Leakage Delay Research Articles

Stability Analysis for Stochastic Markovian Jumping Neural Networks with Leakage Delay

The stability problem for a class of stochastic neural networks with Markovian jump parameters and leakage delay is addressed in this study. The sufficient condition to ensure an exponentially stable stochastic neural networks system is presented and proven with Lyapunov functional theory, stochastic stability technique and linear matrix inequality method. The effect of leakage delay on the stability of the neural networks system is discussed and numerical examples are provided to show the correctness and effectiveness of the research results .

Stochastic H∞ filtering for neural networks with leakage delay and mixed time-varying delays

This paper deals with the problem of H∞ filtering for stochastic neural networks (SNNs) with a mixed of time-varying interval delays, time-varying distributed delays, and leakage delays. A novel quintuple integral Lyapunov–Krasovskii functional (LKF) is constructed to improve the performance of the SNN. Sufficient criteria can be obtained by applying the linear matrix inequality (LMI) approach and developing a new mathematical analysis, which ensures the filtering error system is asymptotically stable in the mean square. Finally, simulation results are provided to show the superiority and usefulness of the proposed method.

Adaptive Exponential Synchronization for Stochastic Competitive Neural Networks with Time-Varying Leakage Delays and Reaction-Diffusion Terms

We study the exponential synchronization problem for a class of stochastic competitive neural networks with different timescales, as well as spatial diffusion, time-varying leakage delays, and discrete and distributed time-varying delays. By introducing several important inequalities and using Lyapunov functional technique, an adaptive feedback controller is designed to realize the exponential synchronization for the proposed competitive neural networks in terms of p-norm. According to the theoretical results obtained in this paper, the influences of the timescale, external stimulus constants, disposable scaling constants, and controller parameters on synchronization are analyzed. Numerical simulations are presented to show the feasibility of the theoretical results.

Robust stability of uncertain Markovian jump neural networks with mode-dependent time-varying delays and nonlinear perturbations

In this paper, the problem of delay-dependent stability is investigated for uncertain Markovian jump neural networks with leakage delay, two additive time-varying delay components, and nonlinear perturbations. The Markovian jumping parameters in the connection weight matrices and two additive time-varying delay components are assumed to be different in the system model, and the Markovian jumping parameters in each of the two additive time-varying delay components are also different. The relationship between the time-varying delays and their upper delay bounds is efficiently utilized to study the suggested system in two cases: with known or unknown parameters, which leads to more information of the lower and upper bounds of the time-varying delays that can be used. By constructing a newly augmented Lyapunov-Krasovskii functional and using the extended Wirtinger inequality and a reciprocally convex method, several sufficient criteria are derived to guarantee the stability of the proposed model. Numerical examples and their simulations are given to show the effectiveness and advantage of the proposed method.

Pseudo Almost Periodic Solutions for High-Order Hopfield Neural Networks with Time-Varying Leakage Delays

In this paper, high-order Hopfield neural networks with time-varying leakage delays are investigated. By applying Lyapunov functional method and differential inequality techniques, a set of sufficient conditions are obtained for the existence and exponential stability of pseudo almost periodic solutions of the model. Some simulations are carried out to support the theoretical findings. Our results improve and generalize those of the previous studies.

Robust stability analysis for uncertain recurrent neural networks with leakage delay based on delay-partitioning approach

This paper focuses on the issue of robust stability analysis for recurrent neural networks (RNNs) with leakage delay. By constructing a novel Lyapunov–Krasovskii functional together with the reciprocally convex approach and the free-weighting matrix technique, some less conservative stability criteria in terms of linear matrix inequalities for RNNs are derived. The new contribution of this paper is that a novel delay-partitioning method is proposed, and some new zero equalities are introduced. Finally, several examples are given to demonstrate the effectiveness of the proposed methods. The simulated results reveal that the leakage delay has great influence on the dynamical systems, and it cannot be neglected.

Further results on passivity analysis of delayed neural networks with leakage delay

This paper is concerned with the passivity problem for neural networks with leakage delay and time-varying transmission delay. Using some novel Lyapunov-Krasovskii (L-K) functionals, and combining with the Wirtinger integral inequality, some less conservative delay-dependent passivity conditions are proposed in terms of linear matrix inequalities (LMIs). Different from the existing approaches, the model transformation is abandoned in this paper, and the proposed L-K functionals incorporate the interconnected terms related to both the leakage delay and the time-varying delay. Numerical examples show that the obtained conditions are less conservative.

