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Stabilization of two-dimensional nonlinear systems described by Fornasini-Marchesini and Roesser models

Stabilization of two-dimensional nonlinear systems described by Fornasini-Marchesini and Roesser models
Stabilization of two-dimensional nonlinear systems described by Fornasini-Marchesini and Roesser models

The paper considers nonlinear two-dimensional systems described by the Fornasini-Marchesini or Roesser state-space models. Conditions for such systems to have a physically motivated exponential stability property are derived using vector Lyapunov functions. A form of passivity, termed exponential passivity, is introduced and used, together with a vector storage function, to develop a feedback based control law that guarantees exponential stability of the controlled system. For cases where noise is present, stochastic dissipativity in the second moment is defined and then a particular case of this property, termed passivity in the mean square, is used, together with a vector storage function, to develop a feedback based control law such that the controlled system also has this property. Two physically motivated particular cases, a system with nonlinear actuator dynamics and additive noise and a linear system with state-dependent noise, respectively, are also considered to demonstrate the effectiveness of the new results.

2D systems, Dissipativity, Exponential stability, Nonlinear systems, Passivity, Stabilization, Stochastic stability, Vector Lyapunov functions
0363-0129
3848-3866
Pakshin, Pavel
8bee1030-fcdf-4e47-abca-72b2d07fd20a
Emelianova, Julia
04343da6-8438-40e3-b128-fc773905ea16
Gałkowski, Krzysztof
ce0d0509-675e-4d30-b2c4-2ca46c22dbe5
Rogers, Eric
611b1de0-c505-472e-a03f-c5294c63bb72
Pakshin, Pavel
8bee1030-fcdf-4e47-abca-72b2d07fd20a
Emelianova, Julia
04343da6-8438-40e3-b128-fc773905ea16
Gałkowski, Krzysztof
ce0d0509-675e-4d30-b2c4-2ca46c22dbe5
Rogers, Eric
611b1de0-c505-472e-a03f-c5294c63bb72

Pakshin, Pavel, Emelianova, Julia, Gałkowski, Krzysztof and Rogers, Eric (2018) Stabilization of two-dimensional nonlinear systems described by Fornasini-Marchesini and Roesser models. SIAM Journal on Control and Optimization, 56 (5), 3848-3866. (doi:10.1137/16M1076575).

Record type: Article

Abstract

The paper considers nonlinear two-dimensional systems described by the Fornasini-Marchesini or Roesser state-space models. Conditions for such systems to have a physically motivated exponential stability property are derived using vector Lyapunov functions. A form of passivity, termed exponential passivity, is introduced and used, together with a vector storage function, to develop a feedback based control law that guarantees exponential stability of the controlled system. For cases where noise is present, stochastic dissipativity in the second moment is defined and then a particular case of this property, termed passivity in the mean square, is used, together with a vector storage function, to develop a feedback based control law such that the controlled system also has this property. Two physically motivated particular cases, a system with nonlinear actuator dynamics and additive noise and a linear system with state-dependent noise, respectively, are also considered to demonstrate the effectiveness of the new results.

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More information

Accepted/In Press date: 7 August 2018
e-pub ahead of print date: 25 October 2018
Keywords: 2D systems, Dissipativity, Exponential stability, Nonlinear systems, Passivity, Stabilization, Stochastic stability, Vector Lyapunov functions

Identifiers

Local EPrints ID: 427893
URI: http://eprints.soton.ac.uk/id/eprint/427893
ISSN: 0363-0129
PURE UUID: 9cea81ff-4058-45c0-8ad0-69e145e987e5
ORCID for Eric Rogers: ORCID iD orcid.org/0000-0003-0179-9398

Catalogue record

Date deposited: 01 Feb 2019 17:30
Last modified: 07 Oct 2020 01:34

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Contributors

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

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