Linear Convex Combination Technique Research Articles

Synchronization of delayed memristive neural networks by establishing novel Lyapunov functional

This paper inquires into the synchronization for delayed chaotic memristive neural networks. First, a novel criterion is proposed to determine whether a quadratic function is negative or not on a closed interval without regard for its convexity or concavity. Then, a novel Lyapunov functional is established which is based on Chen et al.’s integral inequalities. Next, by applying Moon et al.’s inequality, Chen et al.’s integral inequalities, linear convex combination technique and the novel criterion, two novel delay-dependent criteria are presented to realize the global asymptotical synchronization for the chaotic memristive neural networks. Finally, an example is given out to explain the effectiveness of the theoretical results.

Stochastic stability of fuzzy Markovian jump neural networks by multiple integral approach

PurposeThe purpose of this paper is to develop a methodology for the stochastically asymptotic stability of fuzzy Markovian jumping neural networks with time-varying delay and continuously distributed delay in mean square.Design/methodology/approachThe authors perform Briat Lemma, multiple integral approach and linear convex combination technique to investigate a class of fuzzy Markovian jumping neural networks with time-varying delay and continuously distributed delay. New sufficient criterion is established by linear matrix inequalities conditions.FindingsIt turns out that the obtained methods are easy to be verified and result in less conservative conditions than the existing literature. Two examples show the effectiveness of the proposed results.Originality/valueThe novelty of the proposed approach lies in establishing a new Wirtinger-based integral inequality and the use of the Lyapunov functional method, Briat Lemma, multiple integral approach and linear convex combination technique for stochastically asymptotic stability of fuzzy Markovian jumping neural networks with time-varying delay and continuously distributed delay in mean square.

Novel stability conditions of fuzzy neural networks with mixed delays under impulsive perturbations

This paper investigates the problem of stability of fuzzy neural networks with time-varying and continuously distributed delays under impulsive perturbations. Two new delay-dependent criteria are obtained in terms of linear convex combination technique, the reciprocal convex lemma, Wirtinger-based integral inequality, and the quadratic convex combination method. The first presented criterion does not require all the symmetric matrices involved in the employed quadratic Lyapunov–Krasovskii functional to be positive definite. Furthermore, the conservatism of delay-dependent stability conditions can be reduced due to the relaxation on the positive-definiteness of some Lyapunov matrices. It is shown numerically that the stability criteria proposed in this paper are less conservative than some of the latest results in the literature.

On synchronization for chaotic memristor-based neural networks with time-varying delays

This paper investigates the synchronization problem for chaotic memristor-based neural networks with time-varying delays. First, a novel lemma is proposed to deal with the switching jump parameters. Then, a novel inequality is established which is a multiple integral form of the Wirtinger-based integral inequality. Next, by applying the reciprocally convex combination approach, linear convex combination technique, auxiliary function-based integral inequalities and a free-matrix-based inequality, several novel delay-dependent conditions are established to achieve the globally asymptotical synchronization for the chaotic memristor-based neural networks. Finally, a numerical example is provided to demonstrate the effectiveness of the theoretical results.

Stochastic synchronization of neutral-type chaotic impulse neural networks with leakage delay and Markovian jumping parameters

Purpose The purpose of this paper is to develop a methodology for the stochastically asymptotic synchronization problem for a class of neutral-type chaotic neural networks with both leakage delay and Markovian jumping parameters under impulsive perturbations. Design/methodology/approach The authors perform drive-response concept and time-delay feedback control techniques to investigate a class of neutral-type chaotic neural networks with both leakage delay and Markovian jumping parameters under impulsive perturbations. New sufficient criterion is established without strict conditions imposed on the activation functions. Findings It turns out that the approach results in new sufficient criterion easy to be verified but without the usual assumption of the differentiability and monotonicity of the activation functions. Two examples show the effectiveness of the obtained results. Originality/value The novelty of the proposed approach lies in removing the usual assumption of the differentiability and monotonicity of the activation functions, and the use of the Lyapunov functional method, Jensen integral inequality, a novel Gu’s lemma, reciprocal convex and linear convex combination technique for the stochastically asymptotic synchronization problem for a class of neutral-type chaotic neural networks with both leakage delay and Markovian jumping parameters under impulsive perturbations.

