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Summary: The problem of impulsive stabilization of linear neutral delay systems is investigated by using the impulse‐time‐dependent Lyapunov functions. The construction of impulse‐time‐dependent Lyapunov functions is based on the singular system representation of the impulsively controlled neutral delay system. In order to overcome the difficulty arising from time‐varying state delays, a Razumikhin‐type analysis method is developed and the key technique is to establish the relation between the slow and fast state variables by using a difference inequality. The derived stability criterion weakens the restriction condition on the impulse operators found in the previous result. For constant delay case, an improved stability criterion is derived by applying an impulse‐time‐dependent Lyapunov functional. Next, based on the newly established stability criteria, novel sufficient conditions on the existence of impulsive controllers with range dwell‐time constraint are presented. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

Abstract This paper presents improved criteria for global exponential stability of reaction–diffusion neural networks with time-varying delays. A novel diffusion-dependent Lyapunov functional, which is directly linked to the diffusion terms, is suggested to analyze the role of diffusivity of each neuron on the model dynamics. In the case of Dirichlet boundary conditions, the extended Wirtinger’s inequality is employed to exploit the stabilizing effect of reaction–diffusion terms. In the framework of descriptor system approach, the augmented Lyapunov functional technique is utilized to reduce the conservatism in the values of the time delay bounds. As a result, the derived global stability criteria are more effective than the existing ones. Three numerical examples are provided to illustrate the effectiveness of the proposed methodology. [ABSTRACT FROM AUTHOR]

Abstract: This Letter provides new exponential stability criteria for discrete-time neural networks with variable delays. The main technique is to reduce exponential convergence estimation of the neural network solution to that of one component of the corresponding solution by constructing Lyapunov function based on M-matrix. By introducing the tuning parameter diagonal matrix, the delay-independent and delay-dependent exponential stability conditions have been unified in the same mathematical formula. The effectiveness of the new results are illustrated by three examples. [Copyright &y& Elsevier]

This paper addresses the impulsive observers design problem of perturbed Lipschitz nonlinear systems subject to noisy delayed discrete measurements. The transmission delay, state perturbation, and measurement noise simultaneously hinder the convergence of impulsive observer. To deal with the difficulty, the observation error system with delayed impulses is represented as an augmented system with switching delay-free impulses. By taking into account the switching structure of the impulse dynamics, the impulse observation gain matrix is modelled as a function of the time interval between two consecutive sampling instant and update instant. Such a structure of the observation gain matrix is able to adapt to the variation of sampling period and transmission delay. To obtain a tractable design condition, the idea of piecewise linear interpolation is applied to represent the impulse observation gain matrix as a piecewise linear form, which is determined by finite static impulse gains. A piecewise Lyapunov function which matches the piecewise linear structure of the observation gain is constructed to analyze the exponential input-to-state stability (EISS) property of the observation error system. The EISS gain quantifies the robustness performance of the designed impulsive observer. Sufficient conditions for the existence of the proposed variable gain impulsive observers are presented. Two numerical examples are provided to illustrate the effectiveness of the developed impulsive observation strategy. • A methodology for designing impulsive observers with delayed measurements and disturbances is proposed. • Based on the augmented representation of the observation error system, a piecewise linear gain function is constructed. • The robustness performance of the proposed observers against external disturbance is characterized by the notion of EISS. [ABSTRACT FROM AUTHOR]

This article considers the problems of achieving exponential stability and finite hybrid L2 × l2‐gain with respect to continuous and discrete disturbances for linear neutral time‐delay systems with impulsive effects. In the framework of descriptor system representation, a piecewise timer‐dependent Lyapunov functional is introduced to analyze the double impacts of state‐delay and impulse‐dwell‐time on stability of the underlying system. This functional depends on the state over an impulse interval and the state over a delay interval. Its construction is based on a delay‐fractioning scheme which ensures all delay subintervals contains at most one impulse instant. The relations among the augmented state variables are explored by using the impulse‐timer functions and the Newton–Leibniz formula. It is proved that the positive definiteness property of the functional at nonimpulse instants is not necessary for ensuring stability. The hybrid L2 × l2‐gain analysis is carried out by jointly using the introduced functional and a discrete‐time Lyapunov function. The obtain criteria for exponential stability and hybrid L2 × l2‐gain are expressed in terms of linear matrix inequalities. Their effectiveness is verified through two numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, the problem of impulsive synchronization of two coupled delayed reaction–diffusion neural networks under aperiodic discrete measurements is revisited. Different from the previous static impulsive gain based impulsive synchronization strategy, a novel impulsive synchronization strategy using sampling-interval-dependent impulsive gains is proposed. The time-varying impulsive synchronization gains are able to adapt to the variation of sampling intervals, and thus can improve the synchronization performance. The stability analysis of the resultant synchronization error system is performed by applying an impulse-time-dependent discretized Lyapunov functions based method. Sufficient conditions for the existence of desired impulsive synchronization controllers are derived in terms of a set of linear matrix inequalities (LMIs). These conditions allow to synthesize time-varying impulsive gains. A numerical example is presented to demonstrate the effectiveness of the developed methodology. [ABSTRACT FROM AUTHOR]

