Robust Stabilization of Delay Systems

Abstract

Given a delay system with transfer function $G(s) = {h_2}(s)/{h_1}(s)$, where w${h_1}(s) = \sum\limits_0^{{n_1}} {qi} (s){e^{ - \gamma is}}$, and ${h_2}(s) = \sum\limits_0^{{n_2}} {qi(s)} {e^{ - \beta is}}$, with $0 = {\gamma _0} < \gamma 1 < \ldots < {\gamma _{{n_1}}},0 \leqslant {\beta _0} < \ldots < {\beta _{{n_2}}}$, the p _i being polynomials of degree δ _i , and δ _i < δ ₀ for i ≠ 0, and the q _i polynomials of degree d _i < δ ₀ for each i, the robust stabilization of a class of perturbed coprime factors of this system is considered. Asymptotic estimates are obtained based on recent explicit results on the approximation and stabilization of normalized coprime factors.