Leakage Delay Research Articles

Anti-synchronization of fractional-order complex-valued neural networks with a leakage delay and time-varying delays

In this paper, the anti-synchronization for fractional-order complex-valued neural networks (FCVNNs) with a leakage delay and time-varying delays is investigated. The solution of a fractional-order differential inequality is considered. By using the Laplace transform and the inverse Laplace transform, a new inequality is proved, which provides an important tool for studying the anti-synchronization of the FCVNNs with delays. Two different types of controllers are designed. Based on this new inequality and some inequality techniques, several sufficient conditions are obtained to ensure the anti-synchronization of the FCVNNs with a leakage term and time-varying delays. Finally, two numerical examples are presented to illustrate the validity and feasibility of the main results.

Weighted Pseudo Almost Periodic Synchronization for Clifford-Valued Neural Networks with Leakage Delay and Proportional Delay

Weighted Pseudo Almost Periodic Synchronization for Clifford-Valued Neural Networks with Leakage Delay and Proportional Delay

Fixed-Time Stabilization of Leakage-Delayed Neural Networks Modeled by Delayed Filippov Systems: Leakage-Delay-Dependent Settling-Time

This paper considers the periodicity and fixed-time stabilization of discontinuous neural networks with time-varying leakage and discrete delays, which is more general. Before considering the stability, the existence of periodic solutions in the sense of Filippov should be proved. So, firstly, based on the set-valued mapping, coincidence theorem, Hölder inequality and supremum-infimum principle, the investigation on the leakage-delay-dependent periodic solutions is obtained, which can not only complement the periodic solutions of leakage-delayed neural networks, but also is absolutely different from the almost-periodic solution results. Secondly, by virtue of the integral inequality, new fixed-time stability lemmas of Filippov systems are established, which involve more relaxed assumptions and do not need to input extra parameters. Thirdly, leakage-delay-dependent results on fixed-time stabilization of the proposed neural networks are established via the new fixed-time stability lemmas under modified non-chattering control laws. It is worth mentioning that the settling-times are relevant to the leakage delays, which have not been reported in the literature. Finally, the validity of the proposed results is demonstrated by two numerical examples.

Exponential Stability of a Class of Neutral Inertial Neural Networks with Multi-Proportional Delays and Leakage Delays

This paper investigates the exponential stability of a class of neutral inertial neural networks with multi-proportional delays and leakage delays. By utilizing the Lyapunov stability theory, the approach of parametric variation, and the differential inequality technique, some criteria are acquired that can guarantee that all solutions of the addressed system converge exponentially to the equilibrium point. In particular, the neutral term, multi-proportional delays, and leakage delays are incorporated simultaneously, resulting in a more general model, and the findings are novel and refine the previous works. Finally, one example is provided to indicate that the dynamic behavior is consistent with the theoretical analysis.

A hybrid trigger strategy based mixed impulsive control scheme on uncertain local field neural networks with leakage delay

Solved in this paper is the stabilization of uncertain local field neural networks (ULFNNs) with leakage delay by dint of a mixed impulsive control scheme. The impulsive control instants are decided by a Lyapunov functional-based event triggered scheme and a periodic impulse triggered scheme. Based on the proposed control scheme, sufficient conditions are deduced for eliminating the Zeno behavior and guaranteeing the uniform asymptotic stability (UAS) of the delayed ULFNNs in the framework of Lyapunov functional analysis method. Different from individual event triggered impulse control strategy where the triggered instants may be unexpected, the mixed impulsive control scheme can release the impulse control instants in line with the distance between any two adjacent successful control points, which improves the control performance and also achieves the goal of saving the communication resource. Furthermore, the decay behavior of impulse control signal is considered to make mathematical derivation more practical, and based on this behavior, a criterion is derived to make ensure the exponential stability of delayed ULFNNs. Finally, numerical examples are given to illustrate the effectiveness of the designed controller for the ULFNNs with leakage delay.

Fixed-time stabilization of generalized leakage-delayed neural networks with discontinuous disturbances via mixed-delay-product-type LKF

In this paper, a class of generalized leakage-delayed neural networks with discontinuous disturbances is studied. Due to nonlinearity of the considered neural system, the existence of solutions should be verified. So, by applying the differential inclusion theory and fixed-point theorems of set-valued map, the existence and multiplicity of periodic solutions are proved firstly. Then, by a new designed non-chattering control law without delay terms, the fixed-time stabilization of the error system formulated by the addressed master-slave leakage-delayed neural networks is achieved via mixed-delay-product-type LKF, which is different from the previous related ones. Moreover, the new established result on the fixed-time stabilization is dependent on the leakage delays, which further implies that the leakage delays can affect the stability of the real system. Finally, one example examines the correctness of the main results.

