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IMA Journal of Mathematical Control and Information Advance Access originally published online on September 17, 2008
IMA Journal of Mathematical Control and Information 2008 25(4):393-407; doi:10.1093/imamci/dnn003
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© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

On robust stability of linear neutral systems with time-varying delays

Emilia Fridman{dagger}

Department of Electrical Engineering-Systems, Tel Aviv University, Tel Aviv 69978, Israel

{dagger} Email: emilia{at}eng.tau.ac.il

Received on June 13, 2007; Accepted on January 20, 2008

The application of the direct Lyapunov method to the stability analysis of neutral systems with time-varying delays usually encounters a restrictive assumption on the function in the right side of the differential equation. This function is supposed to satisfy the Lipschitz condition with respect to the delayed state derivative with a constant less than 1. In the present paper, we extend the input–output approach to consider the stability of neutral type systems with uncertain time-varying delays and norm-bounded uncertainties. The assumption on the Lipschitzian constant can then be avoided. Sufficient stability criteria are derived in the frequency domain and the time domain, where the descriptor discretized Lyapunov–Krasovskii functional is applied. As a by-product, new necessary conditions for neutral-delay-independent/retarded-delay-dependent stability criteria are obtained. The method can be easily extended to L2-gain analysis and can be applied to design problems.

Keywords: neutral system; time-varying delay; input–output approach; Lyapunov–Krasovskii method.


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