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In this article, we focus on the problems of consensus control for nonlinear uncertain multiagent systems (MASs) with both unknown state delays and unknown external disturbances. First, a nonlinear function approximator is proposed for the system uncertainties deriving from unknown nonlinearity for each agent according to adaptive radial basis function neural networks (RBFNNs). By taking advantage of the Lyapunov-Krasovskii functionals (LKFs) approach, we develop a compensation control strategy to eliminate the effects of state delays. Considering the combination of adaptive RBFNNs, LKFs, and backstepping techniques, an adaptive output-feedback approach is raised to construct consensus tracking control protocols and adaptive laws. Then, the proposed consensus tracking scheme can steer the nonlinear MAS synchronizing to the predefined reference signal on account of the Lyapunov stability theory and inequality properties. Finally, simulation results are carried out to verify the validity of the presented theoretical approach.

This article analyzes the exponentially stable problem of neural networks (NNs) with two additive time-varying delay components. Disparate from the previous solutions on this similar model, switching ideas, that divide the time-varying delay intervals and treat the small intervals as switching signals, are introduced to transfer the studied problem into a switching problem. Besides, delay-dependent switching adjustment indicators are proposed to construct a novel set of augmented multiple Lyapunov-Krasovskii functionals (LKFs) that not only satisfy the switching condition but also make the suitable delay-dependent integral items be in the each corresponding LKF based on each switching mode. Combined with some switching techniques, some less conservativeness stability criteria with different numbers of switching modes are obtained. In the end, two simulation examples are performed to demonstrate the effectiveness and efficiency of the presented methods comparing other available ones.

This paper is concerned with the stability analysis of linear systems with time-varying delays. First, by introducing the quadratic terms of time-varying delays and some integral vectors, a more suitable Lyapunov-Krasovskii functional (LKF) is constructed. Second, two new delay-dependent estimation methods are developed in the stability analysis of linear system with time-varying delays, which include a reciprocally convex matrix inequality and an integral inequality. More information about time-varying delays and more free matrices are introduced into the two estimation approaches, which play a key role for obtaining an accurate upper bound of the integral terms in time derivative of LKFs. Third, based on the novel LKFs and new estimation approaches, some less conservative criteria are derived in the form of linear matrix inequality (LMI). Finally, three numerical examples are applied to verify the advantages and effectiveness of the newly proposed methods.

To derive a less conservative stability criterion via Lyapunov-Krasovskii functional (LKF) method, in previous literature, multiple integral terms are usually introduced into the construction of LKFs. This article generalizes the results of previous literature by proposing a polynomial-type LKF, which contains the LKFs with multiple integral terms as special cases. In addition, a Jacobi–Bessel inequality is presented to bound the derivative of such LKF. As a result, an improved stability criterion of time-delay systems is established. Finally, two numerical examples are given to illustrate the effectiveness, and advantages of our method.

This work deals with the problem of absolute stability analysis for a class of uncertain Lur’e systems with time-varying delays. Novel delay-partitioning approaches are presented, which are dividing the variation interval of the delay into three subintervals. Some new augment Lyapunov–Krasovskii functionals (LKFs) are defined on each of the obtained subintervals which can efficiently make use of the information of the delay and relate to the reciprocally convex combination technique and the Wirtinger-based integral inequality method. Several improved delay-dependent criteria are derived in terms of the linear matrix inequalities (LMIs). The merit of the proposed criteria lies in their less conservativeness and lower numerical complexity than relative literature. Two numerical examples are included to illustrate the effectiveness and the improvement of the proposed method.

This article focuses on designing an event-triggered impulsive fault-tolerant control strategy for the stabilization of memristor-based reaction-diffusion neural networks (RDNNs) with actuator faults. Different from the existing memristor-based RDNNs with fault-free environments, actuator faults are considered here. A hybrid event-triggered and impulsive (HETI) control scheme, which combines the advantages of event-triggered control and impulsive control, is newly proposed. The hybrid control scheme can effectively accommodate the actuator faults, save the limited communication resources, and achieve the desired system performance. Unlike the existing Lyapunov-Krasovskii functionals (LKFs) constructed on sampling intervals or required to be continuous, the introduced LKF here is directly constructed on event-triggered intervals and can be discontinuous. Based on the LKF and the HETI control scheme, new stabilization criteria are derived for memristor-based RDNNs. Finally, numerical simulations are presented to verify the effectiveness of the obtained results and the merits of the HETI control method.

