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This paper studies the dissipative filtering of uncertain singular time-varying delay Markovian jump systems (MJSs) with nonlinear perturbations and generally uncertain transition rates (GUTRs). We focus on the design of a mixed filter, which can include mode-dependent and mode-independent filters in a unified and simple structure. First, a new Lyapunov–Krasovskii functional is proposed through the delay-decomposition approach, and improved Wirtinger-based integral inequalities are used to obtain a sufficient condition to ensure the stochastic admissibility of the considered uncertain nonlinear singular time-varying delay MJSs with dissipative performance. Based on these ingredients, the explicit expression of the desired mixed filter is obtained. Finally, some numerical examples and the filter design of a two-loop circuit network reflect the less conservatism and effectiveness of the method in this article. [ABSTRACT FROM AUTHOR]

With the aid of disturbance observer strategy, this article aims to investigate the disturbance rejection and stabilization problems for periodic piecewise time-varying systems that are subject to time-varying delays, parameter uncertainties, nonlinear perturbations and exogenous disturbances. To be more specific, the periodic piecewise time-varying systems are built by segmenting the fundamental period of periodic systems into a limited number of subintervals. Further, the disturbances engendered from an exogenous system are estimated by deploying the disturbance observer and subsequently, on the premise of disturbance that is esimated, a robust controller protocol is constructed for the considered system. Moreover, by bridging the time-varying periodic piecewise Lyapunov-Krasovskii functional with a matrix polynomial lemma, a set of adequate criteria is framed, which confirms the asymptotic stability of the system that is being addressed. Subsequently, on the premise of established criteria, the design of periodic piecewise gain matrices of devised controller and configured observer are presented. Eventually, the importance and potential of the presented theoretical concepts are evidenced through offering a numerical illustration with the simulation results.

In this paper, a generalized n-species Gilpin–Ayala competition system with saturation effect and nonlinear perturbations is proposed and examined. We first develop a new mathematical technique called “stochastic ϵ -threshold method”, to tackle the nonlinear perturbations and study the competitive coexistence, which includes the existence of ergodic stationary distribution as well as stochastic positive periodic solution. It should be mentioned that the method can be successfully applied to the species coexistence of other biological models. Then, we establish sufficient conditions for exponential extinction of competing species. Finally, several numerical examples are provided to support our theoretical results and analyze the impact of key parameters. [ABSTRACT FROM AUTHOR]

In this paper, we examine an n-species Lotka-Volterra competition system with general infinite distributed delays and nonlinear perturbations. The stochastic boundedness and extinction are first studied. Then we propose a new p-stochastic threshold method to establish sufficient conditions for the existence of stationary distribution ℓ(·). By solving the corresponding Fokker--Planck equation, we derive the approximate expression of the distribution ℓ (·) around its quasi-positive equilibrium. For the stochastic system with periodic coefficients, we use the p-stochastic threshold method again to obtain the existence of positive periodic solution. Besides, the related competition exclusion and moment estimate of species are shown. Finally, some numerical simulations are provided to substantiate our analytical results. [ABSTRACT FROM AUTHOR]

The main concern of this paper is finite-time stability (FTS) for uncertain discrete-time stochastic nonlinear systems (DSNSs) with time-varying delay (TVD) and multiplicative noise. First, a Lyapunov–Krasovskii function (LKF) is constructed, using the forward difference, and less conservative stability criteria are obtained. By solving a series of linear matrix inequalities (LMIs), some sufficient conditions for FTS of the stochastic system are found. Moreover, FTS is presented for a stochastic nominal system. Lastly, the validity and improvement of the proposed methods are shown with two simulation examples. [ABSTRACT FROM AUTHOR]

