Mixed Time-varying Delays Research Articles

Lagrange Stability of Competitive Neural Networks with Multiple Time-Varying Delays

In this paper, the Lagrange stability of competitive neural networks (CNNs) with leakage delays and mixed time-varying delays is investigated. By constructing delay-dependent Lyapunov functional, combining inequality analysis technique, the delay-dependent Lagrange stability criterion are obtained in the form of linear matrix inequalities. And the corresponding global exponentially attractive set (GEAS) is obtained. On this basis, by exploring the relationship between the leakage delays and the discrete delay, a better GEAS of the system is obtained from the six different sizes of the two types of delays. Finally, three examples of numerical simulation are given to illustrate the effectiveness of the obtained results.

[formula omitted] anti-synchronization of switching inertial neural networks with leakage delays and mixed time-varying delays

In this paper, the H∞ anti-synchronization problem of switching inertial neural networks with constant leakage delays and time-varying mixed delays is addressed. A direct analysis method based on parameterized system solutions is proposed to solve the problem we studied. The advantages of this method are that the variable substitution is not required for the system model and no Lyapunov–Krasovskii functional is constructed, which simplifies the proof process. In addition, the resulting anti-synchronization conditions consisting of some simple scalar inequalities can be easily solved by business softwares, and less computational complexity is involved. It is worth noting that the problem addressed in this paper has not been studied at present, and the limitation on the parity of activation functions in the existing literatures is removed, which reduces conservativeness. Finally, the reliability of the theoretical results is verified by numerical simulations.

A novel direct method to [formula omitted] synchronization of switching inertial neural networks with mixed time-varying delays

In this paper, the H∞ synchronization problem of switching inertial neural networks with mixed time-varying delays is discussed. A parameterized system solution-based direct analysis method combined with minimum residence time method is proposed to solve the considered problem. The advantage of this method is that no model transformation or construction of Lyapunov–Krasovskii functional is required, thus reducing the complexity of derivation process. In addition, the resulting synchronization conditions composed of some simple scalar inequalities can be easily solved via MATLAB. Finally, the reliability of the theoretical results is illustrated by numerical simulations.

Exponential stabilization of the class of the switched systems with mixed time varying delays in state and control

This paper presents the problem of exponential stabilization of switched systems with mixed time-varying delays in state and control. Based on the partitioning of the stability state regions into convex cones, a constructive geometric design for switching laws is put forward. By using an improved Lyapunov–Krasovskii functional in combination with matrix knowledge, we design a state feedback controller that guarantees the closed-loop system to be exponentially stable. The obtained conditions are given in terms of linear matrix inequalities (LMIs), which can be effectively decoded in polynomial time by various computational tools such as the LMI tool in MATLAB software. A numerical example is proposed to illustrate the effectiveness of the obtained results.

Fixed-Time Synchronization for Fractional-Order Cellular Inertial Fuzzy Neural Networks with Mixed Time-Varying Delays

Due to the widespread application of neural networks (NNs), and considering the respective advantages of fractional calculus (FC), inertial neural networks (INNs), cellular neural networks (CNNs), and fuzzy neural networks (FNNs), this paper investigates the fixed-time synchronization (FDTS) issues for a particular category of fractional-order cellular-inertial fuzzy neural networks (FCIFNNs) that involve mixed time-varying delays (MTDs), including both discrete and distributed delays. Firstly, we establish an appropriate transformation variable to reformulate FCIFNNs with MTD into a differential first-order system. Then, utilizing the finite-time stability (FETS) theory and Lyapunov functionals (LFs), we establish some new effective criteria for achieving FDTS of the response system (RS) and drive system (DS). Eventually, we offer two numerical examples to display the effectiveness of our proposed synchronization strategies. Moreover, we also demonstrate the benefits of our approach through an application in image encryption.

Further analysis of stabilization of neutral type singular systems with mixed time‐varying delays and multiple random states

AbstractIn this paper, the stabilization problem of neutral type singular systems (NTSSs) with mixed time‐varying delays and multiple random states is further analyzed. Lyapunov Krasovskill functional (LKF) and generalized Itô formula, together with linear matrix inequality (LMI), are used to represent a new stability criterion for NTSSs with mixed time‐varying delays (MTVDs) in multiple random states. First, the regularity, impulse free, and stochastic stability of the system are satisfied by designing a state feedback controller (SFC). Second, on the basis of Leibniz Newton formula, the stability criterion is also feasible by integrating zero value equation technology, and then combined with singular decomposition, the gain of SFC is obtained. Finally, our paper is a further analysis of the latest literature, so two numerical examples are used to verify the feasibility and effectiveness of this method.