In this paper, the stability analysis problem of time-varying delay systems is studied. Based on recent research on Lyapunov-Krasovskii functionals (LKFs), relaxed conditions have been found to weaken some matrices in terms of LKFs, which means that some integral terms cannot be strictly positive definite. Therefore, motivate by this consideration, a new relaxed condition is constructed to weaken some matrices in constructed LKF. Then, for the sake of obtaining more information of time delays, dynamic delay interval (DDI) method was introduced to address the double integral terms with time-varying delay. Furthermore, some recent technologies are employed to process derivatives of LKF. As a consequence, a less conservative result is obtained. The examples given by previous papers are used to demonstrate the superiority of our work.

This paper is concerned with the construction of strict Lyapunov–Krasovskii functionals (LKFs) for analyzing the input-to-state stability (ISS) problem of nonlinear time-varying time-delay systems. With the help of a known non-strict LKF, a series of strict LKFs are constructed for both continuous and discrete time-varying time-delay systems. The proposed LKFs are linear functionals of the known non-strict LKF. Compared with previous results, the proposed strict LKFs are more general. Taking advantage of the concepts of uniformly exponentially stable (UES) and uniformly exponentially expanding (UEE), the assumption of boundedness on the scalar function is not required. The effectiveness of the proposed theoretical results is illustrated by a couple of numerical examples.

In this paper, a novel adaptive fuzzy tracking control strategy is developed for nonlinear time-varying delayed systems with full state constraints. State constraints and time delays are normally found in various real-life plants, which are two important factors for degrading system performance significantly. In the framework of adaptive control, the effects of state constraints and time-varying delays are removed simultaneously. The integral Barrier Lyapunov functionals (IBLFs) are applied to achieve full-state-constraint satisfactions and remove the need of the transformed error constraints in previous BLFs. The unknown time-varying delays are completely compensated by introducing the separation technique and Lyapunov–Krasovskii functionals (LKFs). The unknown functions existing in systems are approximated by employing fuzzy logic systems (FLSs). With the help of less-adjustable parameters, only one parameter is needed to be adjusted online in each step of control design. The novel strategy can guarantee that a satisfactory tracking performance is achieved and the signals existing in the closed-loop system are bounded. Finally, by presenting simulation results, the efficiency of the proposed approach is revealed.

In this paper, for a class of uncertain stochastic nonlinear systems with input time-varying delays, an adaptive neural dynamic surface control (DSC) method is proposed. To approximate the unknown continuous functions online, the neural network approximation technique was applied, and based on the DSC scheme, the desired controller was constructed. A compensation system is presented to compensate for the effect of the input delay. The Lyapunov–Krasovskii functionals (LKFs) were employed to compensate for the effect of the state delay. Compared with the existing works, based on using the DSC scheme with the nonlinear filter and stochastic Barbalat’s lemma, the asymptotic regulation performance of this closed-loop system can be guaranteed under the developed controller. To certify the availability for the designed control method, some simulation results are presented.

The sea ice modeling community is progressing towards pan-Arctic simulations that explicitly resolve leads in the simulated sea ice cover. Evaluating these simulations against observations poses new challenges. A new feature-based evaluation of simulated deformation fields is introduced, and the results are compared to a scaling analysis of sea ice deformation. Leads and pressure ridges – here combined into linear kinematic features (LKFs) – are detected and tracked automatically from deformation and drift data. LKFs in two pan-Arctic sea ice simulations with a horizontal grid spacing of 2 km are compared with an LKF dataset derived from the RADARSAT Geophysical Processor System (RGPS). One simulation uses a five-class ice thickness distribution (ITD). The simulated sea ice deformation follows a multi-fractal spatial and temporal scaling, as observed from RGPS. The heavy-tailed distribution of LKF lengths and the scale invariance of LKF curvature, which points to the self-similar nature of sea ice deformation fields, are reproduced by the model. Interannual and seasonal variations in the number of LKFs, LKF densities, and LKF orientations in the ITD simulation are found to be consistent with RGPS observations. The lifetimes and growth rates follow a distribution with an exponential tail. The model overestimates the intersection angle of LKFs, which is attributed to the model's viscous-plastic rheology with an elliptical yield curve. In conclusion, the new feature-based analysis of LKF statistics is found to be useful for a comprehensive evaluation of simulated deformation features, which is required before the simulated features can be used with confidence in the context of climate studies. As such, it complements the commonly used scaling analysis and provides new useful information for comparing deformation statistics. The ITD simulation is shown to reproduce LKFs sufficiently well for it to be used for studying the effect of directly resolved leads in climate simulations. The feature-based analysis of LKFs also identifies specific model deficits that may be addressed by specific parameterizations, for example, a damage parameter, a grounding scheme, and a Mohr–Coulombic yield curve.