This article is focused on the design of an output tracking control scheme for a class of continuous-time periodic piecewise time-varying systems (PPTVSs) with actuator saturation and nonlinear perturbations. The energy-to-peak tracking performance is studied based on an equivalent condition on the definiteness property of matrix polynomials. Considering the actuator saturation and nonlinear perturbation, matrix polynomial-based sufficient conditions are derived through the Lyapunov method using periodic matrix functions. From a perspective of subinterval segmentation aimed at PPTVSs, the proposed conditions can achieve less conservatism for tracking the output of a periodic time-varying reference system, while the controller gains can be computed using convex optimization. Moreover, a heuristic algorithm is constructed to simultaneously guarantee the closed-loop state convergence and the output tracking performance. The reduction in conservatism and the effectiveness of algorithm are demonstrated by illustrative case studies. [ABSTRACT FROM AUTHOR]

This paper studies the convergence behavior of a type of T-S fuzzy system with interval time-varying delay and nonlinear perturbations. A delay partitioning method is used to construct a modified Lyapunov Krasovskii functional(LKF) including triple-integral terms and augmented factors, which is introduced from these equidistant subintervals. In addition, the Free-Matrix-Based integral inequality is employed to avoid the overabundance of the enlargement when dealing with the derivative of the LKF. Eventually, much less conservative results are presented. Numerical analyses are conducted to demonstrate the evaluation of this proposed research development. [ABSTRACT FROM AUTHOR]

This paper deals with the stability and stabilization problems of time-delay systems with nonlinear perturbations. The perturbations are modelled by a nonlinear function of current and/or delayed states. By utilizing Lyapunov–Krasovskii functional, sufficient conditions are obtained in terms of LMIs for the different types of perturbations. The stabilization problem is originally non-convex because of the coupling between the Lyapunov matrices and the controller gains. In order to decouple decision variables, the Young's relation is used in a judicious manner. Numerical examples are given to demonstrate that the proposed method can provide a state feedback controller for a larger delay range than existing methods. [ABSTRACT FROM AUTHOR]

The finite-time H∞ control problem for an Itô-type stochastic system with nonlinear perturbation and time delay is investigated. First, the finite-time H∞ control problem for a nonlinear time-delay stochastic system is presented taking into consideration both the transient performance and the capability to attenuate the disturbance of a closed-loop system in a given finite-time interval. Second, using the Lyapunov-Krasoviskii functional method and the matrix inequality technique, some sufficient conditions for the existence of finite-time H∞ state feedback controller and dynamic-output feedback controller for nonlinear time-delay stochastic systems are obtained. These conditions guarantee the mean-square finite-time bounded-ness of the closed-loop systems and determine the H∞ control performance index. Third, this problem is transformed into an optimization problem with matrix inequality constraints, and the corresponding algorithms are given to optimize the H performance index and obtain the maximum time-delay. Finally, a numerical example is used to illustrate the effectiveness of the proposed method.

We prove that whenever a sequence of bounded operators (Am)m∈ℤ{(A_{m})_{m\in\mathbb{Z}}} acting on a Banach space X admits an exponential dichotomy and a sequence of differentiable maps fm:X→X{f_{m}\colon X\to X}, m∈ℤ{m\in\mathbb{Z}}, has bounded and Hölder derivatives, the nonautonomous dynamics given by xm+1=Am⁢xm+fm⁢(xm){x_{m+1}=A_{m}x_{m}+f_{m}(x_{m})}, m∈ℤ{m\in\mathbb{Z}}, has various shadowing properties. Hence, we extend recent results of Bernardes Jr. et al. in several directions. As a nontrivial application of our results, we give a new proof of the nonautonomous Grobman–Hartman theorem.

Let $(A_m)_{m \in {\mathop Z}}$ be a sequence of bounded linear maps acting on an arbitrary Banach space X and admitting an exponential trichotomy and let $f_m:X \to X$ be a Lispchitz map for every $m\in {\mathop Z} $. We prove that whenever the Lipschitz constants of $f_m$ , $m \in {\mathop Z} $ , are uniformly small, the nonautonomous dynamics given by $x_{m+1}=A_mx_m+f_m(x_m)$ , $m\in {\mathop Z} $ , has various types of shadowing. Moreover, if X is finite dimensional and each $A_m$ is invertible we prove that a converse result is also true. Furthermore, we get similar results for one-sided and continuous time dynamics. As applications of our results, we study the Hyers–Ulam stability for certain difference equations and we obtain a very general version of the Grobman–Hartman's theorem for nonautonomous dynamics. [ABSTRACT FROM AUTHOR]

