Delay-range-dependent stabilization of uncertain dynamic systems with interval time-varying delays

In this paper, the problem of delay-range-dependent stabilization criterion for uncertain dynamic systems with time-varying delays is considered. The time-varying delays considered is assumed to be belong to a given interval in which lower bound of delay is not restricted to zero. By constructing a suitable augmented Lyapunov's functional and utilizing free weight matrices, the criterion for stabilization is established in terms of linear matrix inequalities. Three numerical examples are given to show the effectiveness of proposed method. Time delays often occur in many industrial systems such as chemical processes, biological systems, population dynamics, neural networks, large-scale systems, network control systems, and so on. The occurrence of the time delays may deteriorate system performance or even cause instability. Therefore, stability analysis and controller synthesis have been one of the most challenging issues [1–3]. Since delay-dependent stability criteria are less conservative than delay-independent ones when the size of time delays is small, many researchers have focused on delay-dependent stabilization and stability [4–7]. In delay-dependent stabilization and stability criteria, the main concern is to enlarge the feasible region of criteria for guaranteeing asymptotic stability of time-delay systems in a given time-delay interval. To do this, Park [8] proposed a new bounding lemma to reduce the conservatism of the stability criteria by introducing free variables in cross terms. Moon [9] proposed a stabilizing controller design method of uncertain time-delay systems by utilizing Park's lemma [8]. Fridman and Shaked [10,11] presented a descriptor approach to design a stabilizing controller of time-delay systems. Yue [12] utilized neutral model transformation to obtain stability criteria for systems with discrete and distributed delays. Kwon and Park [13] proposed a method of designing controller for uncertain time-delay systems by introducing free weight variables in transformation operator. Recently , by adding zero equations with free variables, an improved stability or stabilization method has been investigated [6,14–17]. In Ref. [15], augmented Lyapunov's functionals were proposed to increase the feasible region of stability criteria by taking integral terms of states as augmented ones. On the other hand, the stability analysis of dynamic systems with interval time-varying delays has been a focused topic of theoretical and practical importance [6,18,19] in very recent years. Interval time-varying delay means that a time delay varies in an interval in which the lower bound is not restricted to be zero. A typical example of dynamic systems with interval time-varying delays is networked control systems [20]. However, few …