Genetic Regulatory Networks (GRNs) play an important role for the development and evolution of biological systems. On the basis of the development for DNA microarray technologies, a profound study for GRNs becomes possible at genome scale. In this article, the global dissipativity and corresponding attractive set for the GRNs with stochastic disturbances and time-delays are investigated based on Lyapunov theory. Stochastic disturbances are considered into both the feedback regulation process and the translation process for reflecting the inherent noise perturbations on a foundation of factual knowledge. Through the resort to the several appropriate Lyapunov-Krasovskii Functionals (LKFs) combining with Itô's formula and different inequality techniques, some corresponding sufficient conditions and the attractive set are obtained for the GRNs in linear matrix inequality form, which are easy to verify by the numerical software. Finally, one three-node GRN is proposed and analyzed to illustrate the validity of the proposed results by using the Field-Programmable Gate Array (FPGA) hardware simulation tool.

This paper is concerned with the stability analysis of linear continuous-time delay-difference systems with multiple delays. Firstly, a new method for testing the L2-exponential stability of the considered system is proposed, which is easier to use than the one in the existing literature. In view of the conservatism and the complexity of the obtained stability conditions in the existing literature, a complete Lyapunov–Krasovskii functional (LKF) is constructed by analyzing the relationship among the multiple delays. Sufficient conditions for both L2-exponential stability and exponential stability are then derived based on the constructed LKFs, which are delay-independent. Exponential convergence rate for the considered system is also investigated by a new method, which is shown to be equivalent to the existing approach by using weighted LKFs. Robust stability under parameter uncertainties is also investigated. Numerical examples are provided to demonstrate the effectiveness and less conservativeness of the proposed method.

We study in this paper the mean square exponential stability of neutral-type linear stochastic time-delay systems with three different delays by using the Lyapunov–Krasovskii functionals (LKFs) based approach. First, for a specified augmented state vector, a complete augmented LKF is constructed to contain all possible integrals so that its time-derivatives (understood in the deterministic sense) can be written as a linear function of the augmented vector. The redundant variables in the LKF are eliminated so as to reduce the computational burden. Moreover, the absolute value requirement of certain terms in the constructed LKFs are removed by analyzing carefully the complex relationship among these three different time delays. Then, for ten different cases of time delays, sufficient stability conditions in terms of linear matrix inequalities are obtained with the help of the Ito formula and properties of stochastic integrals. The degenerated cases that the delays satisfy some equalities are also discussed. A numerical example is employed to illustrate the effectiveness of the proposed approach.

Delay-dependent stability analysis of linear systems with a time-varying delay is investigated in this paper. Firstly, instead of developing a Lyapunov–Krasovskii functional (LKF) including augmented non-integral quadratic terms as usual, this paper proposes two augmented-integral-function based LKFs, which can reflect closer relationships among system states. Secondly, to bound the derivative of LKF more accurately, a new integral inequality with several free matrices is developed. Compared with the free-matrix-based integral inequality, this inequality can provide additional freedom due to the free matrices introduced. Then, by employing those LKFs and the improved integral inequality, several delay-dependent stability criteria are established for two types of delays. Finally, two numerical examples are given to demonstrate the superiority of the proposed method.

For stability analysis of time-varying time-delay systems, it is known that time-derivatives (time-shifts in the discrete-time setting) of the Lyapunov–Krasovskii functionals (LKFs) for both internal stability and input-to-state stability (ISS) can be indefinite, which can improve the resulting stability conditions in some cases. However, the non-strict LKFs may be insufficient and inconvenient to use in practice. In this paper, based on the non-strict ISS LKFs for time-varying time-delay systems and with the help of uniformly asymptotically stable (UAS) and uniformly exponentially bounded (UEB) scalar functions, three classes of strict ISS LKFs are constructed such that their time-derivatives are strictly negative definite along the trajectories of the considered system. A general construction of strict ISS LKFs by using the positive definite and uniformly bounded solution to a scalar Lyapunov differential equation is established, which includes the proposed three classes of strict ISS LKFS as special cases. The approaches are also extended to deal with a Lyapunov inequality whose right hand side is indefinite and nonlinear. Both continuous-time and discrete-time systems are considered. The effectiveness of the proposed methods is illustrated by some examples borrowed from the literature.