The main concern of this paper is finite-time stability (FTS) for uncertain discrete-time stochastic nonlinear systems (DSNSs) with time-varying delay (TVD) and multiplicative noise. First, a Lyapunov–Krasovskii function (LKF) is constructed, using the forward difference, and less conservative stability criteria are obtained. By solving a series of linear matrix inequalities (LMIs), some sufficient conditions for FTS of the stochastic system are found. Moreover, FTS is presented for a stochastic nominal system. Lastly, the validity and improvement of the proposed methods are shown with two simulation examples.

Based on a sliding mode control, a multi‐area decentralised load frequency control power system with time‐varying delays and non‐linear perturbations is designed in this study. Due to the destabilising effect of delay on the global system, it is necessary to design a control system to accommodate vast time delays so as to manage the deviation in frequency and interchange power. By taking advantage of the system structure and disturbance bounds, robustness is improved. A sliding surface is designed, and the stability of the corresponding sliding motion is analysed based on Lyapunov–Razumikhin function. A delay dependent decentralised sliding mode control is synthesised to drive the system to the sliding surface and maintain a sliding motion afterwards. The obtained results are applied to a two‐area interconnected power system to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In a cyber-physical micro-grid system, wherein the control functions are executed through open communication channel, stability is an important issue owing to the factors related to the time-delay encountered in the data transfer. Transfer of feedback variable as discrete data packets in communication network invariably introduces inevitable time-delays in closed loop control systems. This delay, depending upon the network traffic condition, inherits a time-varying characteristic; nevertheless, it adversely impacts the system performance and stability. The load perturbations in a micro-grid system are considerably influenced by the presence of fluctuating power generators like wind and solar power. Since these non-conventional energy sources are integrated into the power grid through power electronic interface circuits that usually works at high switching frequency, noise signals are introduced into the micro-grid system and these signals gets super-imposed to the load variations. Based on this back ground, in this paper, the delay-dependent stability issue of networked micro-grid system combined with timevarying feedback loop delay and uncertain load perturbations is investigated, and a deeper insight has been presented to infer the impact of time-delay on the variations in the system frequency. The classical Lyapunov-Krasovskii method is employed to address the problem, and using a standard benchmark micro-grid system, and the proposed stability criterion is validated. [ABSTRACT FROM AUTHOR]

This paper address the stochastic stability of neutral markovian jumping systems with nonlinear perturbations. By constructing novel Lyapunov functionals which contain an augmented Lyapunov functional, and combining with the new inequalities, new delay-dependent stochastic stability criteria for the nominal systems are obtained. The asymptotically stable condition is a special case for the stochastic stability condition as the systems without markovian jump. Numerical examples show that the derived conditions are much less conservative than those given in the existing literature. [ABSTRACT FROM AUTHOR]

The exponential stability problem of uncertain neutral complex system with Markovian switching is investigated in the presence of nonlinear perturbations and partial information on transition rates. The study begins to consider the related nominal systems and construct a novel augmented stochastic Lyapunov functional which contains some triple-integral terms to reduce the conservatism. Then the exponential stability criteria are developed by utilizing Lyapunov stability theory, reciprocally convex lemma and free-weighting matrices. The results are further extended to the corresponding uncertain case. Finally, numerical examples are given to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

In this study, the exponential stability problem of impulsive system is investigated via sampled‐data control in the presence of random time‐varying delays and non‐linear perturbations. In particular, the time delays are considered to be randomly time varying and they obey the Bernoulli distributions. The authors' main attention is focused on the design of a sampled‐data controller to ensure an exponential stability for the closed‐loop system. By extending the first‐ and second‐order reciprocal convex approach, an efficient method called third‐order reciprocal convex technique is used to manipulate the main results. Through the construction of a suitable Lyapunov–Krasovskii functional combined with input delay approach and Briat lemma, several delay‐dependent sufficient conditions for the concerned system are derived in the form of linear matrix inequalities which can be readily solved by utilising the valid software packages. Some numerical examples are given to illustrate the effectiveness of the developed control technique. [ABSTRACT FROM AUTHOR]

