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**Stabilization of networked control systems with nonuniform random sampling periods.**
*(English)*
Zbl 1214.93093

Summary: A new linear delayed delta operator switched system model is proposed to describe networked control systems with packets dropout and network-induced delays. The plant is a continuous-time system, which is sampled by time-varying random sampling periods. A general delta domain Lyapunov stability criterion is given for delta operator switched systems with time delays. Sufficient conditions for asymptotic stability of closed-loop networked control systems with both packets dropout and network-induced delays are presented in terms of Linear Matrix Inequalities (LMIs). A verification theorem is given to show the solvability of the stabilization conditions by solving a class of finite LMIs. Both the case of data packets arrive instantly and the case of invariant sampling periods in delta operator systems are given, respectively. Three numerical examples are given to illustrate the effectiveness and potential of the developed techniques.

### MSC:

93D20 | Asymptotic stability in control theory |

93D30 | Lyapunov and storage functions |

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

93C57 | Sampled-data control/observation systems |

93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |

### Keywords:

networked control systems; delta operator systems; random sampling periods; switched systems; stabilization
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\textit{H. Yang} et al., Int. J. Robust Nonlinear Control 21, No. 5, 501--526 (2011; Zbl 1214.93093)

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