\(L_{\infty}\) approximation and nuclearity of delay systems (Q1101050)

Single-input single-output delay systems with transfer functions \(G(s,e^{-h_ 1s},...,e^{-h_ ks})\), where G is real rational, are considered. If h(t), \(t\geq 0\), is the impulse reponse corresponding to G, the associated Hankel operator is defined as \((\Gamma u)(t)=\int^{\infty}_{0}h(t+s)u(s)ds\). \(\Gamma\) is nuclear if its sequence of singular values is summable. Theorem 2.1 gives explicit necessary and sufficient conditions for the simultaneous nuclearity of \(\Gamma\) and the finiteness of the number of unstable poles of G. Theorem 3.1 establishes the uniform convergence in the right halfplane of the spectral approximations to G (with rate of convergence estimated). Two numerical examples are presented.