H∞ control of networked control systems with short time-varying delays

The H_infin control problem is studied in this paper for networked control systems (NCSs) with short time-varying delays. By considering state feedback controllers, the closed-loop NCS is described as a discrete-time linear uncertain system model, and the uncertain part reflects the effect of the variation nature of the network-induced delays on the system dynamics. Then, a sufficient condition is derived for the closed-loop NCS to be asymptotically stable and achieve a prescribed noise attenuation level. The obtained condition establishes the quantitative relation between the H_infin noise attenuation performance and two delay parameters, namely, the allowable delay upper bound (ADB) and the allowable delay variation range (ADVR). Furthermore, design procedures for the H_infin controllers are also presented. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed method.