This paper is concerned with the positivity and impulsive stabilization of equilibrium points of delayed neural networks (DNNs) subject to bounded disturbances. With the aid of the continuous dependence theorem for impulsive delay differential equations, a relaxed positivity condition is derived, which allows the neuron interconnection matrix to be Metzler if the activation functions satisfy a certain condition. The notion of input-to-state stability (ISS) is introduced to characterize internal global stability and disturbance attenuation performance for impulsively controlled DNNs. The ISS property is analyzed by employing a time-dependent max-separable Lyapunov function which is able to capture the positivity characterization and hybrid structure of the considered DNNs. A ranged dwell-time-dependent ISS condition is obtained, which allows to design an impulsive control law via partial state variables. As a byproduct, an improved global exponential stability criterion for impulse-free positive DNNs is obtained. The applicability of the achieved results is illustrated through three numerical examples. • A relaxed positivity condition for impulsively controlled DNNs is proposed. • A novel time-dependent max-separable Lyapunov function is introduced for ISS analysis. • An improved criterion for positivity and global exponential stability of DNNs is obtained. [ABSTRACT FROM AUTHOR]

This paper deals with the impulsive stabilization problem for a class of linear singular systems with time-delays. The stabilization is achieved by only exerting impulsive action on the slow state variables. Two novel Lyapunov methods are presented to determine exponential stability of the impulsively controlled systems. For the case where the time-delay is unknown and may be time-varying, a Lyapunov–Razumikhin method is developed, in which the Razumikhin condition is constructed by exploiting the relation among the fast state variables, the slow state variables, and their initial values. For the case where the delay derivative is strictly less than 1, a descriptor type of impulse-time-dependent Lyapunov functional is introduced, which is discontinuous at impulse times but does not grow along the state trajectories by construction. By using a convex technique, the stability criteria are expressed in terms of linear matrix inequalities (LMIs). Then, the impulsive controllers can be designed in the framework of LMIs. The effectiveness and advantages of the proposed methods are confirmed through simulation results. [ABSTRACT FROM AUTHOR]

In this paper, the intermittent H ∞ synchronization problem for a class of reaction-diffusion neural networks with Dirichlet boundary conditions is investigated. Different from the previous works concerning intermittent synchronization, it is assumed that the response system is subject to external disturbance, and both the control period and the control width may be variable. A switching-time-dependent Lyapunov function combined with the use of the extended Wiritinger's inequality for exploring the stabilizing role of the reaction-diffusion term is employed to analyze the exponential stability and L 2 -gain performance of the synchronization error dynamics. In the framework of linear matrix inequalities, the aperiodically intermittent H ∞ synchronization controller is designed, which guarantees internally exponential stability as well as a prescribed L 2 -gain from the exogenous input to the regulated error output. Two numerical examples are given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, multistability analysis for a class of stochastic delayed Hopfield neural networks is investigated. By considering the geometrical configuration of activation functions, the state space is divided into 2 n + 1 regions in which 2 n regions are unbounded rectangles. By applying Schauder’s fixed-point theorem and some novel stochastic analysis techniques, it is shown that under some conditions, the 2 n rectangular regions are positively invariant with probability one, and each of them possesses a unique equilibrium. Then by applying Lyapunov function and functional approach, two multistability criteria are established for ensuring these equilibria to be locally exponentially stable in mean square. The first multistability criterion is suitable to the case where the information on delay derivative is unknown, while the second criterion requires that the delay derivative be strictly less than one. For the constant delay case, the second multistability criterion is less conservative than the first one. Finally, an illustrative example is presented to show the effectiveness of the derived results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the exponential stability of a class of singularly perturbed stochastic time-delay systems with impulse effect is considered. By using the comparison principle and time scale decomposition, a Lyapunov-based sufficient condition for exponential stability in mean square for a sufficiently small singular perturbation parameter is derived. Some known results are generalized and improved. [ABSTRACT FROM AUTHOR]

In this paper, the problem of robust sampled-dataH∞control of linear uncertain singularly perturbed systems is investigated. The parametric uncertainties are assumed to be time-varying and norm-bounded. Two types of controller design are considered: (1) with a fast sampling in the fast state and a slow one in the slow state, and (2) with a fast sampling in both states. For each type, a time-dependent Lyapunov functional associated with the sampling pattern is introduced to analyse the exponential stability andL2-gain performance of the closed-loop system. Linear matrix inequalities based solutions of the robust sampled-dataH∞control problem are derived. The new results are proved theoretically to be less conservative than the existing results. An illustrative example is given which substantiates the usefulness of the proposed method. [ABSTRACT FROM PUBLISHER]

This paper is concerned with the stabilization problem of delayed neural networks via a periodically intermittent controller. Two cases of time-varying bounded delays are considered: one is the time-varying delay without any constraints on the delay derivative, while the other is the time-varying delay with the delay derivative less than 1. For the first case, a piecewise time-invariant Lyapunov function-based method is applied, and the derived stability criterion improves an existing result. For the second case, a piecewise time-varying Lyapunov functional is introduced to establish a new stability criterion. Then, the obtained stability criteria are employed to design periodically intermittent controllers. Finally, two numerical examples are provided to illustrate the merits of the proposed approach. [ABSTRACT FROM AUTHOR]