Power delay optimization of nanoscale 4×1 multiplexer using CMOS based voltage doubler circuit

This paper represents a low leakage, highly efficient and delay improved 4×1 MUX with MOS based voltage doubler circuit cum augmented sleep transistors MOS configuration with nanoscale structure. The unique newly designed voltage doubler circuit is implemented as an additional circuit at the output of the implemented proposed design to step-up the voltage. It means that the output peak voltage is doubled due to the transient of both positive and negative cycles. This stepped-up voltage may be exploited as a stabilized supply for specific applications. The voltage doubler circuit is not enough to improve the overall performance of proposed 4×1 MUX design. In order to integrate the optimization criterion of leakage power and delay performance, the voltage doubler circuit is utilized along with the MOS configuration of augmented sleep transistors. To minimize the parameter of leakage power dissipation the MOS based voltage doubler circuit cum augmented sleep transistors MOS configuration is introduced. This will mitigate the redundant unused leakage power dissipation of the circuit. This additional circuitry brings out the aspired level of output voltage for the proposed and implemented 4×1 MUX with better performance parameters. The whole simulation has been done for the 45 nm technology. It is finally summarized that the leakage power dissipation is minimized up to 55% just around and the delay performance is also improved up to a desired level due to the utilization of MOS based voltage doubler circuit with the MOS configuration of augmented sleep transistors. In this paper, different combinations of MOS based augmented voltage doubler circuit implemented at the output of 4×1 MUX are represented.

Exponential stability for fuzzy BAM cellular neural networks with distributed leakage delays and impulses

This paper is concerned with a class of fuzzy BAM cellular neural networks with distributed leakage delays and impulses. By applying differential inequality techniques, we establish some sufficient conditions which ensure the exponential stability of such fuzzy BAM cellular neural networks. An example is given to illustrate the effectiveness of the theoretical results. The results obtained in this article are completely new and complement the previously known studies.

Existence and Global Exponential Stability of Almost Periodic Solutions for Shunting Inhibitory Cellular Neural Networks with Distributed Leakage Delays on Time Scales

In this paper, we deal with a class of shunting inhibitory cellular neural networks (SICNNs) with distributed leakage delays on time scales. Some sufficient conditions which ensure the existence and exponential stability of almost periodic solutions for such class of SICNNs are obtained by applying the exponential dichotomy of linear differential equations, Lapunov functional method and contraction mapping principle. An example is given to illustrate the effectiveness of the theoretical results. The results obtained in this paper are completely new and complement the previously known studies.

Further Results on Dissipativity Criterion for Markovian Jump Discrete-Time Neural Networks with Two Delay Components Via Discrete Wirtinger Inequality Approach

This paper is concerned with strict $$(\mathcal {Q}, \mathcal {S}, \mathcal {R})-\gamma $$(Q,S,R)-? - dissipativity and passivity analysis for discrete-time Markovian jump neural networks involving both leakage and discrete delays expressed in terms of two additive time-varying delay components. The discretized Wirtinger inequality is utilized to bound the forward difference of finite-sum term in the Lyapunov functional. By constructing a suitable Lyapunov---Krasovskii functional, sufficient conditions are derived to guarantee the dissipativity and passivity criteria of the proposed neural networks. These conditions are presented in terms of linear matrix inequalities (LMIs), which can be efficiently solved via LMI MATLAB Toolbox. Finally, numerical examples are given to illustrate the effectiveness of the proposed results.

Dissipativity and passivity analysis for discrete‐time complex‐valued neural networks with leakage delay and probabilistic time‐varying delays

SummaryIn this paper, the problem of dissipativity and passivity analysis is investigated for discrete‐time complex‐valued neural networks with time‐varying delays. Both leakage and discrete time‐varying delays have been considered. By constructing a suitable Lyapunov–Krasovskii functional and by using discretized Jensen's inequality approach, sufficient conditions have been established to guarantee the (Q,S,R) − γ dissipativity and passivity of the addressed discrete‐time complex‐valued neural networks. These conditions are derived in terms of complex‐valued linear matrix inequalities (LMIs), which can be checked numerically using Yet Another LMI Parser toolbox in Matrix Laboratory. Finally, three numerical examples are established to illustrate the effectiveness of the obtained theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.

