Stability Of Complex-valued Neural Networks Research Articles

Stability analysis for complex-valued neural networks with fractional order

In the context of complex-valued rectangular b-metric spaces, the present study investigates the stability of complex-valued neural networks (CVNNs) with fractional order. Using the generalized contraction principle, we address the suitable condition for uniform stability of fractionally ordered CVNNs and establish the existence and uniqueness of the equilibrium point. Few numerical results are presented to show the feasibility and correctness of the results presented.

Adaptive event-trigger-based sampled-data stabilization of complex-valued neural networks: a real and complex LMI approach

Adaptive event-trigger-based sampled-data stabilization of complex-valued neural networks: a real and complex LMI approach

Uniform Stability of Complex-Valued Neural Networks of Fractional Order With Linear Impulses and Fixed Time Delays.

As a generation of the real-valued neural network (RVNN), complex-valued neural network (CVNN) is based on the complex-valued (CV) parameters and variables. The fractional-order (FO) CVNN with linear impulses and fixed time delays is discussed. By using the sign function, the Banach fixed point theorem, and two classes of activation functions, some criteria of uniform stability for the solution and existence and uniqueness for equilibrium solution are derived. Finally, three experimental simulations are presented to illustrate the correctness and effectiveness of the obtained results.

Finite-time stabilization of complex-valued neural networks with proportional delays and inertial terms: A non-separation approach

This article mainly dedicates on the issue of finite-time stabilization of complex-valued neural networks with proportional delays and inertial terms via directly constructing Lyapunov functions without separating the original complex-valued neural networks into two real-valued subsystems equivalently. First of all, in order to facilitate the analysis of the second-order derivative caused by the inertial term, two intermediate variables are introduced to transfer complex-valued inertial neural networks (CVINNs) into the first-order differential equation form. Then, under the finite-time stability theory, some new criteria with less conservativeness are established to ensure the finite-time stabilizability of CVINNs by a newly designed complex-valued feedback controller. In addition, for reducing expenses of the control, an adaptive control strategy is also proposed to achieve the finite-time stabilization of CVINNs. At last, numerical examples are given to demonstrate the validity of the derived results.

具有反应扩散项的变时滞复数域神经网络的指数稳定性

The exponential stability of complex-valued neural networks with time-varying delays and reaction-diffusion terms was studied. Firstly, the addressed systems were separated into their real parts with the complex-valued activation functions assumed to be divided into the real parts and imaginary parts. Secondly, some sufficient conditions for ensuring the exponential stability of the equilibrium states of the systems were established based on the vector Lyapunov function method and the M-matrix theory. The obtained criteria have no free variables and reduced conservatism compared with the existing results. A numerical example proves the correctness of the obtained results.

A waiting-time-based event-triggered scheme for stabilization of complex-valued neural networks

This paper addresses the global stabilization of complex-valued neural networks (CVNNs) via event-triggered control. First, a waiting-time-based event-triggered scheme is designed to reduce the data transmission rate. Therein, an exponential decay term is introduced into the predefined threshold function, which may postpone the triggering instant of the necessary data and therefore reduce the frequency of data transmission. Then, with the help of the input delay approach, a time-dependent piecewise-defined Lyapunov–Krasovskii functional is constructed for closed-loop system to formulate a less conservative stability criterion. In addition, by resorting to matrix transformation, the co-design method for both the feedback gains and the trigger parameters is derived. Finally, a numerical example is given to illustrate the feasibility and superiority of the proposed event-triggered scheme and the obtained theoretical results.

Effects of leakage delay on global asymptotic stability of complex‐valued neural networks with interval time‐varying delays via new complex‐valued Jensen's inequality

SummaryThis paper investigates the global asymptotic stability analysis for a class of complex‐valued neural networks with leakage delay and interval time‐varying delays. Different from previous literature, some sufficient information on a complex‐valued neuron activation function and interval time‐varying delays has been considered into the record. A suitable Lyapunov‐Krasovskii functional with some delay‐dependent terms is constructed. By applying modern integral inequalities, several sufficient conditions are obtained to guarantee the global asymptotic stability of the addressed system model. All the proposed criteria are formulated in the structure of a complex‐valued linear matrix inequalities technique, which can be checked effortlessly by applying the YALMIP toolbox in MATLAB linear matrix inequality. Finally, two numerical examples with simulation results have been provided to demonstrate the efficiency of the proposed method.

Global Asymptotic Stability for Complex-Valued Neural Networks with Time-Varying Delays via New Lyapunov Functionals and Complex-Valued Inequalities

By constructing novel Lyapunov functionals and using some new complex-valued inequalities, a new LMI-based sufficient condition on global asymptotic stability of equilibrium point for complex-valued recurrent neural networks with time-varying delays is established. In our result, the assumption for boundedness in existing papers on the complex-valued activation functions is removed and the matrix inequalities used in recent papers are replaced with new matrix inequalities. On the other hand, we construct new Lyapunov functionals which are different from those constructed in existing papers. Hence, our result is less conservative, new and complementary to the previous results.

Global asymptotic stability of complex-valued neural networks with additive time-varying delays

In this paper, we extensively study the global asymptotic stability problem of complex-valued neural networks with leakage delay and additive time-varying delays. By constructing a suitable Lyapunov-Krasovskii functional and applying newly developed complex valued integral inequalities, sufficient conditions for the global asymptotic stability of proposed neural networks are established in the form of complex-valued linear matrix inequalities. This linear matrix inequalities are efficiently solved by using standard available numerical packages. Finally, three numerical examples are given to demonstrate the effectiveness of the theoretical results.

