Robust stabilization of delay systems by approximation of coprime factors

Abstract

Given a delay system with transfer function G(s) = h 2(s) h 1(s) , where h 1( s) = ∑ 0 1 n p i ( s) e − γ i s , and h 2( s) = ∑ 0 2 n q i ( s) e − β i s , with 0 = γ 0< γ 1 < … < γ n1 , 0 ⩽ β 0 < … < β n2 , the p i being polynomials of degree δ i , and δ i < δ 0for 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 results on the approximation and stabilization of normalized coprime factors. An explicit formula is given for the normalized coprime factor stability margin for the case of a multivariable transfer function of the form G( s) = e − sT R( s), with R rational.