New results on stability and stabilisation of systems with interval time-varying delay

Abstract

This study is concerned with the stability and stabilisation for systems with interval time-varying delay. First, by appropriately choosing Lyapunov functional and using Finsler's lemma, a new delay-dependent stability criteria involving the minimum and maximum delay bounds is obtained. Second, new results for delay-dependent stabilisation of systems with interval time-varying delay are provided on the basis of a linear matrix inequality (LMI) framework. Both state- and observer-based output feedback controllers are designed. Differing existing design approach of observer-based controller, a single-step approach is proposed to overcome the drawback of the two-step LMI approach often encountered in the literature, and the conditions are also delay dependent. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method.