Detections of bifurcation in a fractional-order Cohen-Grossberg neural network with multiple delays.

The dynamics of integer-order Cohen-Grossberg neural networks with time delays haslatelydrawn tremendous attention. It reveals that fractional calculus plays a crucial role oninfluencing the dynamical behaviors of neural networks(NNs). This paper deals with the problem of the stability and bifurcation of fractional-order Cohen-Grossberg neural networks (FOCGNNs) with two different leakage delay and communication delay. The bifurcation results with regard to leakage delay are firstly gained. Then, communication delay is viewed as a bifurcation parameter to detect the critical values of bifurcations for the addressed FOCGNN, and the communication delay induced-bifurcation conditions are procured. We further discover that fractional orders can enlarge(reduce) stability regions of the addressed FOCGNN. Furthermore, we discover that, for the same system parameters, the convergence time to the equilibrium point of FONN is shorter(longer) than that of integer-order NNs. In this paper, the present methodology to handle the characteristic equation with triple transcendental terms in delayed FOCGNNs is concise, neoteric and flexible in contrast with the prior mechanisms owing to skillfullykeeping away from theintricate classified discussions. Eventually, the developedanalyticresults are nicelyshowcased by the simulation examples.

Finite-Time State Estimation of Switched Neural Networks with Both Time-Varying Delays and Leakage Delay

In this thesis, we deal with the issues of the finite-time state estimation (FTSE) for a set of switched neural networks (SNNs), in which the hybrid effects of time-varying delays and leakage delay are taken into consideration. Therefore, the model of SNNs under discussion is quite comprehensive and more practical. In the light of an applicable piecewise Lyapunov-Krasovskii (L-K) functional which has double integral terms, some novel sufficient criteria are put forward with the average dwell time (ADT) technique, so that the estimation error system is finite-time boundedness (FTB). It is crucial to notice that the estimation results in our work are time-delay dependent, which depend on the leakage delay as well as the upper bound of the time-varying delays. The results show that the unknown gain matrix of the state estimator is achieved by solving a series of linear matrix inequalities (LMIs), which can be effortlessly tested with the MATLAB Toolbox. Moreover, by combining with free weight matrix method in the proof process, the results we obtained do not require the differentiability of time-varying delays any more, which is less conservative than some existing results. Finally, an example is performed with its numerical simulations to corroborate the efficiency of the theoretical results.

Sliding-Mode Synchronization Control of Complex-Valued Inertial Neural Networks With Leakage Delay and Time-Varying Delays

This work explores the synchronization problem of two nonidentical complex-valued inertial neural networks (CVINNs) considering time-varying delays, leakage delay, and external disturbances. The entire analysis does not use reduced-order conversion, nor does it involve the separation of real and imaginary parts, but directly focuses on the original system. First, an integral sliding-mode surface suitable for the system is proposed. Second, the efficient sliding-mode control laws are designed, under which the state trajectories of the closed-loop dynamic error systems can be driven onto the predefined sliding-mode surface in finite time. Then, not requiring the time-varying delays to be differentiable, by constructing innovative Lyapunov–Krasovskii functionals, the synchronization criteria are obtained in the forms of the linear matrix inequality techniques. Eventually, for the systems with different types of activation functions, the corresponding numerical verification and comparison are carried out.

Cluster synchronization of coupled complex-valued neural networks with leakage and time-varying delays in finite-time

<abstract><p>In cluster synchronization (CS), the constituents (i.e., multiple agents) are grouped into a number of clusters in accordance with a function of nodes pertaining to a network structure. By designing an appropriate algorithm, the cluster can be manipulated to attain synchronization with respect to a certain value or an isolated node. Moreover, the synchronization values among various clusters vary. The main aim of this study is to investigate the asymptotic and CS problem of coupled delayed complex-valued neural network (CCVNN) models along with leakage delay in finite-time (FT). In this paper, we describe several sufficient conditions for asymptotic synchronization by utilizing the Lyapunov theory for differential systems and the Filippov regularization framework for the realization of finite-time synchronization of CCVNNs with leakage delay. We also propose sufficient conditions for CS of the system under scrutiny. A synchronization algorithm is developed to indicate the usefulness of the theoretical results in case studies.</p></abstract>

