Output synchronization for heterogeneous system via semi-Markov switching scheme with mode-switching delay

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. (C) 2020 Elsevier Inc. All rights reserved.