Finite-region boundedness and [formula omitted]-dissipativity of 2-D singular Roesser systems with mixed time-varying delays

This paper is concerned with the problems of finite-region boundedness and dissipativity analysis of two-dimensional (2-D) singular Roesser systems with mixed directional time-varying delays. The concepts of singular finite-region boundedness (SFRB), which deduces the property of singular finite-region stability (SFRS) when exogenous disturbance is ignored, and finite-region (Q,S,R)-dissipativity are first proposed. Then, by using an energy function constructed as a weighted 2-D Lyapunov–Krasovskii functional, and by utilizing zero-type free matrix equations, new delay- and time-region-dependent conditions, which guarantee the properties of finite-region stability and dissipativity with respect to a quadratic supplied rate function, are derived. The obtained results are shown to encompass and extend existing works in the literature. The effectiveness of the analysis results is validated by numerical examples.

Stability of port-Hamiltonian systems with mixed time delays subject to input saturation

In this paper, we investigate the stability of port-Hamiltonian systems with mixed time-varying delays as well as input saturation. Three types of time delays, including state delay, input delay, and output delay, are all assumed to be bounded. By introducing the output feedback control law and utilizing serval Lyapunov–Krasovskii functionals, we present three delay-dependent stability criteria in terms of the linear matrix inequality. Meanwhile, we use Wirtinger’s inequality, constraint conditions, and Lyapunov–Krasovskii functionals of triple and quadruple integral form to obtain less conservative results. Some numerical examples demonstrate and support our results.

Guaranteed cost control of fractional-order switched systems with mixed time-varying delays

Guaranteed cost control of fractional-order switched systems with mixed time-varying delays

Matrix measure-based distributed impulsive consensus on nonlinear multi-agent systems with mixed time-varying delays

This paper concentrates on researching the global and exponential leader-following consensus issue for an array of nonlinear multi-agent systems with the system time-varying delay and the distributed time-varying delay. An innovative distributed impulsive controller is proposed to force the states of all agents to track the trajectories of leader agent. By jointly introducing the matrix measure protocol, the comparison principle for impulsive systems, and the average impulsive interval, sufficient criteria for the realization of leader-following consensus are derived. In addition, considering different functions of impulsive signal, two different convergence rates are precisely estimated by utilizing the parameter variation formula, respectively. Finally, two numerical examples are given to demonstrate the effectiveness of proposed control strategy and the rightness of theoretical analysis.

Finite-Time and Fixed-Time Synchronization of Delayed Memristive Neural Networks via Adaptive Aperiodically Intermittent Adjustment Strategy.

This article investigates the finite-time and fixed-time synchronization for memristive neural networks (MNNs) with mixed time-varying delays under the adaptive aperiodically intermittent adjustment strategy. Different from previous works, this article first employs the aperiodically intermittent adjustment feedback control and adaptive control to drive the MNNs to achieve synchronization in finite time and fixed time. First of all, according to the theories of set-valued mappings and differential inclusions, the error MNNs is derived, and its finite-time and fixed-time stability problems are discussed by applying the Lyapunov function method and some LMI techniques. Moreover, by meticulously designing an effective aperiodically intermittent adjustment with adaptive updating law, sufficient conditions that guarantee the finite-time and fixed-time synchronization of the drive-response MNNs are obtained, and the settling time is explicitly estimated. Finally, three numerical examples are provided to illustrate the validity of the obtained theoretical results.

Robust stability and $${H_\infty }$$ control problem for 2-D nonlinear uncertain switched system with mixed time-varying delays under fuzzy rules

Robust stability and $${H_\infty }$$ control problem for 2-D nonlinear uncertain switched system with mixed time-varying delays under fuzzy rules

Caputo−Wirtinger integral inequality and its application to stability analysis of fractional-order systems with mixed time-varying delays

Various techniques of integral inequality are widely used to establish the delay-dependent conditions for the dynamics of differential systems so that the conservatism of conditions can be reduced. In the integer-order systems, the integral term of ∫τωp˙T(s)Sp˙(s)ds often appears in the derivative of Lyapunov−Krasovskii functional, and how to scale down this term to obtain less conservative condition is a key problem. Similarly, the integral term of ∫τω(Dsα0Cp(s))TS0CDsαp(s)ds with fractional derivative may also be encountered in the analysis of dynamical behaviors for fractional-order systems. In view of this, the paper intends to construct several novel fractional Wirtinger integral inequalities under the sense of Caputo derivative, and to investigate the stability of fractional-order systems with mixed time-varying delays based on the constructed Caputo−Wirtinger integral inequalities. Meanwhile, in order to analyze the stability for our concerned models by the new inequalities, two new theorems of generalized fractional-order Lyapunov direct method are given. Finally, a numerical example is designed to validate the correctness and practicability of the obtained results.

Saturated and asymmetric saturated control for projective synchronization of inertial neural networks with delays and discontinuous activations through matrix measure method

The projective synchronization work presented in this article is focused on a class of nonlinear discontinuous coupled inertial neural networks with mixed time-varying delays and a cluster topological structure. The synchronization problem for discontinuous coupled inertial neural networks with clustering topology is examined in consideration with the mismatched parameters and the mutual influence among various clusters. To determine the required conditions for network convergence under the influence of an extensive range of impulses, the matrix measure technique and the average impulsive intervals are employed. To illustrate the effectiveness of the theoretical findings, graphical representation of varied impulsive ranges for multiple cases are provided using numerical simulations.

