The consensus problem for multiagent systems (MASs) with semi-Markov jumping parameters under the influence of disturbances is investigated in this article. In the first part of this article, an extended dissipative approach is used for the consensus of MASs with semi-Markovian jumping parameters and external disturbances via nonfragile controller with randomly occurring gain fluctuations. Besides, in the second part of the article, the consensus of stochastic semi-Markovian jumping MASs via nonfragile controller subject to probabilistic time-varying delay is discussed. The primary motive of this article is to develop a robust controller such that the considered MASs with semi-Markov jumping parameters achieve consensus in the presence of external disturbances. For this, the chosen problems are first converted to stabilization problems then by using Lyapunov stability theory and linear matrix inequality approach, the stabilization criterion have been established. At last, two numerical examples are worked out to illustrate the efficiency of the proposed control methodologies.

中文翻译：

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具有扰动的半马尔可夫跳跃多智能体系统一致性的非脆弱控制设计

本文研究了在扰动影响下具有半马尔可夫跳跃参数的多智能体系统（MAS）的一致性问题。在本文的第一部分，一种扩展的耗散方法用于通过具有随机发生的增益波动的非脆弱控制器来实现具有半马尔可夫跳跃参数和外部干扰的 MAS 的一致性。此外，在文章的第二部分，讨论了随机半马尔可夫跳跃 MAS 通过受概率时变延迟影响的非脆弱控制器的共识。本文的主要动机是开发一个鲁棒控制器，使得所考虑的具有半马尔可夫跳跃参数的 MAS 在存在外部干扰的情况下达成共识。为了这，选择的问题首先转化为镇定问题，然后利用李雅普诺夫稳定性理论和线性矩阵不等式方法，建立了镇定准则。最后，通过两个数值例子来说明所提出的控制方法的有效性。