On stabilization for systems with two additive time-varying input delays arising from networked control systems.

*(English)*Zbl 1300.93128Summary: This paper is concerned with the stability and stabilization for systems with two additive time-varying input delays arising from networked control systems. A new Lyapunov functional is constructed and a tighter upper bound of the derivative of the Lyapunov functional is derived by applying a convex polyhedron method. The resulting stability criteria have fewer matrix variables and are less conservative than some existing ones. Based on the stability criteria, a state feedback controller is designed such that the closed-loop system is asymptotically stable. Numerical examples are given to show the less conservatism of the stability criteria and the effectiveness of the designed method.

##### MSC:

93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |

93D15 | Stabilization of systems by feedback |

93D20 | Asymptotic stability in control theory |

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

##### Keywords:

stability and stabilization; systems with time-varying input delays; networked control systems; Lyapunov functional; convex polyhedron method; state feedback controller; asymptotic stability
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\textit{H. Shao} and \textit{Q.-L. Han}, J. Franklin Inst. 349, No. 6, 2033--2046 (2012; Zbl 1300.93128)

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##### References:

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