This paper studies the problem of actuator-nonlinearities compensation in the multi-input uncertain neutral systems. The neutral systems with different unknown time-varying delays, unmodeled dynamics, nonlinear perturbations and disturbances are considered. A new methodology based on the online estimation of the delays to compensate for the effects generated by dead-zone and saturation, acting in series on a system's input are presented. The online estimations of the unknown delays are accomplished by adaptive laws that guarantee the exponential stabilities of the estimated delays. In the presence of state time delay, derivative state time delay, unmodeled dynamics, nonlinear perturbations, disturbances and both input dead-zone and saturation, the asymptotic stability of the closed-loop system is ensured and the state response converge to the origin. Finally, the practicability and the efficacy of the proposed approach is demonstrated via a numerical example. [ABSTRACT FROM AUTHOR]

This study deals with the problem of robust stabilisation for non‐linear time‐delay semi‐Markovian jump systems via sliding mode control (SMC). Such a switching is governed by a semi‐Markovian process which is time‐varying and dependent on the sojourn‐time h. The time delay is considered as time‐varying and meets the requirements of the upper and lower bounds. By introducing free‐connection weighting matrix method and Lyapunov functional, sufficient conditions for the resulting sliding mode dynamics in the form of linear matrix inequalities are derived to guarantee the closed‐loop system robustly stochastically stable for all admissible uncertainties and non‐linear perturbations. Then, an SMC law is synthesised to drive the system trajectories onto the predefined switching surface in a finite time. Finally, an example illustrates the validity of the obtained results. [ABSTRACT FROM AUTHOR]

This paper investigates the robust dynamic output feedback non-fragile control (RDOFNFC) strategy for spacecraft attitude stabilization problem with nonlinear perturbations. The spacecraft attitude dynamics model takes the actuator saturation limits, external disturbances, controller perturbation and model parameter uncertainty into account. To make spacecraft attitude system satisfy H ∞ performance and quadratic stability, with respect to the additive perturbation in initial state and multiplicative perturbation in decay phase, the corresponding RDOFNFC is designed respectively. Based on Lyapunov theory, the controller design is transformed into a multi-objective convex optimization problem based on linear matrix inequalities (LMIs). Simulation results based on the on-orbit servicing spacecraft show good performance under external disturbances, model parameter uncertainty and controller perturbation, which validates the effectiveness and feasibility of the proposed control method. [ABSTRACT FROM AUTHOR]

This study is concerned with the problem of robust H∞ sliding mode control (SMC) of It o^ stochastic delayed Markovian jump systems subject to parameter uncertainties and non‐linear perturbations. Firstly, for the sake of practicality, a common integral sliding surface functional without time‐varying delay is proposed. Then, by using linear matrix inequalities technique, sufficient condition for the robust mean‐square exponential stability of the resulting closed‐loop system with a prescribed disturbance attenuation level γ is derived. Moreover, a novel sliding mode controller is designed such that system trajectories can be kept on the sliding surface almost surely since the initial time. Finally, an example is provided to illustrate the effectiveness of the obtained result. [ABSTRACT FROM AUTHOR]

This study investigates the problem of finite-time control for uncertain systems with nonlinear perturbations. The aim is to design the state-feedback and output-feedback controller which ensure finite-time boundedness and with a desired $H_{\infty}$ performance index υ. Specifically, first, we divide the time-varying delay into non-uniformly subintervals and decompose the corresponding integral intervals to estimate the bounds of integral terms exactly. Second, the conditions obtained in this paper are formulated in terms of linear matrix inequalities (LMIs), which can be efficiently solved via standard numerical software. Finally, numerical examples are presented to demonstrate the effectiveness and advantages of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the problem of delay-dependent stability is investigated for uncertain Markovian jump neural networks with leakage delay, two additive time-varying delay components, and nonlinear perturbations. The Markovian jumping parameters in the connection weight matrices and two additive time-varying delay components are assumed to be different in the system model, and the Markovian jumping parameters in each of the two additive time-varying delay components are also different. The relationship between the time-varying delays and their upper delay bounds is efficiently utilized to study the suggested system in two cases: with known or unknown parameters, which leads to more information of the lower and upper bounds of the time-varying delays that can be used. By constructing a newly augmented Lyapunov-Krasovskii functional and using the extended Wirtinger inequality and a reciprocally convex method, several sufficient criteria are derived to guarantee the stability of the proposed model. Numerical examples and their simulations are given to show the effectiveness and advantage of the proposed method. [ABSTRACT FROM AUTHOR]

