Stability Analysis using New Variant of Halanay’s Inequality

We present a generalized form of Halanay’s inequality, having time varying gain multiplying the delayed term, and constant decay rate. Unlike usual conditions where rate is required to be strictly larger than an upper bound on we provide less restrictive that allow times when can gain. include application continuous systems with switched delay values. This illustrates utility our inequality for proving asymptotic stability in significant cases violate contraction condition was needed prove previous trajectory based results, which are also not amenable Lyapunov function constructions.