Quasi-Synchronization of Heterogeneous Hybrid Stochastic Delayed Networks via Pinning Intermittent Discrete Observation Control

This paper focuses on the quasi-synchronization of heterogeneous hybrid stochastic delayed networks (HHSDNs), in which pinning aperiodically intermittent discrete observation control (PAIDOC) strategy is imposed on the networks. During control intervals, PAIDOC is based on discrete-time state observations and is implemented to a fraction of the network nodes, which is an extension of existing literature. In light of stochastic analysis theory and Lyapunov method, we establish improved quasi-synchronization criteria. Compared with previous quasi-synchronization results on HHSDNs, the piecewise continuous, time-varying, and indefinite functions replace the constant coefficient of the upper bound estimation for the operator of a Lyapunov function in the available literature, i.e., it can be positive or negative along time evolution, which shows wider applications of our results. Especially, our results can be directly applied to examine the quasi-synchronization problem via PAIDOC based on the average control rate. Subsequently, some easily-verified quasi-synchronization criteria are presented and a detailed algorithm about how to design suitable PAIDOC is provided. In the end, the theoretical result is applied to spring-mass-damper systems and numerical examples are presented.
Note to Practitioners
—This paper was motivated by existing results on pinning aperiodically intermittent control about the quasi-synchronization. The existing results mainly require the control method to be continuously sampled and control all nodes of the network, which is difficult to be implemented in practical application. This paper designs a novel hybrid control method named pinning aperiodically intermittent discrete observation control. In addition, we established a lower conservative differential inequality first, which is significantly conducive to analyzing the quasi-synchronization of complex networks. The results obtained are applied on spring-mass-damper systems, demonstrating their effectiveness and it is expected that the proposed approach can be extended to more practical physical engineering systems.