On a Rational Transfer Function-Based Approach to ${cal H}_{\infty }$ Filtering Design for Time-Delay Linear Systems

This paper introduces a new procedure for H_∞ filter design of time-delay linear systems. A finite-order LTI system, called comparison system, is defined in such a way that its H_∞ norm is proven to be strongly related to the one of the time-delay system. Differently from what can be viewed as a common feature of filter design methods available in the literature to date, the one presented here treats the filtering design of time-delay systems with classical numerical routines based on Riccati equation and H_∞ theory of LTI systems. The proposed algorithm is simple, efficient and easy to implement. Illustrative examples are solved and discussed in order to put in evidence the most relevant properties of the theoretical results. Furthermore, a practical application is presented.