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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.

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Stability analysis of 2D Roesser systems via vector Lyapunov functions - Accepted Manuscript
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Accepted/In Press date: 27 February 2017
e-pub ahead of print date: 18 October 2017
Venue - Dates: 20th IFAC World congress, , Toulouse, 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

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Date deposited: 20 Nov 2017 17:30
Last modified: 16 Mar 2024 05:56

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Contributors

Author: Pavel Pakshin
Author: Julia Emelianova
Author: Krzysztof Galkowski
Author: Eric Rogers ORCID iD

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