Analysis of multiple interval delay systems via sufficient and asymptotically necessary comparison system

We examine the stability of linear time-delay systems with several constant, unknown and independent delays, each residing within a known interval excluding zero. The delay elements are replaced with parameter-dependent filters, satisfying three properties, resulting in a delay-free comparison system. The robust stability of this finite-dimensional system guarantees stability of the original time-delay system. This result is unique in the sense that it does not require any a priori knowledge of the stability of the system for some fixed delay. It is shown that if the parameter-dependent filters are constructed in a particular fashion, using Pade approximations, an a priori known upper bound on the degree-of-conservatism of the comparison system may be provided, which is independent of the system data. In this case, the conservatism of the comparison system can be made arbitrarily small. An LMI formulation is then presented for stability analysis of the comparison system.