The Stability of Stochastic Coupled Systems With Time-Varying Coupling and General Topology Structure

Bipartite synchronization of signed networks via aperiodically intermittent control based on discrete-time state observations

In this paper, bipartite synchronization of signed networks with stochastic disturbances via aperiodically intermittent control is investigated. The aperiodically intermittent control presented is based on discrete-time state observations rather than continuous-time ones. To formulate signed networks and exhibit the competitive relation, a structurally balanced signed network is built and all the units are divided into two subcommunities. By employing Lyapunov method and graph theory, some sufficient conditions on bipartite synchronization are given. Meanwhile, when aperiodically intermittent control degenerates into periodically intermittent control and feedback control respectively, two corollaries are also provided to ensure the bipartite synchronization of the signed networks. Ultimately, two applications to coupled single-link robot arms and coupled oscillators are presented and corresponding numerical examples are respectively provided to verify the feasibility and effectiveness of the theoretical results.

Intermittent Discrete Observation Control for Synchronization of Stochastic Neural Networks

In this paper, to investigate the exponential synchronization of stochastic neural networks, a new periodically intermittent discrete observation control (PIDOC) is first proposed. Different from the existing periodically intermittent control, our control in control time is feedback control based on discrete-time state observations (FCDSOs) instead of a continuous-time one. By employing the Lyapunov method, graph theory, and theory of differential inclusions, the exponential synchronization of stochastic neural networks with a discontinuous right-hand side is realized by PIDOC and some sufficient conditions are presented. Especially, when control width tends to control period, PIDOC will be reduced to a general FCDSO and we give some detailed discussions. Then, we provide some corollaries about synchronization in mean square, asymptotical synchronization in mean square, and exponential synchronization of stochastic neural networks under FCDSO. Finally, some numerical simulations are provided to demonstrate our analytical results.

Novel aperiodically intermittent stability criteria for Markovian switching stochastic delayed coupled systems

This paper concerns p th moment exponential stability of stochastic coupled systems with multiple time-varying delays, and Markovian switching topologies via intermittent control. Compared with previous research results, the mathematical model of this kind of stochastic coupled systems with multiple time-varying delays and Markovian switching topologies is studied for the first time. The intermittent control designed in this paper is aperiodical, which is more general in practice. Moreover, the restriction between control width and time delays is removed. By constructing a new differential inequality on delayed dynamical systems with Markovian switching topologies and combining the graph-theoretic approach with M-matrix theory, two sufficient criteria are derived to guarantee p th moment exponential stability of systems. Moreover, the exponential convergence rate has a close relationship with the maximum ratio of the rest width to the aperiodical time span (the sum of the control width and the rest width). Finally, we employ the theoretical results to study the exponential stability of stochastic coupled oscillators with multiple time-varying delays and Markovian switching topologies. Meanwhile, a numerical example is presented to illustrate the effectiveness and feasibility of the proposed results.