Quasi-synchronization of heterogeneous stochastic coupled reaction-diffusion neural networks with mixed time-varying delays via boundary control

In this paper, the quasi-synchronization problem of heterogeneous stochastic coupled neural networks (HSCNNs) is discussed. The effects of the mixed time-varying delay and diffusion phenomenon on the system are considered separately in time and space. Moreover, different from the previous distributed control, boundary control is introduced to realize network synchronization. This not only reduces the space cost of the controller, but also makes it easier to implement. Thus, the mean-square quasi-synchronization of HSCNNs is guaranteed by using matrix inequality and stochastic analysis tools. In addition to focusing on systems with Neumann boundary conditions, we briefly investigate HSCNNs with time-invariant delays and mixed boundary conditions respectively, and provide sufficient conditions to achieve the desired performance. Finally, the correctness of the conclusion is verified by several examples.

Finite-time synchronization of discontinuous fuzzy neural networks with mixed time-varying delays and impulsive disturbances

In this paper, the finite-time synchronization issue is addressed for discontinuous fuzzy neural networks with mixed time-varying delays and impulsive disturbances. The dynamic impulsive gain about the impulsive moment is proposed as an alternative to the previous static impulsive gain. The time-varying impulsive gain can combine the synchronizing and desynchronizing impulses to directly observe their effects on the system, avoiding the classification discussion. In order to study the finite-time synchronization of the drive–response system, we obtain an equivalent system from the original fuzzy neural networks based on the concepts of Filippov solutions and differential inclusion theory. Furthermore, by constructing new Lyapunov functions that combine the 1-norm and the comparative system method, some algebraic sufficient conditions for the synchronization of the drive system and the response system in finite time are established, which are based on two types of novel non-chattering controllers. In addition, the parameters of the system itself can simply demonstrate the sufficient conditions that have been obtained her e, avoiding the time-consuming calculation of matrix inequalities. Moreover, the settling time estimation scheme have been established. Eventually, numerical examples are provided to demonstrate the effectiveness of the control scheme.

Exponential Synchronization of Second-Order Fuzzy Memristor-Based Neural Networks With Mixed Time Delays via Fuzzy Adaptive Control

This article addresses the exponential synchronization problem for a class of fuzzy inertial memsirtor-based neural networks with mixed time-varying delays (FMINNs). Firstly, the inertial items are described as second-order systems and transformed into first-order systems by utilizing a appropriate variable substitution. Then the fuzzy state-feedback control strategy and fuzzy adaptive control strategy are designed to ensure the exponential synchronization under the framework of Filippov solutions. The exponential synchronization algebraic conditions are obtained by choosing a proper Lyapunov-Krasovskii functional (LKF). Finally, two numerical simulations are provided to validate the effectiveness and benefit of the proposed results.

Drive-Response Synchronization for Second-Order Memristor-Based Delayed Neural Networks with Settling Time Estimation via Discontinuous Feedback Control

In this paper, the settling time estimation of synchronization issues for inertial memristive neural networks (IMNNs) with mixed time-varying delays is investigated. First, by using a new reduced order approach and introducing free-weighted coefficients η i and ξ i into variable transformation, the original second-order derivative system is transformed into a first-order differential system. Second, appropriate controllers are designed for IMNNs to guarantee the system synchronization in a settling time. In addition, the settling time is explicitly estimated and dependent on time delays and the initial values of the coupled system. Finally, two numerical examples are presented to demonstrate the effectiveness of the theoretical results.

On reachable set bounding for discrete-time switched nonlinear positive systems with mixed time-varying delays and disturbance

This paper addresses the reachable set bounding for discrete-time switched nonlinear positive systems with mixed time-varying delays and disturbance, which contains switched linear positive systems as a special case. By resorting to a new method that does not involve the common Lyapunov–Krasovskii functional one, explicit criteria to ensure any state trajectory of the system converges exponentially into a prescribed sphere are obtained under average dwell time switching. The results can then be extended to more general time-varying systems. Finally, two numerical examples are used to demonstrate the effectiveness of the obtained results.

Intermittent Exponential Synchronization for Memristor-Based Neural Networks With Inertial Items and Mixed Time-Varying Delays

This article investigates the exponential synchronization problem for a class of memristor-based neural networks with mixed time-varying delays and parameter perturbations, and inertial items are considered (MINNs). A periodically intermittent control protocol is designed to guarantee the exponential synchronization between two MINNs. Then, by adopting nonsmooth analysis, Halanay inequality, and Lyapunov theory, the exponential synchronization criteria for MINNs under the proposed controller are obtained. Furthermore, instead of the reduced-order method, the synchronization of MINNs is considered under the framework of the second-order system directly, which is different from existing literature. Some numerical simulations are presented to show the validity of the proposed criteria in the end.