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**Sampled-data leader-following consensus for nonlinear multi-agent systems with Markovian switching topologies and communication delay.**
*(English)*
Zbl 1307.93241

Summary: This paper is concerned with sampled-data leader-following consensus of nonlinear multi-agent systems with random switching network topologies and communication delay. By modeling the switching of network topologies by a Markov process and considering the effect of communication delay, a new sampled-data consensus control protocol with variable sampling period is proposed. With this protocol, the leader-following consensus problem is equivalently converted to the stability of a class of Markovian jump systems with a time-varying delay. Then, by employing Lyapunov-Krosovskii functional method and the weak infinitesimal operation, a new delay-dependent stability criterion is derived, which ensures that the leader-following consensus can be globally exponentially achieved in mean-square sense. Based on this criterion, the switching consensus controller gains are obtained by solving a set of linear matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of the design method.

### MSC:

93C57 | Sampled-data control/observation systems |

93A14 | Decentralized systems |

68T42 | Agent technology and artificial intelligence |

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

93E03 | Stochastic systems in control theory (general) |

60J75 | Jump processes (MSC2010) |

### Keywords:

sampled-data leader-following consensus; nonlinear multi-agent systems; Markovian switching topologies; communication delay
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\textit{L. Ding} and \textit{G. Guo}, J. Franklin Inst. 352, No. 1, 369--383 (2015; Zbl 1307.93241)

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