov functions. The properties of asymptotic stability in the horizontal and vertical dynamics, respectively, are introduced and analyzed. This new properties arise naturally for repetitive processes where one of the two independent variables is defined over a finite interval. Sufficient conditions for exponential stability in terms of the properties of one vector Lyapunov function are also given as a natural follow on from the asymptotic stability analysis.
2405-8963
4126-4131
Pakshin, Pavel
b237ddfe-eb4d-4fa1-963e-71ae7eb39e51
Emelianova, Julia
054b5aa3-cb10-488f-afb7-252b126cafa4
Galkowski, Krzysztof
322994ac-7e24-4350-ab72-cc80ac8078ef
Rogers, Eric
611b1de0-c505-472e-a03f-c5294c63bb72
Pakshin, Pavel
b237ddfe-eb4d-4fa1-963e-71ae7eb39e51
Emelianova, Julia
054b5aa3-cb10-488f-afb7-252b126cafa4
Galkowski, Krzysztof
322994ac-7e24-4350-ab72-cc80ac8078ef
Rogers, Eric
611b1de0-c505-472e-a03f-c5294c63bb72

Pakshin, Pavel, Emelianova, Julia, Galkowski, Krzysztof and Rogers, Eric (2017) Stability analysis of 2D Roesser systems via vector Lyapunov functions. IFAC-PapersOnLine, 50 (1), 4126-4131. (doi:10.1016/j.ifacol.2017.08.799).

Record type: Article

Abstract

The paper gives new results that contribute to the development of a stability theory for 2D nonlinear discrete and differential systems described by a state-space model of the Roesser form using an extension of Lyapunov’s method. One of the main difficulties in using such an approach is that the full derivative or its discrete counterpart along the trajectories cannot be obtained without explicitly finding the solution of the system under consideration. This has led to the use of a vector Lyapunov function and its divergence or its discrete counterpart along the system trajectories. Using this approach, new conditions for asymptotic stability are derived in terms of the properties of two vector Lyapunov functions. The properties of asymptotic stability in the horizontal and vertical dynamics, respectively, are introduced and analyzed. This new properties arise naturally for repetitive processes where one of the two independent variables is defined over a finite interval. Sufficient conditions for exponential stability in terms of the properties of one vector Lyapunov function are also given as a natural follow on from the asymptotic stability analysis.

Text
Stability analysis of 2D Roesser systems via vector Lyapunov functions - Accepted Manuscript
Download (228kB)

More information

Accepted/In Press date: 27 February 2017
e-pub ahead of print date: 18 October 2017
Venue - Dates: 20th IFAC World congress, France, 2017-07-09 - 2017-07-14

Identifiers

Local EPrints ID: 415680
URI: http://eprints.soton.ac.uk/id/eprint/415680
ISSN: 2405-8963
PURE UUID: edfc8de1-89b1-44df-8220-7689d5b896d7
ORCID for Eric Rogers: ORCID iD orcid.org/0000-0003-0179-9398

Catalogue record

Date deposited: 20 Nov 2017 17:30
Last modified: 07 Oct 2020 04:43

Export record

Altmetrics

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×