A new approximation method for time-delay systems

We develop a rational approximant B_n^α of e^-ds and make a detailed analysis on the approximant B_n^αG of e^-dsG, where G∈RL ². We prove L^p=2,∞ error convergence and provide corresponding error bounds explicitly. Comparative study with other approximants is performed in order to make clear the properties of B_n^α. Making full use of its recursive structure, B_n^α is shown to be a suitable approximant for a class of H^∞ problems involving time delay