Class Of Impulsive Neural Networks Research Articles

Potential Effects of Delay on the Stability of a Class of Impulsive Neural Networks

Aiming at the interference of the delay term in continuous dynamics to the impulsive systems, we study the potential effects of time delay on the stability of a class of impulsive neural networks (INNs) in this paper. Two cases of delay are considered. For the case of small delay, a sufficient condition for the stability of delayed INNs is obtained by virtue of the average impulsive interval (AII) method. The derived results illustrate that within limits, the convergence rate of the system becomes larger with the increase of time delay. For another case, a strict comparison principle is proposed to prove that the impulsive system still maintains the original stability for any large but bounded delay under certain conditions. In particular, as an extension, the stability of delayed INNs for hybrid impulses containing both stabilizing and destabilizing impulses is also discussed. Finally, three examples are simulated to demonstrate the validity of the theoretical results.

Design and Practical Stability of a New Class of Impulsive Fractional-Like Neural Networks.

In this paper, a new class of impulsive neural networks with fractional-like derivatives is defined, and the practical stability properties of the solutions are investigated. The stability analysis exploits a new type of Lyapunov-like functions and their derivatives. Furthermore, the obtained results are applied to a bidirectional associative memory (BAM) neural network model with fractional-like derivatives. Some new results for the introduced neural network models with uncertain values of the parameters are also obtained.

Stability Analysis of Impulsive Neural Networks with Piecewise Constant Arguments

The global exponential stability problem is considered for a class of impulsive neural networks with piecewise constant arguments in this paper. By employing the Banach fixed point theorem and the Razumikhin-type technique, stability criterion is obtained for the existence, uniqueness and global exponential stability of the periodic solution. Typical numerical examples are given to illustrate the improvement in less conservatism of the results.

Delay-dependent passivity analysis of impulsive neural networks with time-varying delays

This paper investigates delay-dependent passivity for a class of impulsive neural networks with bounded or unbounded time-varying delays. By applying Lyapunov–Krasovskii functional and matrix inequality approach, some new delay-dependent passivity conditions are proposed in terms of the full use of the conditions of neuron activation functions and involved time-varying delays. These passivity conditions are presented in accordance with matrix inequalities, which can be easily verified via standard numerical software. Meanwhile, the results derived here include the existing relative results on the passivity for neural networks without impulse effects as special cases and can also be extended to other neural networks with more complex impulse disturbance. Finally, two numerical examples with simulations are given to demonstrate the effectiveness of the proposed criteria.

Existence and stability of periodic solution of impulsive neural systems with complex deviating arguments

This paper discusses a class of impulsive neural networks with the variable delay and complex deviating arguments. By using Mawhin's continuation theorem of coincidence degree and the Halanay-type inequalities, several sufficient conditions for impulsive neural networks are established for the existence and globally exponential stability of periodic solutions, respectively. Furthermore, the obtained results are applied to some typical impulsive neural network systems as special cases, with a real-life example to show feasibility of our results.

Global exponential stability of a class of impulsive neural networks with unstable continuous and discrete dynamics

This paper deals with global exponential stability of a class of impulsive neural networks whose continuous and discrete dynamics are unstable. Assuming that the impulsive neural network under consideration can be decomposed into two lower order impulsive systems, a time-varying weighted Lyapunov function associated with the impulse time sequence is introduced for stability analysis. A novel global exponential stability criterion is derived in terms of linear matrix inequalities (LMIs). By employing the newly obtained stability criterion, a sufficient condition on the existence of a reduced-order impulsive controller is derived. Unlike the previous results concerning impulsive control, the proposed reduced-order impulsive controller only exerts the impulses on a partial set of the state vector. Moreover, the controller gain matrices can be achieved by solving a set of LMIs. Finally, four illustrative examples are given to show the effectiveness of the developed techniques and results.

Existence, Uniqueness, and Stability Analysis of Impulsive Neural Networks with Mixed Time Delays

We study a class of impulsive neural networks with mixed time delays and generalized activation functions. The mixed delays include time-varying transmission delay, bounded time-varying distributed delay, and discrete constant delay in the leakage term. By using the contraction mapping theorem, we obtain a sufficient condition to guarantee the global existence and uniqueness of the solution for the addressed neural networks. In addition, a delay-independent sufficient condition for existence of an equilibrium point and some delay-dependent sufficient conditions for stability are derived, respectively, by using topological degree theory and Lyapunov-Krasovskii functional method. The presented results require neither the boundedness, monotonicity, and differentiability of the activation functions nor the differentiability (even differential boundedness) of time-varying delays. Moreover, the proposed stability criteria are given in terms of linear matrix inequalities (LMI), which can be conveniently checked by the MATLAB toolbox. Finally, an example is given to show the effectiveness and less conservativeness of the obtained results.

Globally Exponential Stability of Impulsive Neural Networks with Given Convergence Rate

This paper deals with the stability problem for a class of impulsive neural networks. Some sufficient conditions which can guarantee the globally exponential stability of the addressed models with given convergence rate are derived by using Lyapunov function and impulsive analysis techniques. Finally, an example is given to show the effectiveness of the obtained results.

Exponential stability and periodicity of impulsive cellular neural networks with time delays

This paper is concerned with the stability and periodicity for a class of impulsive neural networks with delays. By means of the Fixed point theory, Lyapunov functional and analysis technique, some sufficient conditions of exponential stability and periodicity are obtained. We can see that impulses do contribution to the stability and periodicity. An example is given to demonstrate the effectiveness of the obtained results.

Impulsive control for a class of neural networks with bounded and unbounded delays

In this paper, we study the problem of global exponential stability for a class of impulsive neural networks with bounded and unbounded delays and fixed moments of impulsive effect. We establish stability criteria by employing Lyapunov functions and Razumikhin technique. An illustrative example is given to demonstrate the effectiveness of the obtained results.