\(H^\infty\) control for a networked control model of systems with two additive time-varying delays.

*(English)*Zbl 1406.93267Summary: This paper is concerned with \(H^\infty\) control for a networked control model of systems with two additive time-varying delays. A new Lyapunov functional is constructed to make full use of the information of the delays, and for the derivative of the Lyapunov functional a novel technique is employed to compute a tighter upper bound, which is dependent on the two time-varying delays instead of the upper bounds of them. Then the convex polyhedron method is proposed to check the upper bound of the derivative of the Lyapunov functional. The resulting stability criteria have fewer matrix variables but less conservatism than some existing ones. The stability criteria are applied to designing a state feedback controller, which guarantees that the closed-loop system is asymptotically stable with a prescribed \(H^\infty\) disturbance attenuation level. Finally examples are given to show the advantages of the stability criteria and the effectiveness of the proposed control method.

##### MSC:

93D15 | Stabilization of systems by feedback |

93B36 | \(H^\infty\)-control |

93C15 | Control/observation systems governed by ordinary differential equations |

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\textit{H. Shao} et al., Abstr. Appl. Anal. 2014, Article ID 923436, 9 p. (2014; Zbl 1406.93267)

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