Positive trigonometric polynomials for strong stability of difference equations

Positive trigonometric polynomials for strong stability of difference equations

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 ...

The Robustness of Strong Stability of Positive Homogeneous Difference Equations

Motivated by many applications in control engineering, problems of robust stability of dynamical systems have attracted a lot of attention of researchers during the last twenty years. In the study of these problems, the notion of stability radius was proved to be an effective tool, see 1–5 . In this paper, we study the robustness of strong stability of the homogeneous difference equation under ...

Extremal Positive Trigonometric Polynomials

There are various reasons for the interest in the problem of constructing nonnegative trigonometric polynomials. Among them are: Cesàro means and Gibbs’ phenomenon of the the Fourier series, approximation theory, univalent functions and polynomials, positive Jacobi polynomial sums, orthogonal polynomials on the unit circle, zero-free regions for the Riemann zeta-function, just to mention a few....

‘degeneration of Trigonometric Dynamical Difference Equations for Quantum Loop Algebras to Trigonometric Casimir Equations for Yangians’

We show that, under Drinfeld’s degeneration [D] of quantum loop algebras to Yangians, the trigonometric dynamical difference equations [EV] for the quantum affine algebra degenerate to the trigonometric Casimir differential equations [TL] for Yangians.

On the Stability of Trigonometric Functional Equations