This paper is concerned with the master-slave synchronization in a class of neutral neural networks with both leakage and distributed delays. Firstly, based on state feedback controller, the closed-loop error system can be obtained. Then by fully utilizing the information and internal relationship of time-delays, three augmented Lyapunov–Krasovskii functionals (LKFs) are constructed, in which infinite distributed delay and finite one are respectively studied. Especially, some Wirtinger-based inequalities are exploited and an extended reciprocal combination technique (ERCT) is proposed, which can reconsider the previously ignored information. Sufficient conditions are formulated in terms of linear matrix inequalities (LMIs) and can be easily tested. Finally, three numerical examples are given to illustrate the designed schemes.

This paper investigates the stabilization problem of uncertain networked control systems with additive time-varying delays by using nonfragile sampled-data control. Suitable Lyapunov-Krasovskii functional (LKF) is constructed which includes more information about the additive time-varying delays. The main aim of this paper is to design a nonfragile sampled-data control scheme which guarantees asymptotic stability of the considered system. Besides that, the Jensen's and improved integral inequalities are used for estimating the single and double integral terms in the derivative of LKFs and the sufficient conditions are expressed in terms of linear matrix inequalities. Finally, the effectiveness of proposed theoretical results are validated and compared with existing literature by numerical examples and their simulation results.

The present work examines the delay-dependent gain-scheduling feedback control with guaranteed closed-loop stability and induced L2 norm performance for continuous-time linear parameter-varying (LPV) systems with arbitrary time-varying delay. An extension of Lyapunov stability utilizing Krasovskii functionals is considered to derive stability analysis and synthesis conditions for delay-dependent dynamic output feedback LPV control design. The main challenges associated with this approach are selecting appropriate Lyapunov-Krasovskii functionals (LKFs) and finding efficient integral inequalities to bound the derivative of the LKF. Accordingly, a novel modified parameter-dependent LKF candidate along with an affine version of Jensen’s inequality bounding technique are employed leading to the derivation of less conservative sufficient conditions expressed in terms of convex linear matrix inequalities (LMIs). The proposed methodology is compared with past work in the literature in terms of conservatism reduction and performance improvement through a numerical example. Finally, the application of the proposed output-feedback LPV control design is evaluated on the automated mean arterial blood pressure (MAP) regulation in critical patient resuscitation via vasoactive drug infusion. Closed-loop simulation results are presented to illustrate the potential of the introduced LPV gain-scheduling design to provide MAP set-point tracking in the presence of disturbances and varying input delays.

In this paper, non-perturbed and perturbed systems of non-linear differential equations with multiple constant delays are considered. Five new theorems on the qualitative properties of solutions, uniform asymptotic stability (UAS) and instability of trivial solution, boundedness and integrability of solutions, are obtained. The technique of the proofs is based on the construction of two new Lyapunov-Krasovskii functionals (LKFs). An advantage of the new LKFs used here is that they allow to eliminate the Gronwall's inequality and to obtain more convenient conditions. When we compare our results with the related results in the literature, the established conditions here are new, more convenient and general, less conservative, and they are more suitable for applications. We provide three examples to show the applications of the results of this paper.

In this paper, a novel controller is proposed to simultaneously stabilize a collection of singular time-delay systems with actuator saturation constraints. The proposed controller is designed in a manner not only to stabilize the given finite family of systems but also to improve their transient responses. The ability of the designed controller to simultaneously stabilize the collection of considered systems is investigated through a theorem. The sufficient conditions are extracted in the term of LMIs via delay-dependent analysis by selecting appropriate Lyapunov-Krasovskii Functionals (LKFs). The theoretical achievements will also be verified by computer simulations.

In this paper, a class of systems of linear and non-linear delay differential equations (DDEs) of first order with time-varying delay is considered. We obtain new sufficient conditions for uniform asymptotic stability of zero solution, integrability of solutions of an unperturbed system and boundedness of solutions of a perturbed system. We construct two appropriate Lyapunov–Krasovskiĭ functionals (LKFs) as the main tools in proofs. The technique of the proofs depends upon the Lyapunov–Krasovskiĭ method. For illustration, two examples are provided in particular cases. An advantage of the new LKFs used here is that they allow to eliminate using Gronwall’s inequality. When we compare our results with recent results in the literature, the established conditions are more general, less restrictive and optimal for applications.