Mode and Delay-dependent Stochastic Stability Conditions of Fuzzy Neural Networks with Markovian Jump Parameters

This paper investigates the stochastic stability of fuzzy Markovian jumping neural networks with time-varying delay and continuously distributed delay in mean square. By using the reciprocal convex combination approach, Jensen and Jensen-type integral inequality, linear convex combination technique and the free-weight matrix method, several novel mode and delay-dependent sufficient conditions are derived to ensure the stochastic stability of the equilibrium point of the considered networks in mean square. The proposed results can be easily checked via Matlab software. Finally, two numerical examples are given to demonstrate the effectiveness and less conservativeness of our theoretical results over existing literature.

Mode-dependent stochastic stability criteria of fuzzy Markovian jumping neural networks with mixed delays

This paper investigates the stochastic stability of fuzzy Markovian jumping neural networks with mixed delays in mean square. The mixed delays include time-varying delay and continuously distributed delay. By using the Lyapunov functional method, Jensen integral inequality, the generalized Jensen integral inequality, linear convex combination technique and the free-weight matrix method, several novel sufficient conditions are derived to ensure the global asymptotic stability of the equilibrium point of the considered networks in mean square. The proposed results, which do not require the differentiability of the activation functions, can be easily checked via Matlab software. Finally, two numerical examples are given to demonstrate the effectiveness and less conservativeness of our theoretical results over existing literature.

Novel stability condition of stochastic fuzzy neural networks with Markovian jumping under impulsive perturbations

For the first time, this paper investigates the global asymptotic stability of stochastic fuzzy neural networks with mixed delays and Markovian jumping under impulsive perturbations in mean square. The mixed delays include time-varying delay and continuously distributed delay. By using stochastic analysis method, linear convex combination technique, Jensen integral inequality and the free-weight matrix method, a novel sufficient condition is derived to ensure the global asymptotic stability of the equilibrium point of the considered networks in mean square. The proposed result, which is expressed in terms of linear matrix inequalities, can be easily checked via Matlab software. Finally, a numerical example is given to demonstrate the effectiveness and less conservativeness of our theoretical results over existing literature.

New stability results of neutral-type neural networks with continuously distributed delays and impulses

This paper studies the globally asymptotic stability of neutral-type impulsive neural networks with discrete and bounded continuously distributed delays. By using the Lyapunov functional method, quadratic convex combination approach, a novel Gu's Lemma, Jensen integral inequality and linear convex combination technique, several novel sufficient conditions are derived to ensure the globally asymptotic stability of the equilibrium point of the networks. The proposed results, which do not require the differentiability and monotonicity of the activation functions, can be easily checked via Matlab software. Finally, two numerical examples are given to demonstrate the effectiveness of our theoretical results.

Stability analysis of stochastic fuzzy Markovian jumping neural networks with leakage delay under impulsive perturbations

This paper investigates the global asymptotic stability of stochastic fuzzy Markovian jumping neural networks with mixed delays under impulsive perturbations in mean square. The mixed delays include constant delay in the leakage term (i.e., “leakage delay”), time-varying delay and continuously distributed delay. By using the Lyapunov functional method, reciprocal convex approach, linear convex combination technique, Jensen integral inequality and the free-weight matrix method, several novel sufficient conditions are derived to ensure the global asymptotic stability of the equilibrium point of the considered networks in mean square. The proposed results, which do not require the differentiability and monotonicity of the activation functions, can be easily checked via Matlab software. Finally, two numerical examples are given to demonstrate the effectiveness and less conservativeness of our theoretical results over existing literature.

Global Stability of Fuzzy Cellular Neural Networks with Mixed Delays and Leakage Delay Under Impulsive Perturbations

This paper investigates the global asymptotic stability of a kind of fuzzy cellular neural networks with mixed delays under impulsive perturbations. The mixed delays include constant delay in the leakage term (i.e., “leakage delay”), time-varying delays, and continuously distributed delays. By using the quadratic convex combination method, reciprocal convex approach, Jensen integral inequality, and linear convex combination technique, several novel sufficient conditions are derived to ensure the global asymptotic stability of the equilibrium point of the considered networks. The proposed results, which do not require the differentiability and monotonicity of the activation functions, can be easily checked via Matlab software. Finally, two numerical examples are given to demonstrate the effectiveness and less conservativeness of our theoretical results over existing literature.