A method for determining the non-existence of a common quadratic Lyapunov function for switched linear systems based on particle swarm optimisation

M.A. Duarte-Mermoud, R.H. Ordóñez-Hurtado and P. Zagalak

International Journal of Systems Science, 2012, vol. 43, issue 11, 2015-2029

Abstract: The existence of a common quadratic Lyapunov function (CQLF) for a switched linear system guarantees its global asymptotic stability. Even if progress in finding the conditions for the existence/non-existence of a CQLF is significant, especially in switched linear systems consisting of N second-order systems or two systems of order n, the general case of N systems of order n still remains open. In this article, a sufficient condition for the non-existence of a CQLF for N systems of order n is derived. Based on the condition, a new method for determining the non-existence of a CQLF, using particle swarm optimisation, was designed and is described. Examples illustrating the proposed method are introduced at the end of this article.

Date: 2012
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DOI: 10.1080/00207721.2012.687787

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