This chapter focuses on studying the state estimation problem for continuous-time systems with time-varying delay and constructing a proper Lyapunov–Krasovskii functional (LKF), which is crucial for deriving less conservative estimation criteria. The main idea of previous LKFs are by employing more state information, and all they are composed of positive definite terms. In this chapter, we propose a delay-product-type LKF with negative definite terms and estimate its derivative by the third-order Bessel–Legendre (B-L) based integral inequality together with mixed convex combination approaches. Based on the novel LKF, we obtain the desired estimator gain matrices and the H ∞ performance index by solving a set of linear matrix inequalities (LMIs). Finally, we give numerical examples to demonstrate the effectiveness of the proposed method.

In this paper, an adaptive neural network control method is described to stabilize a continuous stirred tank reactor (CSTR) subject to unknown time-varying delays and full state constraints. The unknown time delay and state constraints problem of the concentration in the reactor seriously affect the input-output ratio and stability of the entire system. Therefore, the design difficulty of this control scheme is how to debar the effect of time delay in CSTR systems. To deal with time-varying delays, Lyapunov–Krasovskii functionals (LKFs) are utilized in the adaptive controller design. The convergence of the tracking error to a small compact set without violating the constraints can be identified by the time-varying logarithm barrier Lyapunov function (LBLF). Finally, the simulation results on CSTR are shown to reveal the validity of the developed control strategy.

This paper deals with the problem of delay-dependent robust dissipativity analysis for uncertain neural networks with additive time varying delays by using a more general activation function approach. Different from previous literature, some sufficient information on neuron activation function and additive time-varying delays have been considered. By constructing suitable Lyapunov–Krasovskii functionals (LKFs) with some new integral terms, and estimating their derivative by using newly developed single integral inequality that includes Jensen’s inequality and Wirtinger-based integral inequality as a special case. A new delay-dependent less conservative global asymptotic stability and dissipative criteria have been established in the form of linear matrix inequalities (LMIs) technique. The effectiveness and advantages of the proposed results are verified by available standard numerical packages.

In this paper, the stability of time-delayed neural networks (DNN) is further analyzed. First, an augmented N-dependent Lyapunov-Krasovskii functional (LKF) is designed, where the non-integral terms are augmented with delay-dependent items and some additional state variables, and the integrated vector in the single-integral terms is also augmented by adding some integral interval-dependent items. The novel LKF complements some coupling information between the neuron activation function and other state variables. Second, a new delay-dependent stability criterion is proposed via the above LKF application. Third, in order to further demonstrate the advantages of the new LKF, two corollaries are also given under other simplistic LKFs. Finally, some common numerical examples are presented to show the effectiveness of the proposed approach.

In this article, we construct new specific conditions for the asymptotic stability (AS) and boundedness (B) of solutions to nonlinear Volterra integro-differential equations (VIDEs) of first order with a constant retardation. Our analysis is based on the successful construction of suitable Lyapunov–Krasovskii functionals (LKFs). The results of this paper are new, and they improve and complete that can be found in the literature. Keywords: Volterra integro-differential equation, First order, Retardation, Asymptotic stability, Boundedness, Lyapunov–Krasovskii functional

In this paper, the stability problem of discrete-time systems with time-varying delay is considered. Some new stability criteria are derived by using a switching technique. Compared with the Lyapunov–Krasovskii functional (LKF) approach, the method used in this paper has two features. First, a switched model, which is equivalent to the original system and contains more delay information, is introduced. It means that the criteria obtained by using the LKF method can be regarded as stability criteria for the switched system under arbitrary switching. Second, when the switching signal is known, the stability problem for the switched model under constrained switching is considered and piecewise LKFs are adopted to obtain stability criteria. Since constrained switching is less conservative than arbitrary switching if the switching signal is known, one can know that the obtained results in this paper are less conservative than some existing ones. Two examples are given to illustrate the effectiveness of the obtained results.