This paper addresses improved stability results for T-S fuzzy systems with mixed delays and nonlinear perturbations. By introducing the geometric sequence division (GSD) method, the discrete delay interval can be separated into multiple subintervals with unequal lengths based on the common ratio α. Meanwhile integral partitioning method is applied to deal with the distributed delay. A Lyapunov-Krasovskii functional (LKF) is newly established with augmented factors and triple integral terms which are constructed by means of the length of every subintervals. In addition, in order to reduce the enlargement when we deal with the estimation of the LKF derivative, a free-matrix-based integral inequality, an extended reciprocal convex combination, and free weight matrices techniques are employed. A stability analysis of the delayed T-S fuzzy systems is presented with much less conservative criteria. At the end numerical examples are given to demonstrate the significant improvements of this proposed design. [ABSTRACT FROM AUTHOR]

This article reports on an investigation into robust guaranteed cost control (GCC) for uncertain switched neutral systems (USNSs) with interval time-varying mixed delays and nonlinear perturbations via dynamic output feedback. Delay-dependent sufficient conditions are suggested to guarantee the robust exponential stability and to obtain robust GCC for USNSs using the average dwell time approach and the piecewise Lyapunov function technique in terms of a set of linear matrix inequalities. The problem of uncertainty in the system model is solved by deploying the Yakubovich lemma. Lastly, two examples (i.e., a numerical example and the water-quality dynamic model for the Nile River) are given to verify the efficiency of the propounded theories. © 2016 Wiley Periodicals, Inc. Complexity 21: 555-578, 2016 [ABSTRACT FROM AUTHOR]

This paper presents improved stability results by introducing a new delay partitioning method based on the theory of geometric progression to deal with T-S fuzzy systems in the appearance of interval time-varying delays and nonlinear perturbations. A common ratio $$\alpha$$ is applied to split the delay interval into multiple unequal subintervals. A modified Lyapunov-Krasovskii functional (LKF) is constructed with triple-integral terms and augmented factors including the length of every subintervals. In addition, the recently developed free-matrix-based integral inequality is employed to combine with the extended reciprocal convex combination and free weight matrices techniques for avoiding the overabundance of the enlargement when deducing the derivative of the LKF. Eventually, this developed research work can efficiently obtain the maximum upper bound of the time-varying delay with much less conservatism. Numerical results are conducted to illustrate the remarkable improvements of this proposed method. [ABSTRACT FROM AUTHOR]

In this paper, a novel delay partitioning method is proposed by introducing the theory of geometric progression for the stability analysis of T–S fuzzy systems with interval time-varying delays and nonlinear perturbations. Based on the common ratio α , the delay interval is unequally separated into multiple subintervals. A newly modified Lyapunov–Krasovskii functional (LKF) is established which includes triple-integral terms and augmented factors with respect to the length of every related proportional subintervals. In addition, a recently developed free-matrix-based integral inequality is employed to avoid the overabundance of the enlargement when dealing with the derivative of the LKF. This innovative development can dramatically enhance the efficiency of obtaining the maximum upper bound of the time delay. Finally, much less conservative stability criteria are presented. Numerical examples are conducted to demonstrate the significant improvements of this proposed approach. [ABSTRACT FROM AUTHOR]

