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Lyapunov functions and L2 gain bounds for systems with slope restricted nonlinearities

Lyapunov functions and L2 gain bounds for systems with slope restricted nonlinearities
Lyapunov functions and L2 gain bounds for systems with slope restricted nonlinearities

The stability and L2 performance analysis of systems consisting of an interconnection of a linear-time-invariant (LTI) system and a static nonlinear element which is Lipschitz, slope restricted and sector bounded is revisited. The main thrust of the paper is to improve and extend an existing result in the literature to enable (i) concise and correct conditions for asymptotic stability of the interconnection and (ii) reasonably tight bounds on the L2 gain between an exogenous input and a given output to be obtained. Numerical examples indicate that the proposed algorithm performs well compared to competing results in the literature.

Absolute stability, Anti-windup, Saturation
0167-6911
1-6
Turner, Matthew C.
6befa01e-0045-4806-9c91-a107c53acba0
Kerr, Murray
76b8a9fa-3b7a-433d-90c8-61a3570f3475
Turner, Matthew C.
6befa01e-0045-4806-9c91-a107c53acba0
Kerr, Murray
76b8a9fa-3b7a-433d-90c8-61a3570f3475

Turner, Matthew C. and Kerr, Murray (2014) Lyapunov functions and L2 gain bounds for systems with slope restricted nonlinearities. Systems and Control Letters, 69 (1), 1-6. (doi:10.1016/j.sysconle.2014.04.002).

Record type: Article

Abstract

The stability and L2 performance analysis of systems consisting of an interconnection of a linear-time-invariant (LTI) system and a static nonlinear element which is Lipschitz, slope restricted and sector bounded is revisited. The main thrust of the paper is to improve and extend an existing result in the literature to enable (i) concise and correct conditions for asymptotic stability of the interconnection and (ii) reasonably tight bounds on the L2 gain between an exogenous input and a given output to be obtained. Numerical examples indicate that the proposed algorithm performs well compared to competing results in the literature.

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More information

Accepted/In Press date: 13 April 2014
e-pub ahead of print date: 4 May 2014
Published date: July 2014
Keywords: Absolute stability, Anti-windup, Saturation

Identifiers

Local EPrints ID: 439241
URI: http://eprints.soton.ac.uk/id/eprint/439241
ISSN: 0167-6911
PURE UUID: c34fd7f5-40a0-4d54-800a-8f67bacd1896

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Date deposited: 07 Apr 2020 16:31
Last modified: 18 Jan 2024 19:11

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Contributors

Author: Matthew C. Turner
Author: Murray Kerr

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