This paper addresses an improved stability criterion for an interval time-delayed neural networks (NNs) including neutral delay and leakage delay. By proposing a suitable Lyapunov–Krasovskii functionals (LKFs) together with the Auxiliary function-based integral inequality (AFBII) and reciprocally convex approach (RCC) approach. The major purpose of this research is put forward to the consideration of inequality techniques together with a suitable LKFs, and mixed with the Leibniz–Newton formula within the structure of linear matrix inequalities (LMIs). It is amazing that, the leakage delay has a disrupting impact on the stability behaviour of such system and they cannot be neglected. Finally, numerical examples have been demonstrated to showing feasibility and applicability of the developed technique. In addition, the developed stability criteria tested for feasibility of the benchmark problem to explore the real-world application in the sense of discrete time-delay and leakage delay as a process variable in the system model.

This paper is concerned with the stability analysis of Lur’e systems with sector-bounded nonlinearity and two additive time-varying delay components. In order to accurately understand the effect of time delays on the system stability, the extended matrix inequality for estimating the derivative of the Lyapunov–Krasovskii functionals (LKFs) is employed to achieve the conservatism reduction of stability criteria. It reduces estimation gap of the popular reciprocally convex combination lemma (RCCL). Combining the extended matrix inequality and two types of LKFs lead to several stability criteria, which are less conservative than the RCCL-based criteria under the same LKFs. Finally, the advantages of the proposed criteria are demonstrated through two examples.

This paper focuses on the stability analysis for neutral systems with discrete and distributed constant time-delays. Lyapunov-Krasovskii functionals (LKFs) are constructed by non uniformly dividing the whole delay interval into multiple segments and choosing proper functionals with different weighting matrices coressponding to different segments in the LKFs. By employing these LKFs, some new delay-derivative-dependent stability criteria are established for the neutral system in the delay partition approach. By utilizing the delay partition approach, the obtained stability criteria are stated in terms of linear matrix inequalities. Finally, some numerical examples are provided to illustrate the effectiveness of the proposed approach less conservative than the existing ones.

This paper investigates the problems of exponential stability and dissipativity of generalized neural networks (GNNs) with time-varying delay signals. By constructing a novel Lyapunov-Krasovskii functionals (LKFs) with triple integral terms that contain more advantages of the state vectors of the neural networks, and the upper bound on the time-varying delay signals are formulated. We employ a new integral inequality technique (IIT), free-matrix-based (FMB) integral inequality approach, and Wirtinger double integral inequality (WDII) technique together with the reciprocally convex combination (RCC) approach to bound the time derivative of the LKFs. An improved exponential stability and strictly (Q,S,R)-γ-dissipative conditions of the addressed systems are represented by the linear matrix inequalities (LMIs). Finally, four interesting numerical examples are developed to verify the usefulness of the proposed method with a practical application to a biological network.

In this paper, a new inner product space is defined, which has a standard orthogonal basis. Based on this basis, an improved integral inequality is established, which is used to construct a new Lyapunov–Krasovskii functionals (LKFs). Thus, a less conservative exponential stability criterion of time-delay systems is obtained, which is in form of linear matrix inequalities(LMIs). Finally, non-conservatism of this exponential stability criterion can be not only numerically illustrated by an example, but also rigorously proved in theory.

This paper is concerned with the stability analysis of linear continuous-time delay-difference systems with three delays. Firstly, a new method for testing the L 2 -exponential stability of the considered system is proposed, which is easier to use than the one in the existing literature. In view of the conservatism and the complexity of the obtained stability conditions in the existing literature, a complete Lyapunov-Krasovskii functional (LKF) is constructed by analyzing the relationship among the three delays. Sufficient conditions for both L 2 -exponential stability and exponential stability are then derived based on the constructed LKFs, which are delay-independent. A numerical example is provided to demonstrate the effectiveness and less conservativeness of the proposed method.

This paper is concerned with the delay-dependent stability analysis of linear systems with a time-varying delay. Two types of improved Lyapunov–Krasovskii functionals (LKFs) are developed to derive less conservative stability criteria. First, a new delay-product-type LKF, including single integral terms with time-varying delays as coefficients is developed, and two stability criteria with less conservatism due to more delay information included are established for different allowable delay sets. Second, the delay-product-type LKF is further improved by introducing several negative definite quadratic terms based on the idea of matrix-refined-function-based LKF, and two stability criteria with more cross-term information and less conservatism for different allowable delay sets are also obtained. Finally, a numerical example is utilized to verify the effectiveness of the proposed methods.