Weighted pseudo almost periodic solutions of octonion-valued neural networks with mixed time-varying delays and leakage delays

<abstract><p>In this paper, we propose a class of octonion-valued neural networks with leakage delays and mixed delays. Considering that the multiplication of octonion algebras does not satisfy the associativity and commutativity, we can obtain the existence and global exponential stability of weighted pseudo almost periodic solutions for octonion-valued neural networks with leakage delays and mixed delays by using the Banach fixed point theorem, the proof by contradiction and the non-decomposition method. Finally, we will give one example to illustrate the feasibility and effectiveness of the main results.</p></abstract>

System decomposition method-based global stability criteria for T-S fuzzy Clifford-valued delayed neural networks with impulses and leakage term

<abstract><p>This paper investigates the global asymptotic stability problem for a class of Takagi-Sugeno fuzzy Clifford-valued delayed neural networks with impulsive effects and leakage delays using the system decomposition method. By applying Takagi-Sugeno fuzzy theory, we first consider a general form of Takagi-Sugeno fuzzy Clifford-valued delayed neural networks. Then, we decompose the considered $ n $-dimensional Clifford-valued systems into $ 2^mn $-dimensional real-valued systems in order to avoid the inconvenience caused by the non-commutativity of the multiplication of Clifford numbers. By using Lyapunov-Krasovskii functionals and integral inequalities, we derive new sufficient criteria to guarantee the global asymptotic stability for the considered neural networks. Further, the results of this paper are presented in terms of real-valued linear matrix inequalities, which can be directly solved using the MATLAB LMI toolbox. Finally, a numerical example is provided with their simulations to demonstrate the validity of the theoretical analysis.</p></abstract>

Finite-/fixed-time synchronization of leakage and discrete delayed Hopfield neural networks with diffusion effects

<abstract><p>In this paper, the problem on finite-/fixed-time synchronization (FFTS) is investigated for a class of diffusive Hopfield neural networks with leakage and discrete delays. Some new and useful criteria independent on time delays but dependent on the diffusion coefficients are established to guarantee the FFTS for the addressed network model under a unified framework. In sharp contrast to the existed results which can only finite-timely or fixed-timely synchronize the systems with both diffusion effects and leakage delays, the theoretical results of this paper are more general and practical. Finally, a numerical example is presented to show the effectiveness of the proposed control methods.</p></abstract>

State estimation of static neural networks with mixed delays: A new parameterized delay interval approach

This work concerns with the issue of H∞ state estimation for static neural networks with both leakage delay and time-varying delay. First, a new parameterized delay interval approach is proposed, where two parameters are introduced to divide the delay interval into four segments. Second, an appropriate Lyapunov–Krasovskii functional (LKF) including non-integral quadratic delay-product-type functional and augmented terms is constructed by combining four delay intervals. Meanwhile, for the sake of cooperating with the constructed LKF effectively, generalized free-weighting-matrix integral inequality (GFWMII) is utilized to derive much less conservative criteria. Finally, a novel criterion is derived which ensures that the considered system is asymptotically stable with prescribed H∞ performance. The effectiveness of the achieved approach is demonstrated by three commonly used numerical examples.

Stability of quaternion-valued neutral-type neural networks with leakage delay and proportional delays

This paper is concerned with the stability issue of quaternion-valued neural networks with neutral delay, proportional delay and leakage delay. Taking use of the principle of homeomorphism, techniques of matrix inequality and Lyapunov stability theory, a main stability criterion is derived in the form of quaternion-valued linear matrix inequality for ensuring the unique existence and global stability of the equilibrium point for the considered quaternion-valued neural networks. An illustrative example and its simulations are given to show the effectiveness of the theoretical result.

State estimation of complex-valued neural networks with leakage delay: A dynamic event-triggered approach

In this paper, the problem of state estimation is investigated for a class of discrete-time complex-valued neural networks (CVNNs) with both leakage delay and discrete time-varying delays. The signal transmission from output sensors to state estimator is implemented via a shared wireless network with limited communication resources. For the aim of reducing the consumption of limited communication resources, the transmission strategy based on dynamic event-triggering is introduced to determine when the updating of the output measurement should be carried out. By taking use of some properties of Hermitian matrix and constructing an appropriate Lyapunov–Krasovskii functional, a sufficient criterion is derived for ensuring the asymptotical stability of the estimation error system without separating the CVNN to its real-part system and imagination one is derived, which is quite different from those approach used in exiting literature. The gain matrix for estimator is designed by resorting to a set of feasible solutions of linear matrix inequalities (LMIs) with complex-valued variables. A numerical example and its simulation results are given to illustrate the validity of the theoretical result.

