New delay-interval stability condition

The delay-dependent stability problem for systems with time-delay varying in an interval is addressed in this article. The new idea in this article is to connect two very efficient approaches: the discretised Lyapunov functional for systems with pointwise delay and the convex analysis for systems with time-varying delay. The proposed method is able to check the stability interval when the time-varying delay d(t) belongs to an interval [r, τ]. The case of unstable delayed systems for r = 0 is also treatable. The resulting criterion, expressed in terms of a convex optimisation problem, outperforms the existing ones in the literature, as illustrated by the numerical examples.