In this paper, output consensus for a series of heterogeneous systems under semi-markov switching topology is investigated. The scenario under consideration is that none of the graph is assumed to be connected and the mode-switching delay is existed. The main technical challenge is model and controller dismatch because of time delay. Assuming every individual system is stabilizable and detectable and mild connectivity assumption on communication topology, the coupled system without model-switching delay can achieve output synchronization by using the Lyapunov method. For the coupled systems with model-switching delay, a bounded output synchronization conclusion can be given. The existence of controller design is also investigated. By the way, we prove an exponentially stable stochastic system, in mean square, with non-vanishing perturbation can achieve uniform boundedness and ultimate boundedness. Finally, two examples are presented to verify our main theories.

本文研究了半马尔可夫切换拓扑下一系列异构系统的输出一致性。所考虑的场景是假定没有图形连接，并且存在模式切换延迟。主要技术挑战是由于时间延迟而导致模型和控制器不匹配。假设每个单独的系统在通信拓扑上都是可稳定且可检测的，且连接性假设适中，则没有模型切换延迟的耦合系统可以使用Lyapunov方法实现输出同步。对于具有模型切换延迟的耦合系统，可以给出有界输出同步结论。还研究了控制器设计的存在。顺便说一下，我们证明了一个均方指数稳定的随机系统，具有不消失的摄动可以实现均匀有界和最终有界。最后，给出两个例子来验证我们的主要理论。