Robust Stability of Time-Varying Delay Systems: The Quadratic Separation Approach

In this article, we are interested in analysing stability of systems that incorporate time-varying delays in their dynamic. The Lyapunov-Krasovskii approach is definitely the most popular method to address this issue and many results have proposed new functionals and enhanced techniques for deriving less conservative stability conditions. In this present work, we propose an original approach: the quadratic separation. To this end, the delay operator properties are exploited to provide delay range stability conditions. In particular,L2-norm of delay-dependent operators are computed so as to reduce the conservatism of the approach. Moreover, the main result is able to assess the stability of non-small delay systems, i.e, it can detect a stability interval for systems that are unstable without any delay. Several examples illustrate the benefit of our methodology.