On the periodic dynamics of memristor-based neural networks with leakage and time-varying delays

In this paper, the periodic dynamics have been studied for a general kind of memristor-based neural networks with leakage and time-varying delays. Some new sufficient conditions have been derived ensuring that the existence, uniqueness and globally exponential stability of the periodic solution for the neural network by using differential inclusions theory, the topological degree theory in set-valued analysis and Lyapunov function technique and so on. As a special case, we have shown that the existence, uniqueness and global exponential stability of equilibrium point for the autonomous neural networks with leakage delays.

Exponential Stability of Almost Periodic Solutions for Memristor-Based Neural Networks with Distributed Leakage Delays.

In this letter, we deal with a class of memristor-based neural networks with distributed leakage delays. By applying a new Lyapunov function method, we obtain some sufficient conditions that ensure the existence, uniqueness, and global exponential stability of almost periodic solutions of neural networks. We apply the results of this solution to prove the existence and stability of periodic solutions for this delayed neural network with periodic coefficients. We then provide an example to illustrate the effectiveness of the theoretical results. Our results are completely new and complement the previous studies Chen, Zeng, and Jiang ( 2014 ) and Jiang, Zeng, and Chen ( 2015 ).

A study on state estimation for discrete-time recurrent neural networks with leakage delay and time-varying delay

We investigate state estimation for a class of discrete-time recurrent neural networks with leakage delay and time-varying delay. The design method for the state estimator to estimate the neuron states through available output measurements is given. A novel delay-dependent sufficient condition is obtained for the existence of state estimator such that the estimation error system is globally asymptotically stable. Based a novel double summation inequality and reciprocally convex approach, an improved stability criterion is obtained for the error-state system. Two numerical examples are given to demonstrate the effectiveness of the proposed design methods. The simulation results show that the leakage delay has a destabilizing influence on a neural network system.

Sampled-Data Stabilization for Fuzzy Genetic Regulatory Networks with Leakage Delays.

This paper deals with the sampled-data stabilization problem for Takagi-Sugeno (T-S) fuzzy genetic regulatory networks with leakage delays. A novel Lyapunov-Krasovskii functional (LKF) is established by the non-uniform division of the delay intervals with triplex and quadruplex integral terms. Using such LKFs for constant and time-varying delay cases, new stability conditions are obtained in the T-S fuzzy framework. Based on this, a new condition for the sampled-data controller design is proposed using a linear matrix inequality representation. A numerical result is provided to show the effectiveness and potential of the developed design method.

Neutral impulsive shunting inhibitory cellular neural networks with time-varying coefficients and leakage delays.

In this article, we consider a class of neutral impulsive shunting inhibitory cellular neural networks with time varying coefficients and leakage delays. We study the existence and the exponential stability of the piecewise differentiable pseudo almost-periodic solutions and establish sufficient conditions for the existence and exponential stability of such solutions. An example is provided to illustrate the theory developed in this work.

Oscillation of impulsive neutral delay generalized high-order Hopfield neural networks

In this paper, the existence and the exponential stability of piecewise differentiable pseudo-almost periodic solutions for a class of impulsive neutral high-order Hopfield neural networks with mixed time-varying delays and leakage delays are established by employing the fixed point theorem, Lyapunov functional method and differential inequality. Numerical example with graphical illustration is given to illuminate our main results.

Passivity analysis of stochastic neural networks with leakage delay and Markovian jumping parameters

The problem of passivity analysis of stochastic neural networks with leakage delay and Markovian jumping parameters is considered in this article. By utilizing the Lyapunov functional method, the Itô differential rule and matrix analysis techniques, we establish sufficient criterion such that the stochastic neural networks is passive in the sense of expectation. The derived criteria are expressed in terms of linear matrix inequalities that can be easily checked by using the standard numerical software. Illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed results.

Piecewise Pseudo Almost Periodic Solution for Impulsive Generalised High-Order Hopfield Neural Networks with Leakage Delays

Existence of piecewise differentiable pseudo almost-periodic solutions for a class of impulsive high-order Hopfield neural networks with leakage delays are established by employing the fixed point theorem, differential inequality and Lyapunov functionals. The results of this paper are new and they supplement previously known works. Numerical example with graphical illustration is given to illuminate our main results.