A collection of control time varying delayed systems: Lyapunov Razumikhin-Approach

Abstract Time delay is frequently a source of instability in several modern systems. Therefore, stability and control is of practical and theoretical importance. Based on a common control Lyapunov Razumikhin approach, we study the problem of stabilization for a collection of time varying delay systems. We prove that if a collection of systems with varying delay satisfies some conditions then a delay feedback law, which renders the collection of closed loop systems asymptotically stable, is explicitly constructed. AMS classification: 93C10,93D15, 93D20.