A Convex Optimization Approach to Stability of Systems with Uncertain Delays

In this paper we develop a convex optimization approach to stability analysis of linear systems with interval time-varying delay, by using the standard and the delay-partitioning-based Lyapunov-Krasovskii Functionals (LKFs). We introduce novel LKFs with matrices that depend on the time-delays. These functionals allow the derivation of the condition for stability, which depend on both, the upper and the lower bounds on delay derivatives. A numerical example is given which illustrates the efficiency of the new stability criteria.