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A switched system approach to ${H}_{\infty }$ control of networked control systems with time-varying delays. (English) Zbl 1214.93044
Summary: This paper is concerned with the ${H}_{\infty }$ control problem for a class of Networked Control Systems (NCSs) with time-varying delay that is less than one sampling period. By applying a new working mode of the actuator and considering state feedback controllers, a new discrete-time switching system model is proposed to describe the NCS. Based on the obtained switching system model, a sufficient condition is derived for the closed-loop NCS to be exponentially stable and ensure a prescribed ${H}_{\infty }$ performance level. The obtained condition establishes relations among the delay length, the delay variation frequency, and the system performances of the closed-loop NCS. Moreover, a convex optimization problem is formulated to design the ${H}_{\infty }$ controllers which minimize the ${H}_{\infty }$ performance level. An illustrative example is given to show the effectiveness of the proposed results.
##### MSC:
 93B36 ${H}^{\infty }$-control 93C30 Control systems governed by other functional relations 93C35 Multivariable systems, multidimensional control systems 93D20 Asymptotic stability of control systems 93C15 Control systems governed by ODE
##### References:
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