Mittag–Leffler stability and synchronization of neutral-type fractional-order neural networks with leakage delay and mixed delays

In recent years, there have been a lot of studies focusing on the dynamics of fractional-order neural networks (FONNs). One problem is that the standard Lyapunov theory does not apply to fractional-order systems, so these studies rely on the use of Halanay-type lemmas to develop sufficient criteria for certain dynamic properties of FONNs, which frequently results in much more conservative criteria than the ones obtained for integer-order neural networks. The present research uses the Halanay-type lemma in a novel way, in order to obtain less conservative sufficient criteria than previous studies. On the other hand, the previous research only considers FONNs with some types of delays, thus limiting their applicability in real-life scenarios, where possibly many more types of delays are relevant. To address this issue, the paper discusses very general FONNs that include neutral-type delay, leakage delay, time-varying delays, and distributed delay. This is the first time such a general model for the fractional-order scenario has been developed, to our awareness. Three theorems, each based on a distinct Lyapunov-like function, are used to construct sufficient criteria, given in terms of linear matrix inequalities, which ensure, respectively, the Mittag–Leffler stability and synchronization, using two different and general state feedback control schemes, of the proposed networks. The usage of the free weighting matrix approach, among the first times in the context of FONNs, also significantly contributes to reducing the conservatism of the deduced sufficient conditions. One numerical example is provided to illustrate each of the three theorems.

A direct analysis method to Lagrangian global exponential stability for quaternion memristive neural networks with mixed delays

This paper mainly studies the global exponential stability in Lagrange sense (GESLS) of quaternion memristive neural networks (QMNNs) with leakage delays, unbounded distributed delays and time-varying discrete time delays. In the process of research, instead of traditional decomposition into real-valued memristive neural networks (RMNNs) or complex-valued memristive neural networks (CMNNs), we consider the QMNN as a whole, and then give a sufficient condition related to time delays to ensure that the considered QMNN is GESLS. An example is provided to illustrate validity of theoretical results obtained in the end. The method proposed in the present text has two merits: (1) According to the definition of GESLS directly, no Lyapunov–Krasovskii functional (LKF) is required, which avoids massive calculations and solutions of high-dimensional matrix inequalities; (2) It is available not only to QMNNs, but also to RMNNs and CMNNs.

H∞ State Estimation for BAM Neural Networks With Binary Mode Switching and Distributed Leakage Delays Under Periodic Scheduling Protocol.

This article is concerned with the H∞ state estimation problem for a class of bidirectional associative memory (BAM) neural networks with binary mode switching, where the distributed delays are included in the leakage terms. A couple of stochastic variables taking values of 1 or 0 are introduced to characterize the switching behavior between the redundant models of the BAM neural network, and a general type of neuron activation function (i.e., the sector-bounded nonlinearity) is considered. In order to prevent the data transmissions from collisions, a periodic scheduling protocol (i.e., round-robin protocol) is adopted to orchestrate the transmission order of sensors. The purpose of this work is to develop a full-order estimator such that the error dynamics of the state estimation is exponentially mean-square stable and the H∞ performance requirement of the output estimation error is also achieved. Sufficient conditions are established to ensure the existence of the required estimator by constructing a mode-dependent Lyapunov-Krasovskii functional. Then, the desired estimator parameters are obtained by solving a set of matrix inequalities. Finally, a numerical example is provided to show the effectiveness of the proposed estimator design method.

Unified dissipativity state estimation for delayed generalized impulsive neural networks with leakage delay effects

This paper examined for the first time the challenge of unified dissipativity state estimation of delayed generalized impulsive neural networks (GINNs) with leaky delay effects. To estimate the upper bounds of the Lyapunov Krasovskii functionals (LKFs), the tighter integral inequality (TII) and reciprocally convex inequality (RCI) approaches are employed, and certain criteria are provided in the form of linear matrix inequalities (LMIs). As a response, a new delayed-dependent criterion for establishing whether the estimated error network is unified dissipative is developed. By modifying the values of the suitable matrices, the notion of a unified dissipativity-based estimating state may be used to find the multi-dynamic state estimation of GINNs. The recommended technique’s benefit is displayed by multiple numerical examples, one of which was sponsored by a practical implementation of the benchmark problem (i.e., the quadruple-tank process system (QTPS)) that is involved with reasonable issues, particularly the impulse impacts in the sense of a unified dissipativity performance.