The problem of finite‐time stability for uncertain time‐varying delay systems with non‐linear perturbations and parametric uncertainties and switched time‐delay systems is studied. New integral inequality with exponential function is proposed to solve the stability problem. By using a suitable form of Lyapunov–Krasovskii‐like functional (LKLF) with exponential function, the integral inequality and estimations of LKLF in the initial and the current time, new delay‐dependent and less conservative stability criteria have been derived in terms of linear matrix inequalities. The average dwell time approach is used to study the FTS of switched time‐delay systems. Five numerical examples are given to show the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This study is concerned with the problem of leakage-delay-dependent stability analysis of Markovian jumping linear systems with time-varying delays and nonlinear perturbations. Mixed time-varying delays, which include leakage, discrete, and distributed delays, pertaining to the proposed system are addressed. Based on an improved Lyapunov–Krasovskii functional with triple integral terms and by employing the model transformation technique and the reciprocal convex method, the sufficient conditions for the delay-dependent stability of the considered system are derived. Moreover, the sufficient conditions obtained are formulated in terms of linear matrix inequalities to achieve the global asymptotical stability in mean square of the considered delayed system. Finally, numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper investigates almost sure exponential stability and feedback stabilization for switched time-delay systems with nonlinear stochastic perturbations. The main contributions of this paper are threefold: (i) based on the non-convolution type multiple Lyapunov functionals and the mathematical induction approach, a mean-square exponential stability condition for nonlinear stochastic switched systems is first established, such that the obtained average dwell time does not rely on any given decay rate; (ii) by using the method developed in part (i) and the stochastic analysis techniques and limit methods in probability, an almost sure exponential stability criterion for switched delayed systems with nonlinear stochastic uncertainties is presented, and then a state feedback controller for the systems under consideration is designed; and (iii) when certain assumptions are made on the nonlinear stochastic perturbations, the results in this paper are further improved by relaxing some conditions. The effectiveness of the proposed method is demonstrated by three illustrative examples. [ABSTRACT FROM AUTHOR]

In this paper, the problem of finite-time stability for discrete-time system with time-varying delay and nonlinear perturbations is investigated. By constructing a novel Lyapunov–Krasovskii functional and employing a new summation inequality named discrete Wirtinger-based inequality, reciprocally convex approach and zero equality, the improved finite-time stability criteria are derived to guarantee that the state of the system with time-varying delay does not exceed a given threshold when fixed time interval. Furthermore, the obtained conditions are formulated in forms of linear matrix inequalities which can be solved by using some standard numerical packages. Finally, three numerical examples are given to show the effectiveness and less conservatism of the proposed method. [ABSTRACT FROM AUTHOR]

This paper addresses the stabilization problem of neutral systems. The neutral systems assumed to be subjected to nonlinear perturbations and mixed time-varying delays. Specifically, the adaptive control method is used to stabilize the unknown neutral systems. If the system states and the delayed states with its derivatives are available for measurement, a new and less conservative adaptive control algorithm is proposed, and sufficient conditions for the existence of the adaptive control are derived based on Lyapunov's stability theory. The main idea is to make all the stability conditions of the system depend on desired arbitrary matrices, not on the given system matrices. This is accomplished by the adaptation process. Illustrative examples with numerical simulations are studied. The simulation results show the effectiveness of the proposed design methods. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper considers the problem of robust stability for a class of linear systems with interval time-varying delay and nonlinear perturbations. Less conservative stability criteria was put forward by using delay-partitioning approach. By decomposing the delay interval into multiple equidistant subintervals, new Lyapunov–Krasovskii (L–K) functional contains some triple-integral terms and augment terms which are introduced on these intervals, thus resulting in being much less conservative than most existing results in the literature. In addition, in deriving the stability conditions in linear matrix inequality (LMI) framework, neither model transformations nor superfluous free-weighting matrix are employed for dealing the cross-terms that emerge from the time derivative of the L–K functional; instead, they are dealt using tighter integral inequalities which only contain a minimal number of slack matrix variables. Numerical examples are given to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

The delay-range-dependent stochastic stability for uncertain neutral Markovian jump systems with interval time-varying delays and nonlinear perturbations is investigated. The perturbations under consideration are time-varying and norm-bounded. By delay interval dividing, a novel augmented Lyapunov functional which contains triple-integral terms to reduce the conservativeness is introduced. Based on the Lyapunov functional approach and the nature of convex combination, some improved delay-range-dependent stochastic stability criteria are obtained in terms of linear matrix inequalities without introducing any free-weighting matrices. Finally, numerical examples are given to illustrate the effectiveness of the developed techniques. [ABSTRACT FROM AUTHOR]

