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Journal Articles Automatica Year : 2011

On the Conservatism of the Sum-of-Squares Method for Analysis of Time-Delayed Systems

Abstract

In this paper, we present a converse Lyapunov result which shows that using polynomial Lyapunov functionals to prove the stability of linear time-delay systems is not conservative. This result motivates the sum-of-squares approach to stability analysis of linear time-delay systems. This main result is based on an extension of the Weierstrass approximation theorem to show that linear varieties of polynomials can be used to approximate linear varieties of the space of continuous functions.

Dates and versions

hal-00761334 , version 1 (05-12-2012)

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Matthew M. Peet, Pierre-Alexandre Bliman. On the Conservatism of the Sum-of-Squares Method for Analysis of Time-Delayed Systems. Automatica, 2011, 47 (11), pp.2406-2411. ⟨10.1016/j.automatica.2011.08.010⟩. ⟨hal-00761334⟩
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