Quantized feedback control scheme on coupled systems with time delay and distributed delay: A finite-time inner synchronization analysis

In this paper, finite-time inner synchronization of coupled systems on a network with time delay and distributed delay (CSNTD) is investigated. And here, time delay and distributed delay are both taken into consideration when modelling a realistic network. Different from common feedback control, the controller we design is quantized, which is more realistic and reasonable. By using Lyapunov method and Kirchhoff's Matrix Tree Theorem, some sufficient criteria are derived to guarantee finite-time inner synchronization of CSNTD. It should be underlined that the method is first applied to studying the issue of finite-time inner synchronization of CSNTD and the synchronization time we obtain has a close relationship with the topological structure of the network. Moreover, to verify our theoretical results, we present an application to coupled oscillators with time delay and distributed delay, and a sufficient criterion is obtained. Ultimately, a numerical example is given to verify the validity and feasibility of theoretical results.