This paper is concerned with the stability criteria for a discrete-time linear system with interval time-varying delays. By using the time delay division we construct an augmented Lyapunov–Krasovskii functional for two delay subintervals. Moreover, we use a new summation inequality to estimate the derivatives of LKFs more accurately and derive less conservative criteria. Finally, we present two numerical examples to demonstrate that the obtained results are less conservative.

This paper deals with the problem of delay-dependent stability analysis for singular systems with a constant time delay. By employing the Jensen inequality and the Wirtinger-based inequality, new delay-dependent stability criteria are developed. Furthermore, in order to obtain less conservative results, a new method of constructing Lyapunov--Krasovskii functionals (LKFs) is used. It should be pointed out that the positive-definiteness restrictions on some symmetric matrices of the LKFs are removed. All the criteria are proposed in terms of strict linear matrix inequalities. Finally, numerical examples are given to demonstrate the less conservatism of the results.

The H∞ performance analysis and controller design for linear networked control systems (NCSs) are presented. The NCSs are considered a linear continuous system with time-varying interval input delay by assuming that the sensor is time-driven and the logic Zero-order-holder (ZOH) and controller are event-driven. Based on this model, the delay interval is divided into two equal subintervals for H∞ performance analysis. An improved H∞ stabilization condition is obtained in linear matrix inequalities (LMIs) framework by adequately considering the information about the bounds of the input delay to construct novel Lyapunov–Krasovskii functionals (LKFs). For the purpose of reducing the conservatism of the proposed results, the bounds of the LKFs differential cross terms are properly estimated without introducing any slack matrix variables. Moreover, the H∞ controller is reasonably designed to guarantee the robust asymptotic stability for the linear NCSs with an H∞ performance level γ. Numerical simulation examples are included to validate the reduced conservatism and effectiveness of our proposed method.

The problem of stability analysis for neural networks (NNs) with interval time-varying delay is investigated. New delay-decomposing approaches which are dividing the variation interval of the delay into two unequal subintervals are proposed. Some new simple Lyapunov–Krasovskii functionals (LKFs) are defined on the obtained subintervals. The integral inequality method and the reciprocally convex technique are utilized to deal with the derivative of the LKFs. Several improved delay-dependent criteria are derived in terms of the linear matrix inequalities (LMIs). Compared with some previous criteria, the proposed ones give the results with less conservatism and lower numerical complexity. Two numerical examples are included to illustrate the effectiveness and the improvement of the proposed method.

In this study, distributed dynamic event-triggered controller containing Markov switching topologies is proposed in Markovian Complex Networks (MCNs). It is proved that the Zeno-behavior is avoided. Considering that the time delay and the controller vary with different modes in practical applications, two terms of the controller are designed to contain Markov switching. And mode-dependent Lyapunov–Krasovskii functions (LKFs) are constructed, whereby the time-varying delay with Markov switching in the controller is perfectly processed. And by constructing a pair of LKFs, some summation terms containing the transition probability are eliminated. In addition, two synchronization criteria for MCNs with input mode delay and Markovian directed communication are established. Finally, numerical simulations are given to illustrate the effectiveness of the proposed method.

This paper establishes a novel non-fragile sampled data control framework for non linear multi-agent systems with additive time varying delays and Markovian jump parameters. The Laplacian matrix represents the interconnection between the agents which are denoted by an undirected graph. Relevant Lyapunov Krasovskii functional (LKF) is constructed which contain major information about the additive time-varying delays. The major goal of this paper is to model a non-fragile sampled-data control scheme which guarantees the stabilization for the proposed system. Apart from that, the Jensen’s and some improved integral inequalities are used for deriving the derivatives of LKFs with single, double and triple integral terms and the adequate conditions are expressed in terms of linear matrix inequalities. At last two numerical examples are given to verify the theoretical results.

The problem of absolute stability analysis for neutral-type Lur’e systems with time-varying delays is investigated. Novel delay-decomposing approaches are proposed to divide the variation interval of the delay into three unequal subintervals. Some new augment Lyapunov–Krasovskii functionals (LKFs) are defined on the obtained subintervals. The integral inequality method and the reciprocally convex technique are utilized to deal with the derivative of the LKFs. Several improved delay-dependent criteria are derived in terms of the linear matrix inequalities (LMIs). Compared with some previous criteria, the proposed ones give the results with less conservatism and lower numerical complexity. Two numerical examples are included to illustrate the effectiveness and the improvement of the proposed method.

