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Stochastic stability of some classes of nonlinear 2D systems

Stochastic stability of some classes of nonlinear 2D systems
Stochastic stability of some classes of nonlinear 2D systems

The paper considers nonlinear discrete and differential stochastic repetitive processes using the state-space model setting. These processes are a special case of 2D systems that originate from the modeling of physical processes. Using the vector Lyapunov function method, sufficient conditions for stability in the mean square are obtained in the stochastic setting, where the vast majority of the currently known results are for deterministic dynamics. Based on these results, the property of stochastic exponential passivity in the second moment is used, together with the vector storage function, to develop a new method for output feedback control law design. An example of a system with nonlinear actuator dynamics and state-dependent noise is given to demonstrate the effectiveness of the new results.

2D systems, differential repetitive processes, discrete repetitive processes, passivity, stabilization, stochastic stability, vector Lyapunov function
0005-1179
89-102
Pakshin, P.V.
b49d7402-75eb-4915-9106-870574fb7c60
Emelianova, J.P.
41c1fa6b-aa49-43b0-86d6-96e0cf212285
Emelianov, M.A.
e0b9b7c0-d81b-4610-8939-f85f6614e3a5
Gałkowski, K.
10df77b7-bc80-420b-bb5a-e10722859361
Rogers, E.
611b1de0-c505-472e-a03f-c5294c63bb72
Pakshin, P.V.
b49d7402-75eb-4915-9106-870574fb7c60
Emelianova, J.P.
41c1fa6b-aa49-43b0-86d6-96e0cf212285
Emelianov, M.A.
e0b9b7c0-d81b-4610-8939-f85f6614e3a5
Gałkowski, K.
10df77b7-bc80-420b-bb5a-e10722859361
Rogers, E.
611b1de0-c505-472e-a03f-c5294c63bb72

Pakshin, P.V., Emelianova, J.P., Emelianov, M.A., Gałkowski, K. and Rogers, E. (2018) Stochastic stability of some classes of nonlinear 2D systems. Automation and Remote Control, 79 (1), 89-102. (doi:10.1134/S0005117918010083).

Record type: Article

Abstract

The paper considers nonlinear discrete and differential stochastic repetitive processes using the state-space model setting. These processes are a special case of 2D systems that originate from the modeling of physical processes. Using the vector Lyapunov function method, sufficient conditions for stability in the mean square are obtained in the stochastic setting, where the vast majority of the currently known results are for deterministic dynamics. Based on these results, the property of stochastic exponential passivity in the second moment is used, together with the vector storage function, to develop a new method for output feedback control law design. An example of a system with nonlinear actuator dynamics and state-dependent noise is given to demonstrate the effectiveness of the new results.

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Stochastic Stability of Some Classes of Nonlinear - Accepted Manuscript
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More information

Accepted/In Press date: 2 January 2018
e-pub ahead of print date: 2 February 2018
Keywords: 2D systems, differential repetitive processes, discrete repetitive processes, passivity, stabilization, stochastic stability, vector Lyapunov function

Identifiers

Local EPrints ID: 418330
URI: http://eprints.soton.ac.uk/id/eprint/418330
ISSN: 0005-1179
PURE UUID: c7552770-5f40-4f66-99d9-f85967fd80fd
ORCID for E. Rogers: ORCID iD orcid.org/0000-0003-0179-9398

Catalogue record

Date deposited: 28 Feb 2018 17:30
Last modified: 07 Oct 2020 01:34

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