Stability Of Inertial Neural Networks Research Articles

Finite-Time Stability of Inertial Neural Networks with Delayed Impulses

This paper studies the finite-time stability (FTS) of the inertial neural networks (INNs) with delayed impulses. Unlike previous related works, we consider the delayed impulses and propose a new impulsive control strategy. We extend the existing FTS results to the cases with delayed impulses. We also establish some global and local FTS criteria of INNs. Moreover, we estimate the settling-time in different cases and investigate the optimization strategy. We present three numerical examples to verify the validity of our theoretical results.

A new method to study global exponential stability of inertial neural networks with multiple time-varying transmission delays

In this article, the global exponential stability (GES) of inertial neural networks (INNs) are directly analyzed by proposing a new parameterized method. The parameterized representations of the states of neurons and their derivatives in the considered INNs are first given by introducing the relevant parameters. Furthermore, the sufficient conditions for the GES of the considered INNs are obtained by using the inequality technique. The obtained stability conditions consist of only a few simple linear scalar inequalities (LSIs) which are convenient to solve. Different from the previous works, the derived GES criteria do not involve any model transformation and any Lyapunov–Krasovskii functional (LKF), which reduces the computational complexity and simplifies the theoretical analysis. The last, a numerical simulation is presented to demonstrate the effectiveness of proposed parameterized method.

Existence, Uniqueness, and Exponential Stability of Uncertain Delayed Neural Networks with Inertial Term: Nonreduced Order Case

In this work, we mainly focus on uncertain delayed neural network system with inertial term. Here, the existence, uniqueness, and exponential stability of inertial neural networks are derived without shifting the second order differential system into first order through substituting variables. Initially, we construct a proper Lyapunov–Krasovskii functional to investigate the stability of novel uncertain delayed inertial neural networks, which is different from the classical Lyapunov functional approach. By utilizing the Kirchhoff’s matrix tree theorem, Cauchy–Schwartz inequality, homeomorphism theorem, and some inequality techniques, the necessary and sufficient conditions are derived for the designed framework. Subsequently, to exhibit the strength of this outcome, we framed a quantitative example.

New findings on global exponential stability of inertial neural networks with both time-varying and distributed delays

ABSTRACT In this manuscript, inertial neural networks with both time- varying and distributed delays are studied. Applying inequality techniques and Lyapunov function approach, a new sufficient condition that guarantees the existence and exponential stability of periodic solutions for the addressed networks is presented. The obtained results supplement some earlier publications that deal with the periodic solutions of inertial neural networks with time- varying delays. Computer simulations are displayed to check the derived analytical results.

Delay-dependent criteria for periodicity and exponential stability of inertial neural networks with time-varying delays

This paper mainly studies the periodicity and exponential stability for a class of inertial neural networks (INNs) with time-varying delays. Without utilizing standard reduced-order transformation, by using the continuation theorem and Cauchy–Schwarz inequality, delay-dependent criteria shown by some algebraic inequalities are derived to ensure the existence of periodic solutions. Furthermore, by means of the fundamental inequality and constructing a modified delay-dependent Lyapunov functional, global exponential stability analysis is obtained based on the derived delay-dependent criteria. In comparison with the reduced order approach applied to the INNs and delay-independent criteria provided for the INNs in the existed literatures, the results obtained in this paper are new. Finally, numerical simulations are carried out to verify the main results.

Effect of fuzziness on the stability of inertial neural networks with mixed delay via non-reduced-order method

ABSTRACTIn this paper, without transforming the original inertial neural networks into the first-order differential equation by some variable substitutions, fuzziness, time-varying and distributed delays are introduced into inertial networks and the existence, the uniqueness and the asymptotic stability for the neural networks are investigated. The existence of a unique equilibrium point is proved by using inequality techniques, and the properties of an M-matrix. By finding a new Lyapunov–Krasovskii functional, some sufficient conditions are derived ensuring the asymptotic stability. Finally, three numerical examples with simulation are presented to show the effectiveness of our theoretical results.

Exponential stability of inertial neural networks involving proportional delays and non-reduced order method

ABSTRACTThis paper studies a class of inertial neural networks involving proportional delays. Without adopting reduced order method, by combining Lyapunov function method with differential inequality approach, some novel assertions are gained to validate the global generalised exponential stability of the addressed model, which are new and complement some previous works. In the end, some examples with their numerical simulations are carried out to substantiate the correctness of the theoretical findings.

Robust delay-dependent stability of uncertain inertial neural networks with impulsive effects and distributed-delay

The robust stability problem of uncertain inertial neural networks with impulsive effects and distributed-delay is considered in the present paper. The average impulsive interval and differential inequality for delay differential equations are used to obtain the global exponential stability of the inertial neural networks. The robust distributed-delay-dependent stability criteria here are proposed in terms of both linear matrix inequalities and algebraic inequalities. Our results can not only be used to obtain the stability of the uncertain inertial neural network with impulsive disturbance, but also be utilized to design the impulsive control for the uncertain inertial neural networks. The novel criteria complement and extend the previous works on uncertain inertial neural network with/without impulsive effects. Typical numerical examples are used to test the validity of the developed stability criteria finally.

Global asymptotic and robust stability of inertial neural networks with proportional delays

This paper is concerned with the global asymptotic stability and global robust stability of inertial neural networks with proportional delays. First, by using linear matrix inequality and constructing appropriate Lyapunov functional, several sufficient conditions are obtained for the global asymptotic stability of inertial neural networks with proportional delays. Furthermore, the problem of global robust stability of the network under the assumptions that the network parameters are uncertain and bounded is studied. Finally, some simulation examples are presented to demonstrate the effectiveness of the proposed method.

Global Lagrange stability for inertial neural networks with mixed time-varying delays

This paper concerns with the global Lagrange stability of inertial neural networks with discrete and distributed time-varying delays. By choosing a proper variable substitution, the inertial neural networks can be rewritten as a first-order differential system. Based on the Lyapunov functional method, inequality techniques and analytical method, several sufficient conditions are derived to guarantee the global exponential stability of the inertial neural networks in Lagrange sense. Meanwhile, the global exponential attractive set is also given. Simulation results demonstrate the effectiveness of the theoretical results.