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IMA Journal of Applied Mathematics Advance Access published online on April 22, 2009
IMA Journal of Applied Mathematics, doi:10.1093/imamat/hxp019
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© The Author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Stability of equilibria of some switched non-linear systems with applications to control synthesis for electrohydraulic servomechanisms

A. Halanay{dagger}

Department of Mathematics 1, University Politehnica of Bucharest, Splaiul Independentei 313, Bucharest 060042, Romania

I. Ursu{ddagger}

Elie Carafoli National Institute for Aerospace Research, Bd. Iuliu Maniu 220, Bucharest 061126, Romania

{dagger} Email: halanay{at}mathem.pub.ro

{ddagger} Email: iursu{at}incas.ro

Received on April 28, 2007; Accepted on February 25, 2009

Stability of the zero solution is analyzed for a family of switched systems indexed by a parameter, each system having {lambda} = 0 in the spectrum of the Jacobian matrix calculated in zero. It is proved that existence of a common quadratic Lyapunov function for some lower dimensional linear systems is sufficient to ensure local uniform stability of the zero solution of the switched non-linear system and a regular asymptotic behaviour. An application to control synthesis for stabilizing equilibria in a switched non-linear control system modelling an electrohydraulic servomechanism is given.

Keywords: switched system; common quadratic Lyapunov function; Lyapunov stability; Hurwitz matrix.


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