The Sixth International Symposium on Neural Networks (ISNN 2009)

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

Exponential stability analysis for discrete-time impulsive delay neural networks with and without uncertainty

This brief studies the global asymptotic stability and the global exponential stability of neural networks with unbounded time-varying delays and with bounded and Lipschitz continuous activation functions. Several sufficient conditions for the global exponential stability and global asymptotic stability of such neural networks are derived. The new results given in the brief extend the existing relevant stability results in the literature to cover more general neural networks.

In this paper, we study the existence of periodic solutions of time-invariant static recurrent neural networks by using the fixed point theory, Poineare map and Lyapunov function combined with inequality techniques. The static recurrent neural network is a kind of neural network which studies the external states of neurons as variables. And its global robust exponential stability. This paper introduces the research status of artificial neural network, summarizes the research background and development of static recurrent neural network dynamic system, and introduces the main work of this paper. Using the fixed point theory, M. The existence of periodic solutions and the global robust exponential stability of the static recursive neural network with variable delays and the existence of almost periodic solutions of the static recursive neural network of the partitioned time are studied by combining the properties of the matrix and the Lyapunov function combined with the inequality technique. Global exponential stability, the stability conditions of the corresponding problem are obtained respectively, and the results of the related research are generalized. Using Lyapunov. The stability of the quasi - static neural recursive neural network and the stability of the periodic solution are studied. The condition of the stationary static recursive neural network is obtained and the correctness of the condition is illustrated. Considering the influence of stochastic perturbation on the dynamic behavior of static recurrent neural network, the static recursive neural network with time delay and the static recursive neural network with distributed time delay are studied by using the infinitesimal operator, Ito formula and the convergence theorem of martingales. Global critical exponential stability of quasi - static neural network with stochastic perturbation. The static recursive neural network with Markovian modulation and the time-delay static recurrent neural network model considering both random perturbation and Markovian switching are studied. The linear matrix inequality, the finite state space Markov chain property and the Lyapunov-krasovskii function, The judgment condition of the global exponential stability of the system is obtained. Firstly, the global exponential stability problem of quasi - static neural neural network with time - delay and recursive neural network is studied by using the generalized Halanay inequality. Then the stability of the Markovian response sporadic static recurrent neural network is studied by combining the properties of Markov chain.

Global exponential stability of discrete-time recurrent neural network for solving quadratic programming problems subject to linear constraints

In this paper, we consider the sufficient conditions for the stability of periodic solutions of static recurrent neural networks with impulsive delay. In this paper, we study the time - delay static recurrent neural network affected by pulse. The results show that the neural network is stable when the pulse function is linear and relatively small, and a condition for the periodic solution with exponential stability is obtained. This paper introduces the research status of artificial neural network, summarizes the research background and development of static recurrent neural network dynamic system, and introduces the main work of this paper. Using the fixed point theory, M. The existence of periodic solutions and the global robust exponential stability of the static recursive neural network with variable delays and the existence of almost periodic solutions of the static recursive neural network of the partitioned time are studied by combining the properties of the matrix and the Lyapunov function combined with the inequality technique. Global exponential stability, the stability conditions of the corresponding problem are obtained respectively, and the results of the related research are generalized. Using Lyapunov. The stability of the quasi - static neural recursive neural network and the stability of the periodic solution are studied. The condition of the stationary static recursive neural network is obtained and the correctness of the condition is illustrated. Considering the influence of stochastic perturbation on the dynamic behavior of static recurrent neural network, the static recursive neural network with time delay and the static recursive neural network with distributed time delay are studied by using the infinitesimal operator, Ito formula and the convergence theorem of martingales. Global critical exponential stability of quasi - static neural network with stochastic perturbation. The static recursive neural network with Markovian modulation and the time-delay static recurrent neural network model considering both random perturbation and Markovian switching are studied. The linear matrix inequality, the finite state space Markov chain property and the Lyapunov-krasovskii function, The judgment condition of the global exponential stability of the system is obtained. Firstly, the global exponential stability problem of quasi - static neural neural network with time - delay and recursive neural network is studied by using the generalized Halanay inequality. Then the stability of the Markovian response sporadic static recurrent neural network is studied by combining the properties of Markov chain.

New results of global robust exponential stability of neural networks with delays

The problem of global exponential stability analysis of Impulsive high-order Hopfield-type neural networks with time-varying delays and reaction–diffusion terms has been investigated in this paper. Using the Lyapunov function method and M-matrix theory, we establish the global exponential stability of the neural networks with its estimated exponential convergence rate. As an illustration, a numerical example is given using the results.

The article addresses the problem of global robust exponential stability of interval neural networks with time-varying delays. On the basis of linear matrix inequality technique and M-matrix theory, some novel sufficient conditions for the existence, uniqueness, and global robust exponential stability of the equilibrium point for delayed interval neural networks are presented. It is shown that our results improve and generalize some previously published ones. Some numerical examples and simulations are given to show the effectiveness of the obtained results.

Further analysis on global robust exponential stability of neural networks with time-varying delays

Some improved criteria for global robust exponential stability of neural networks with time-varying delays

This brief presents new theoretical results on the global exponential stability of neural networks with time-varying delays and Lipschitz continuous activation functions. These results include several sufficient conditions for the global exponential stability of general neural networks with time-varying delays and without monotone, bounded, or continuously differentiable activation function. In addition to providing new criteria for neural networks with time-varying delays, these stability conditions also improve upon the existing ones with constant time delays and without time delays. Furthermore, it is convenient to estimate the exponential convergence rates of the neural networks by using the results.

Global exponential stability of discrete-time recurrent neural networks with impulses

This paper investigates the existence, uniqueness, and global exponential stability (GES) of the equilibrium point for a large class of neural networks with globally Lipschitz continuous activations including the widely used sigmoidal activations and the piecewise linear activations. The provided sufficient condition for GES is mild and some conditions easily examined in practice are also presented. The GES of neural networks in the case of locally Lipschitz continuous activations is also obtained under an appropriate condition. The analysis results given in the paper extend substantially the existing relevant stability results in the literature, and therefore expand significantly the application range of neural networks in solving optimization problems. As a demonstration, we apply the obtained analysis results to the design of a recurrent neural network (RNN) for solving the linear variational inequality problem (VIP) defined on any nonempty and closed box set, which includes the box constrained quadratic programming and the linear complementarity problem as the special cases. It can be inferred that the linear VIP has a unique solution for the class of Lyapunov diagonally stable matrices, and that the synthesized RNN is globally exponentially convergent to the unique solution. Some illustrative simulation examples are also given.

In this paper, with assuming global Lipschitz conditions on the activation functions, applying idea of vector Lyapunov function, Young inequality and Halanay differential inequality with delay, the global exponential stability of the equilibrium point for a class of cellular neural networks with distributed delays and large impulses is investigated, the sufficient conditions for globally exponential stability of neural networks are obtained.