Global exponential stability of complex-valued neural networks with both time-varying delays and impulsive effects

In this paper, the global exponential stability of complex-valued neural networks with both time-varying delays and impulsive effects is discussed. By employing Lyapunov functional method and using matrix inequality technique, several sufficient conditions in complex-valued linear matrix inequality form are obtained to ensure the existence, uniqueness and global exponential stability of equilibrium point for the considered neural networks. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. The proposed stability results are less conservative than some recently known ones in the literatures, which is demonstrated via two examples with simulations.

Stability criterion of complex-valued neural networks with both leakage delay and time-varying delays on time scales

In this paper, the problem on the global exponential stability of complex-valued neural networks with both leakage delay and time-varying delays on time scales is discussed. By constructing appropriate Lyapunov–Krasovskii functionals and using matrix inequality technique, a delay-dependent condition to assure the global exponential stability for the considered neural networks is established. The condition is expressed in complex-valued linear matrix inequality, which can be checked numerically using the effective YALMIP toolbox in MATLAB. An example with simulations is given to show the effectiveness of the obtained result.

Further analysis of global [formula omitted]-stability of complex-valued neural networks with unbounded time-varying delays

In this paper, we consider the problem of global μ-stability for complex-valued neural networks (CVNNs) with unbounded time-varying delays and it has been widely investigated. Under mild conditions, some new sufficient conditions for global μ-stability of considered CVNNs are derived. Moreover, some new sufficient conditions are obtained to ensure the global μ-stability of CVNNs in the form of complex-valued LMIs as well as real-valued LMIs by using an appropriate Lyapunov–Krasovskii functional and linear matrix inequalities (LMIs). Both of complex-valued LMIs as well as real-valued LMIs are easily solved by using standard numerical algorithms. Finally, two numerical examples are presented to demonstrate the effectiveness and usefulness of our theoretical results.

Stability analysis of complex-valued neural networks with probabilistic time-varying delays

In this paper, the stability of complex-valued neural networks with probabilistic time-varying delays is investigated. Two important integral inequalities that include Jensen׳s inequality as a special case are developed. By constructing proper Lyapunov–Krasovskii functional and employing inequality technique, several delay-distribution-dependent sufficient conditions are obtained to guarantee the global asymptotic and exponential stability of the addressed neural networks. These conditions are expressed in terms of complex-valued LMIs, which can be checked numerically using the effective YALMIP toolbox in MATLAB. An example with simulations is given to show the effectiveness of the obtained results.

Complete Stability Analysis of Complex-Valued Neural Networks with Time Delays and Impulses

In this paper, we extensively study the analysis of complete stability of complex-valued neural networks with time delay and impulsive effects. Using stability theory, impulsive effects and by constructing appropriate Lyapunov---Krasovskii functional, some sufficient conditions for the existence and complete stability of complex-valued neural networks with time delay and impulsive effects are derived in the form of complex-valued linear matrix inequality (LMIs) as well as real-valued LMIs. Finally, four numerical examples are given to establish the effectiveness of our theoretical results via standard numerical software.

Exponential stability of complex-valued neural networks with mixed delays

This paper investigates the problem of the dynamic behaviors of a class of complex-valued neural networks with mixed time delays. Some sufficient conditions for assuring the existence, uniqueness and exponential stability of the equilibrium point of the system are derived using the vector Lyapunov function method, homeomorphism mapping lemma and the matrix theory. The obtained results not only are convenient to check, but also generalize the previously published corresponding results. A numerical example is used to show the effectiveness of the obtained results.

Boundedness and complete stability of complex-valued neural networks with time delay.

In this paper, the boundedness and complete stability of complex-valued neural networks (CVNNs) with time delay are studied. Some conditions to guarantee the boundedness of the CVNNs are derived using local inhibition. Moreover, under the boundedness conditions, a compact set that globally attracts all the trajectories of the network is also given. Additionally, several conditions in terms of real-valued linear matrix inequalities (LMIs) for complete stability of the CVNNs are established via the energy minimization method and the approach that converts the complex-valued LMIs to real-valued ones. Examples with simulation results are given to show the effectiveness of the theoretical analysis.

Global stability of complex-valued neural networks with both leakage time delay and discrete time delay on time scales

In this paper, the complex-valued neural networks with both leakage time delay and discrete time delay as well as two types of activation functions on time scales are considered. By using the fixed point theory, a criterion for checking the existence, uniqueness of the equilibrium point for the considered complex-valued neural networks is presented. By constructing appropriate Lyapunov–Krasovskii functionals, and employing the free weighting matrix method, several delay-dependent criteria for checking the global stability of the addressed complex-valued neural networks are established in linear matrix inequality (LMI), which can be checked numerically using the effective LMI toolbox in MATLAB. Three examples with simulations are given to show the effectiveness and less conservatism of the proposed criteria.

Global Stability of Complex-Valued Neural Networks on Time Scales

In this paper, activation dynamics of complex-valued neural networks are studied on general time scales. Besides presenting conditions guaranteeing the existence of a unique equilibrium pattern, its global exponential stability is discussed. Some numerical examples for different time scales are given in order to highlight the results.