Stability of linear systems with interval time-delay

The stability of linear time-delay systems with a delay interval excluding zero is investigated. A delay-free comparison system is formed by replacing the delay element with a parameter-dependent filter. Robust stability of this parameter-dependent comparison system, guarantees stability of the original time-delay system. The novelty of this result is that it does not require any a priori knowledge of the stability of the system for some fixed delay. Using a particular parameter-dependent filter based on the Pade approximation, an upper bound on the degree-of-conservatism of the comparison system may be provided, which is independent of the system considered. In this case, it is shown that the conservatism can be made arbitrarily small. Two methods are presented for stability analysis of the comparison system.