Positive trigonometric polynomials for strong stability of difference equations

2010/11/05 by Henrion, Didier, Vyhlidal, Tomas
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1011.1331

Abstract

We follow a polynomial approach to analyse strong stability of linear difference equations with rationally independent delays. Upon application of the Hermite stability criterion on the discrete-time homogeneous characteristic polynomial, assessing strong stability amounts to deciding positive definiteness of a multivariate trigonometric polynomial matrix. This latter problem is addressed with a converging hierarchy of linear matrix inequalities (LMIs). Numerical experiments indicate that certificates of strong stability can be obtained at a reasonable computational cost for state dimension and number of delays not exceeding 4 or 5.

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