This paper is concerned with passivity of a class of delayed neural networks. In order to derive less conservative passivity criteria, two Lyapunov–Krasovskii functionals (LKFs) with delay-dependent matrices are introduced by taking into consideration a second-order Bessel–Legendre inequality. In one LKF, the system state vector is coupled with those vectors inherited from the second-order Bessel–Legendre inequality through delay-dependent matrices, while no such coupling of them exists in the other LKF. These two LKFs are referred to as the coupled LKF and the noncoupled LKF, respectively. A number of delay-dependent passivity criteria are derived by employing a convex approach and a nonconvex approach to deal with the square of the time-varying delay appearing in the derivative of the LKF. Through numerical simulation, it is found that: 1) the coupled LKF is more beneficial than the noncoupled LKF for reducing the conservatism of the obtained passivity criteria and 2) the passivity criteria using the convex approach can deliver larger delay upper bounds than those using the nonconvex approach.

In this paper, we focus on the problem of exponential stability analysis of linear discrete-time systems with two constant delays. The proper Lyapunov-Krasovskii functionals (LKFs) are constructed. By employing WDOPs-based summation inequalities, an exponential stability criterion is obtained, which is given in terms of linear matrix inequalities (LMIs), and exponential estimates of all solutions of linear discrete-time systems with two constant delays are also obtained. An example illustrates that the presented WDOPs-based summation inequality method can get the exponential stability criterion with larger decay rate than the existence.

This paper studies the problem ofH∞state estimation for a class of delayed static neural networks. The purpose of the problem is to design a delay-dependent state estimator such that the dynamics of the error system is globally exponentially stable and a prescribedH∞performance is guaranteed. Some improved delay-dependent conditions are established by constructing augmented Lyapunov-Krasovskii functionals (LKFs). The desired estimator gain matrix can be characterized in terms of the solution to LMIs (linear matrix inequalities). Numerical examples are provided to illustrate the effectiveness of the proposed method compared with some existing results.

In this paper, a class of uncertain neural networks with discrete interval and distributed time-varying delays and Markovian jumping parameters (MJPs) are carried out. The Markovian jumping parameters are modeled as a continuous-time, finite-state Markov chain. By using the Lyapunov-Krasovskii functionals (LKFs) and linear matrix inequality technique, some new delay-dependent criteria is derived to guarantee the mean-square asymptotic stability of the equilibrium point. Numerical simulations are given to demonstrate the effectiveness of the proposed method. The results are also compared with the existing results to show the less conservativeness.

The field of Arctic sea ice prediction on “weather time scales” is still in its infancy with little existingunderstanding of the limits of predictability. This is especially true for sea ice deformation alongso-called Linear Kinematic Features (LKFs) including leads that are relevant for marine operations.Here the potential predictability of the sea ice pack in the wintertime Arctic up to ten days aheadis determined, exploiting the fact that sea ice-ocean models start to show skill at representing seaice deformation at high spatial resolutions. Results are based on ensemble simulations with a high-resolutionsea ice-ocean model driven by atmospheric ensemble forecasts. The predictability of LKFsas measured by different metrics drops quickly, with predictability being almost completely lost after4–8 days. In contrast, quantities such as sea ice concentration or the location of the ice edge retainhigh levels of predictability throughout the full 10-day forecast period. It is argued that the rapiderror growth for LKFs is mainly due to the chaotic behaviour of the atmosphere associated with thelow predictability of near surface wind divergence and vorticity; initial condition uncertainty for icethickness is found to be of minor importance as long as LKFs are initialized at the right locations.

This paper is primarily concerned with the event-triggered adaptive containment control for the second-order linear multi-agent systems (MASs) subject to time-varying input delays. Different from traditional methods, the triggering thresholds can be time-variable and achieved online, which are regulated by the triggering error. Then the number of transmitted data is modulated by two adaptive laws that play a crucial role in deciding whether to release the current data or not. By selecting two augmented types of Lyapunov-Krasovskii functionals (LKFs) and applying three effective inequalities, these earlier ignored information can be recollected and the field of application can be greatly enlarged. Moreover, the issues on delay-dependence respectively take uniform input delay and nonuniform input ones into consideration, in which the inter-relationship among time-delays can be involved. Finally, two MAS examples are exploited to illustrate our theoretical results.