This paper concerns the stability analysis for singular systems with time-varying delay and nonlinear perturbations. Two cases of time-varying delay, which is differentiable (Case 1) or not differentiable (Case 2), are considered. The considered nonlinear perturbations includes the norm-bounded uncertainties as a special case. Some delay-dependent stability criteria are derived by using a delay decomposition approach. In the delay decomposition approach, the entire delay interval is divided into multiple sub-intervals for which different energy functions are defined for building new Lyapunov–Krasovskii functional. Some numerical and practical examples are given to show the effectiveness and significant improvement of the proposed method. [ABSTRACT FROM PUBLISHER]

In this paper, the problem of exponential stability for neutral system with time-varying delay and nonlinear perturbations is investigated. By using the technology of model transformations, based on a linear matrix inequality (LMI) and a generalized Lyapunov-Krasovskii function, a new criterion for exponential stability with delay dependence is obtained. Due to a new integral inequality, the result is less conservative. Finally, some numerical examples are presented to illustrate the effectiveness of the method. [ABSTRACT FROM AUTHOR]

This letter is concerned with robust stability of fractional-order linear delayed system with nonlinear perturbations over finite time interval. By using inequality technique, two new sufficient conditions for the finite time stability for such systems with order α: 0 α ≤ 0.5 and 0.5 < α < 1 are presented, respectively. A numerical example is presented to demonstrate the validity and feasibility of the obtained results. [ABSTRACT FROM AUTHOR]

Abstract: This paper studies the stability problem for a class of dynamical systems with leakage delay and nonlinear perturbations based on linear matrix inequality (LMI) approach. Some sufficient conditions which are dependent on the leakage delay are derived to ensure the global asymptotic stability by using Lyapunov–Krasovskii functional method and free weighting matrix technique. Two examples and their simulations are given to show the effectiveness and advantage of the present results. [Copyright &y& Elsevier]

Abstract: This paper investigates the stabilization of a class of nonlinear systems with distributed delays using impulsive control and switching control. Stabilizing impulsive forces as well as destabilizing disturbance impulses are considered. Verifiable sufficient conditions are established which guarantee the asymptotic or exponential stability of switched and impulsive systems with distributed delays. Results are found for when the impulses are applied at pre-specified times or at the switching instances. The criteria found are based on a special type of state-dependent switching rule which partitions the state space into stabilizing subregions. The main results are proved using a common Lyapunov functional. [Copyright &y& Elsevier]

Nonlinear perturbations of Friedmann-Lemaitre cosmologies with dust and a cosmological constant $$\Lambda >0$$ have recently attracted considerable attention. In this paper our first goal is to compare the evolution of the first and second order perturbations by determining their asymptotic behaviour at late times in ever-expanding models. We show that in the presence of spatial curvature K or a cosmological constant, the density perturbation approaches a finite limit both to first and second order, but the rate of approach depends on the model, being power law in the scale factor if $$\Lambda >0$$ but logarithmic if $$\Lambda =0$$ and $$K<0$$ . Scalar perturbations in general contain a growing and a decaying mode. We find, somewhat surprisingly, that if $$\Lambda >0$$ the decaying mode does not die away, i.e. it contributes on an equal footing as the growing mode to the asymptotic expression for the density perturbation. On the other hand, the future asymptotic regime of the Einstein-de Sitter universe ( $$K=\Lambda =0$$ ) is completely different, as exemplified by the density perturbation which diverges; moreover, the second order perturbation diverges faster than the first order perturbation, which suggests that the Einstein-de Sitter universe is unstable to perturbations, and that the perturbation series do not converge towards the future. We conclude that the presence of spatial curvature or a cosmological constant stabilizes the perturbations. Our second goal is to derive an explicit expression for the second order density perturbation that can be used to study the effects of including a cosmological constant and spatial curvature. [ABSTRACT FROM AUTHOR]