Approximation Of Time-Delay Systems

We propose a new method for approximating time-delays in dynamical systems. A weighted II-infinity norm criterion is minimized to obtain rational approximation of e(-sd). We report the approximation in a diagram relating both the amount of time delay and the bandwidth to the order of the approximating rational function for a given level of infinity norm. The obtained approximations are compared to the widely used Fade's approximation. Examples are used for illustrations