Positive trigonometric polynomials for strong stability of difference equations

Didier Henrion (1, 2) , Tomas Vyhlidal (3)

1 LAAS - Laboratoire d'analyse et d'architecture des systèmes
2 FEL CTU - Faculty of Electrical Engineering [Prague]
3 CTU/FME - Faculty of Mechanical Engineering [Prague]

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.

Domaines: Optimisation et contrôle [math.OC]

Didier Henrion, Tomas Vyhlidal. Positive trigonometric polynomials for strong stability of difference equations. World IFAC Congress (IFAC 2011), Aug 2011, Milan, Italy. p.296-301. ⟨hal-00532796⟩