This paper establishes an exponential H infin synchronization method for a class of uncertain master and slave neural networks (MSNNs) with mixed time delays, where the mixed delays comprise different neutral, discrete, and distributed time delays. The polytopic and the norm-bounded uncertainties are separately taken into consideration. An appropriate discretized Lyapunov-Krasovskii functional and some free-weighting matrices are utilized to establish some delay-dependent sufficient conditions for designing delayed state-feedback control as a synchronization law in terms of linear matrix inequalities under less restrictive conditions. The controller guarantees the exponential H infin synchronization of the two coupled MSNNs regardless of their initial states. Detailed comparisons with existing results are made, and numerical simulations are carried out to demonstrate the effectiveness of the established synchronization laws.

New Delay-Dependent Exponential $H_{\infty}$ Synchronization for Uncertain Neural Networks With Mixed Time Delays

New criteria for synchronization stability of general complex dynamical networks with coupling delays

In this paper, we introduce a new class of discrete-time neural networks (DNNs) with Markovian jumping parameters as well as mode-dependent mixed time delays (both discrete and distributed time delays). Specifically, the parameters of the DNNs are subject to the switching from one to another at different times according to a Markov chain, and the mixed time delays consist of both discrete and distributed delays that are dependent on the Markovian jumping mode. We first deal with the stability analysis problem of the addressed neural networks. A special inequality is developed to account for the mixed time delays in the discrete-time setting, and a novel Lyapunov-Krasovskii functional is put forward to reflect the mode-dependent time delays. Sufficient conditions are established in terms of linear matrix inequalities (LMIs) that guarantee the stochastic stability. We then turn to the synchronization problem among an array of identical coupled Markovian jumping neural networks with mixed mode-dependent time delays. By utilizing the Lyapunov stability theory and the Kronecker product, it is shown that the addressed synchronization problem is solvable if several LMIs are feasible. Hence, different from the commonly used matrix norm theories (such as the M-matrix method), a unified LMI approach is developed to solve the stability analysis and synchronization problems of the class of neural networks under investigation, where the LMIs can be easily solved by using the available Matlab LMI toolbox. Two numerical examples are presented to illustrate the usefulness and effectiveness of the main results obtained.

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Stability and Synchronization of Discrete-Time Markovian Jumping Neural Networks With Mixed Mode-Dependent Time Delays

Finite-time stability and settling-time estimation of nonlinear impulsive systems

Brief paper: Exponential stability of nonlinear time-delay systems with delayed impulse effects

Global exponential stability of impulsive high-order BAM neural networks with time-varying delays

Discrete-time bidirectional associative memory neural networks with variable delays

This paper proposes a new event-triggered scheme, in which each agent has various mechanisms to respectively determine when to exchange information with each of its different neighbors. This kind of event-triggered mechanism avoids two constraints in previous mechanisms: (1) simultaneous event detection; (2) synchronous information transmission to all of neighbors. Thus our proposed scheme can be applied into more general situations. In addition, our scheme is able to guarantee the asymptotic consensus and exclude the Zeno behavior. Furthermore, an alternative self-triggered algorithm is presented to thoroughly exclude continuous event detection. Finally, a numerical example is provided to verify the theoretical analysis.

Jinling Liang

Papers

Global exponential stability of impulsive high-order BAM neural networks with time-varying delays

Discrete-time bidirectional associative memory neural networks with variable delays

Asynchronous information transmission for consensus behavior via an event-triggered mechanism