Consensus of Hybrid Multi-Agent Systems

In this brief, we consider the consensus problem of hybrid multiagent systems. First, the hybrid multiagent system is proposed, which is composed of continuous-time and discrete-time dynamic agents. Then, three kinds of consensus protocols are presented for the hybrid multiagent system. The analysis tool developed in this brief is based on the matrix theory and graph theory. With different restrictions of the sampling period, some necessary and sufficient conditions are established for solving the consensus of the hybrid multiagent system. The consensus states are also obtained under different protocols. Finally, simulation examples are provided to demonstrate the effectiveness of our theoretical results.

Global Synchronization of Multiple Recurrent Neural Networks With Time Delays via Impulsive Interactions

In this paper, new results on the global synchronization of multiple recurrent neural networks (NNs) with time delays via impulsive interactions are presented. Impulsive interaction means that a number of NNs communicate with each other at impulse instants only, while they are independent at the remaining time. The communication topology among NNs is not required to be always connected and can switch ON and OFF at different impulse instants. By using the concept of sequential connectivity and the properties of stochastic matrices, a set of sufficient conditions depending on time delays is derived to ascertain global synchronization of multiple continuous-time recurrent NNs. In addition, a counterpart on the global synchronization of multiple discrete-time NNs is also discussed. Finally, two examples are presented to illustrate the results.

Pinning Synchronization of Directed Networks With Switching Topologies: A Multiple Lyapunov Functions Approach

This paper studies the global pinning synchronization problem for a class of complex networks with switching directed topologies. The common assumption in the existing related literature that each possible network topology contains a directed spanning tree is removed in this paper. Using tools from M -matrix theory and stability analysis of the switched nonlinear systems, a new kind of network topology-dependent multiple Lyapunov functions is proposed for analyzing the synchronization behavior of the whole network. It is theoretically shown that the global pinning synchronization in switched complex networks can be ensured if some nodes are appropriately pinned and the coupling is carefully selected. Interesting issues of how many and which nodes should be pinned for possibly realizing global synchronization are further addressed. Finally, some numerical simulations on coupled neural networks are provided to verify the theoretical results.

Synchronization and adaptive control of an array of linearly coupled reaction-diffusion neural networks with hybrid coupling

In this paper, we propose a general array model of coupled reaction-diffusion neural networks with hybrid coupling, which is composed of spatial diffusion coupling and state coupling. By utilizing the Lyapunov functional method combined with the inequality techniques, a sufficient condition is given to ensure that the proposed network model is synchronized. In addition, when the external disturbances appear in the network, a criterion is obtained to guarantee the H∞ synchronization of the network. Moreover, some adaptive strategies to tune the coupling strengths among network nodes are designed for reaching synchronization and H∞ synchronization. Some criteria for synchronization and H∞ synchronization are derived by using the designed adaptive laws. Numerical simulations are presented finally to demonstrate the effectiveness of the obtained theoretical results.

Sampled-data exponential synchronization of complex dynamical networks with time-varying coupling delay

This paper studies the problem of sampled-data exponential synchronization of complex dynamical networks (CDNs) with time-varying coupling delay and uncertain sampling. By combining the time-dependent Lyapunov functional approach and convex combination technique, a criterion is derived to ensure the exponential stability of the error dynamics, which fully utilizes the available information about the actual sampling pattern. Based on the derived condition, the design method of the desired sampled-data controllers is proposed to make the CDNs exponentially synchronized and obtain a lower-bound estimation of the largest sampling interval. Simulation examples demonstrate that the presented method can significantly reduce the conservatism of the existing results, and lead to wider applications.