Liuxiao Guo

Hybrid projective synchronization in a chaotic complex nonlinear system

Hybrid projective synchronization (HPS), in which the different state variables can synchronize up to different scaling factors, is numerically observed in coupled partially linear chaotic complex nonlinear systems without adding any control term in the present paper. The scaling factors of HPS are hardly predictable. Linear feedback control method is thus adopted to control them onto any desired values based on Lyapunov stability theory. Moreover, numerical simulations are given to illustrate and verify the analytical results.

Exponential stability of stochastic memristor-based recurrent neural networks with time-varying delays

Abstract In real nervous systems and in the implementation of very large-scale integration (VLSI) circuits, noise is unavoidable, which leads to the stochastic model of the memristor-based recurrent neural networks. Exponential stability of stochastic memristor-based recurrent neural networks with time-varying delays is studied and some sufficient conditions in terms of inequalities are derived. Numerical examples are given to demonstrate the effectiveness of the proposed stability criteria.

Event-triggered consensus of multi-agent systems with noises

Abstract This paper investigates the issue of mean square consensus for multiple agents affected by noises over directed networks. The centralized and decentralized event-triggered protocols are adopted for driving the agents to converge to the average value of their initial states eventually. Each agent in the network is supposed to update the state according to the information from the neighbors, while the control actuation updates are decided by the proposed event-triggered scheme. The corresponding conditions for guaranteeing the consensus are derived based on the graph theory, the Lyapunov functional approach, and the stochastic theory. Additionally, the consensus for agents in networks with switching topologies is also analyzed. Some numerical examples are presented to demonstrate the effectiveness of the theoretical results.

The existence of generalized synchronization of chaotic systems in complex networks

The paper studies the existence of generalized synchronization in complex networks, which consist of chaotic systems. When a part of modified nodes are chaotic, and the others have asymptotically stable equilibriums or orbital asymptotically stable periodic solutions, under certain conditions, the existence of generalized synchronization can be turned to the problem of contractive fixed point in the family of Lipschitz functions. In addition, theoretical proofs are proposed to the exponential attractive property of generalized synchronization manifold. Numerical simulations validate the theory.

Leader-following consensus of linear multi-agent systems with randomly occurring nonlinearities and uncertainties and stochastic disturbances

For the multi-agent community, one of the key challenges is the agents operating in open environments, in which stochastic noises affect the dynamics of agents. This paper deals with the leader-following consensus problem for a class of linear multi-agent systems model with randomly occurring nonlinearities and uncertainties, and stochastic disturbances. The communication topology is assumed to be undirected and fixed. The stochastic Brownian motions are used to describe the source of extrinsic disturbances. The randomly occurring nonlinearities are introduced to describe the nonlinear intrinsic dynamics occurring in a probabilistic way. The randomly occurring uncertainties are adopted to reflect more realistic dynamical behaviors of the agent systems that are caused by noisy environment. Sufficient conditions are derived to make all follower agents asymptotically reach the state of leader in the mean square sense. Simulation results illustrate the theoretical results.

A delay-partitioning projection approach to stability analysis of stochastic Markovian jump neural networks with randomly occurred nonlinearities

This paper considers the problem of mean square asymptotic stability of stochastic Markovian jump neural networks with randomly occurred nonlinearities. In terms of linear matrix inequality (LMI) approach and delay-partitioning projection technique, delay-dependent stability criteria are derived for the considered neural networks for cases with or without the information of the delay rates via new Lyapunov-Krasovskii functionals. We also establish that the conservatism of the conditions is a non-increasing function of the number of delay partitions. An example with simulation results is given to illustrate the effectiveness of the proposed approach.

Distributed control of cluster synchronisation in networks with randomly occurring non-linearities

This paper is concerned with the issue of mean square cluster synchronisation in complex networks, which consist of non-identical nodes with randomly occurring non-linearities. In order to guarantee synchronisation, distributed controllers depending on the information from the neighbours in the same cluster are applied to each node, meanwhile, the control gains are supposed to be updated according to the given laws. Based on the Lyapunov stability theory, the sufficient synchronisation conditions are derived and proved theoretically. Finally, a numerical example is presented to demonstrate the effectiveness of the results.

Distributed delay control of multi-agent systems with nonlinear dynamics

For multi-agent systems, significantly adding to the complexity of dynamical behaviors are intrinsic nonlinearity and stochastic noises due to environmental uncertainties. This paper deals with the mean square bounded consensus problem of multi-agent systems with intrinsic nonlinear dynamics, where each agent is affected by stochastic noises. Considering the impact of the former behaviors of nonlinear agents, we put forward a novel type of integral distributed delay protocol which is formed as a weighted sum of historical information exchange over all time interval [ t - ? , t ] . Compared with the previous work, the protocol expression of this paper is more general and includes many traditional protocols as its special cases. Based on a Lyapunov-based approach, together with results from matrix theory and algebraic graph theory, sufficient conditions are derived for the mean square bounded consensus. Simulation examples with nonlinear even chaotic agents illustrate the theoretical results. HighlightsA novel type of integral distributed delay protocol is proposed to control multi-agent systems.Sufficient conditions for the mean square bounded consensus are established.Numerical examples of complex nonlinear systems verify the effectiveness of the new protocol.

Stability of uncertain impulsive stochastic fuzzy neural networks with two additive time delays in the leakage term

Abstract This paper is concerned with the stability problem for a class of impulsive neural networks model, which includes simultaneously parameter uncertainties, stochastic disturbances and two additive time-varying delays in the leakage term. By constructing a suitable Lyapunov–Krasovskii functional that uses the information on the lower and upper bound of the delay sufficiently, a delay-dependent stability criterion is derived by using the free-weighting matrices method for such Takagi–Sugeno fuzzy uncertain impulsive stochastic recurrent neural networks. The obtained conditions are expressed with linear matrix inequalities (LMIs) whose feasibility can be checked easily by MATLAB LMI Control toolbox. Finally, the theoretical result is validated by simulations.

Finite-time boundedness analysis for a new multi-layer switched system with time-delay

In this paper, the finite-time boundedness problem of a multi-layer switched system subject to average dwell time switching signal, Markov jump and time-varying polytopic uncertainties is investigated. The sufficient conditions guaranteed the conclusion are shown in the form of linear matrix inequalities to ease the formulation, and the switched Lyapunov-Krasovskii approach is used in detail proofs. At last, an illustrative example is employed to demonstrate the efficiency of the main result.