Attracting and invariant sets of non-autonomous reaction-diffusion neural networks with time-varying delays

In this paper, a class of non-autonomous reaction-diffusion neural networks with time-varying delays is investigated. By establishing a new differential inequality and employing the properties of spectral radius of nonnegative matrix and diffusion operator, the global attracting and positive invariant sets and exponential stability of non-autonomous reaction-diffusion neural networks with time-varying delays are obtained. Our results do not require the conditions of boundedness of the coefficient of neural networks. One example is given to illustrate the effectiveness of our conclusion.     

Global dynamics for non-autonomous reaction-diffusion neural networks with time-varying delays

In this paper, a class of non-autonomous reaction-diffusion neural networks with time-varying delays is considered. Novel methods to study the global dynamical behavior of these systems are proposed. Employing the properties of diffusion operator and the method of delayed inequalities analysis, we investigate global exponential stability, positive invariant sets and global attracting sets of the neural networks under consideration. Furthermore, conditions sufficient for the existence and uniqueness of periodic attractors for periodic neural networks are derived and the existence range of the attractors is estimated. Finally two examples are given to demonstrate the effectiveness of these results.     

Dissipativity and periodic attractor for non-autonomous neural networks with time-varying delays

In this paper, a model is considered to describe the dynamics of a class of non-autonomous neural networks with time-varying delays. By applying the properties of M-matrix, the techniques of inequality analysis and the Banach fixed point theorem, we obtain a series of new criteria on the dissipativity and existence of periodic attractor. Our results can extend and improve earlier ones.     

Delay-dependent stability analysis for impulsive neural networks with time varying delays

In this paper, the global exponential stability and global asymptotic stability of the neural networks with impulsive effect and time varying delays is investigated. By using Lyapunov–Krasovskii-type functional, the quality of negative definite matrix and Cauchy criterion, we obtain the sufficient conditions for global exponential stability and global asymptotic stability of such model, in terms of linear matrix inequality (LMI), which depend on the delays. Two examples are given to illustrate the effectiveness of our theoretical results.     

Stable reinforcement learning with recurrent neural networks

In this paper,we present a technique for ensuring the stability of a large class of adaptively controlled systems.We combine IQC models of both the controlled system and the controller with a method of filtering control parameter updates to ensure stable behavior of the controlled system under adaptation of the controller.We present a specific application to a system that uses recurrent neural networks adapted via reinforcement learning techniques.The work presented extends earlier works on stable reinforcement learning with neural networks.Specifically,we apply an improved IQC analysis for RNNs with time-varying weights and evaluate the approach on more complex control system.     

New stability criteria for BAM neural networks with time-varying delays

In this paper, the exponential stability is investigated for a class of time-delay BAM neural networks (NNs). Time delays of two layers are taken into account separately rather than as a whole with the idea of delay fractioning. Then we generalize the result to time-varying interval delay condition. Exploiting the known constant part of delay sufficiently to estimate the upper bounds, we can derive an improved stability for BAM NNs with time-varying interval delay. Two examples are provided to demonstrate the less conservatism and effectiveness of the proposed linear matrix inequality (LMI) conditions.     

Delay dependent stability criteria for recurrent neural networks with time varying delays

This paper aims to present some delay-dependent global asymptotic stability criteria for recurrent neural networks with time varying delays. The obtained results have no restriction on the magnitude of derivative of time varying delay, and can be easily checked due to the form of linear matrix inequality. By comparison with some previous results, the obtained results are less conservative. A numerical example is utilized to demonstrate the effectiveness of the obtained results.     

Global exponential stability analysis for cellular neural networks with variable coefficients and delays

Some sufficient conditions for the global exponential stability of cellular neural networks with variable coefficients and time-varying delays are obtained by a method based on a delayed differential inequality. The method, which does not make use of Lyapunov functionals, is simple and effective for the stability analysis of cellular neural networks with variable coefficients and time-varying delays. Some previous results in the literature are shown to be special cases of our results.      

On the stability of linear composite systems with delays

It is shown that the stability of composite feedback control systems with delays both in the state and the input can be checked from the stabilities of the individual isolated subsystems, if the composite system matrix has a certain new structure called the GKK-structure; and if the numerators and denominators of the determinants of the overall system transfer matrix and of the isolated system transfer matrices contain some term of a certain expansion called the principal term. The GKK-structure includes diagonal dominance, the Hadamard (M-matrix) structure, and normality as special cases.     

Harmless delays for global exponential stability of Cohen–Grossberg neural networks

In this paper, the Cohen–Grossberg neural networks with time delays are considered without assuming any symmetry of connection matrix and differentiability of the activation functions. By constructing a novel Lyapunov functional, new sufficient criteria for the existence of a unique equilibrium and global exponential stability of the network are derived. These criteria are all independent of the magnitudes of delays, and so the delays under these conditions are harmless. Those results are shown to generalize the previous global exponential stability results derived in the literature.