Synchronization of Stochastic Hybrid Coupled Systems via Completely Aperiodically Intermittent Discrete Observation Control
Yan Liu, Wentao Xu, Shuo Sun
Abstract
In this paper, we focus on the synchronization problem of stochastic coupled systems with Markovian switching (SCSMS) via completely aperiodically intermittent discrete observation control (CAIDOC). It is highly emphasized that CAIDOC releases the restrictions that the limits of rest and control widths and the maximum ratio of rest widths. And then, by applying the method of average control rate, the control strategy becomes more practical. Based on the Lyapunov method and the graph theory, some sufficient conditions are obtained to ensure SCSMS to achieve synchronization. Meanwhile, the theoretical results are applied to R <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm{\ddot{o}}$</tex-math> </inline-formula> ssler-like circuits with Markovian switching. Finally, some simulation results are presented to demonstrate the availability of the theoretical results. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper was motivated by existing results on intermittent control and discrete-time state observations control about the synchronization. Existing control approaches have some limitations to some extent. This paper designs a novel hybrid control method named completely aperiodically intermittent discrete observation control, which combines the advantages of completely aperiodically intermittent control and discrete-time state observations control. Based on this control method, the synchronization of stochastic hybrid coupled systems is obtained by using the graph theory and Lyapunov method with less conservative sufficient conditions. Then, as an application of our results, R <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm{\ddot{o}}$</tex-math> </inline-formula> ssler-like circuits are considered. In the future work, we will consider to investigate the synchronization of highly nonlinear coupled systems by using this kind of novel control method.