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This paper studies delay-dependent robust stability problem for neutral system with mixed time-varying delays and nonlinear perturbations. Based on the delay-dividing approach, a novel Lyapunov functional is constructed, and a novel delay-dependent stability criterion is derived to guarantee the robust stability of the neutral system. Expressed in terms of linear matrix inequalities, the stability condition can be checked using the numerically efficient Matlab LMI Control Toolbox. Two numerical examples are provided to demonstrate the effectiveness and the reduced conservatism of the analysis result.

Consider a perturbed KdV equation: ut+uxxx?6uux=??f(u)(x),x???=?/?,???u(x,t)dx=0,$$u_t+u_{xxx}-6uu_x=\epsilon f(u)(x),\quad x\in\mathbb{T}=\mathbb{R}/\mathbb{Z},\;\int_{\mathbb{T}}u(x,t)dx=0, $$ where the nonlinear perturbation defines analytic operators u(?)?f(u(?)) in sufficiently smooth Sobolev spaces. Assume that the equation has an ??-quasi-invariant measure μ and satisfies some additional mild assumptions. Let u??(t) be a solution. Then on time intervals of order ???1, as ???0, its actions I(u??(t,?)) can be approximated by solutions of a certain well-posed averaged equation, provided that the initial datum is μ-typical.

This paper deals with the control problems of semilinear fractional delay evolution equations. Under rather mild conditions, we study the topological structure of solution sets (compactness and Rδ-property). Then, the information about the structure is employed to show the invariance of a reachability set of the control problem under nonlinear perturbations. Finally, we present an example to illustrate the feasibility of the abstract results.

The problem of finite-time stability for a class of discrete-time switched systems in the presence of both non-Lipschitz perturbation and impulse effects is studied in this paper. Based on the average dwell-time approach, a criterion is proposed which ensures that the system’s state trajectory remains in a bounded region of the state space over a pre-specified finite-time interval if we impose a bound on the initial condition. It is shown that the finite-time stability degree could be greater than one, which is quite different from the existing results for asymptotic stability. Moreover, the total activation time of the Schur stable subsystems does not need to be greater than that of the unstable subsystems. A numerical example is presented to illustrate the effectiveness of the proposed design method.

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.

This paper is concerned with the adaptive observer design of Lur’e differential inclusions with unknown parameters. Under a relaxed assumption on nonlinear perturbation functions, a sufficient condition for the existence of an adaptive full-order observer is established. Comparing with results in the literature, the present conditions are complemented with a numerically reliable computational approach, which can be checked by means of linear matrix inequalities. Furthermore, it is shown that, under the sufficient condition, the existence of a reduced-order observer is guaranteed. Also, the reduced-order observer is designed. The effectiveness of the proposed design is illustrated via a simulation example.

This study is concerned with the problem of robust stability analysis of uncertain neutral system with time-varying delays and nonlinear perturbations. The parameter uncertainties are modeled as a structured linear fractional form. By choosing an augmented novel Lyapunov---Krasovskii functional which contains some triple integral terms and using the lower bound lemma to handle the integral terms, less conservative criteria are obtained. Moreover, the rigorous constraint that the derivatives of time-varying delays must be less than one has been removed. Finally, numerical examples are presented to illustrate the effectiveness of the theoretical results.

In this paper, two new nonlinear difference inequalities are considered, where the inequalities consist of multiple iterated sums and composite function of nonlinear function and unknown function may be involved in each layer. Under several practical assumptions, the inequalities are solved through rigorous analysis, and explicit bounds for the unknown functions are given clearly. Further, the derived results are applied to the stability problem of a class of linear control systems with nonlinear perturbations.

The exponential stability for neutral delay Markovian jump systems with nonlinear perturbations and partially unknown transition rates is investigated in this paper. With creative Lyapunov functional and novel matrix inequalities analysis, delay-range-dependent and rate-dependent exponential stability conditions are presented by reciprocally convex lemma and free weighting matrices. Numerical examples are given to demonstrate the effectiveness of the proposed methods.

Наведено математичну модель формування каверни при дії збурень різної природи, в основі якої лежать теорії потенціальних течій з вільними границями і малих збурень. Виконано аналіз результатів конкретних кавітаційних течій за конусами. Розглянуто метод розрахунку кавітаційних течій за конусами з урахуванням поля гравітації. Використано метод малих збурень вісесиметричної каверни. Диференціальні рівняння задачі лінеаризуються в околі незбуреної поверхні каверни. Побудовано математичну модель задачі у вигляді нескінченної системи нелінійних диференціальних рівнянь другого порядку. Задачу Коші для цієї системи розв’язано за допомогою пакету прикладної математики Matlab. На конкретних течіях показано процес деформування форми каверни під впливом поля гравітації

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.

We study the existence of discrete almost automorphic solutions and asymptotic behavior for non-linear Volterra difference equations of convolution type with infinite delay where the nonlinear perturbation is considered not necessarily globally Lipschitz. The results are a consequence of application of different fixed point theorems, namely, the contraction principle, the Leray-Schauder, the Krasnoselkii and Matkowski's fixed point technique.

In this paper we prove the existence of a solution for a mathematical model of carbon dioxide transport in concrete carbonation process. This model is a parabolic type equation with a nonlinear perturbation such that a coefficient of the time derivative contains a non-local term depending on the unknown function itself.

In this paper, we present a decentralized variable gain robust controller for a class of large-scale serially connected systems with nonlinear perturbations via piecewise Lyapunov functions. The nonlinear perturbation means the interconnections between the subsystems and uncertainties, and the proposed decentralized variable gain robust controller is designed so as to reduce the effect of uncertainties and interconnections. In this paper, on the basis of the concept of piecewise Lyapunov functions, we show sufficient conditions for the existence of the proposed decentralized variable gain robust controller. Finally, numerical examples are presented.

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.

In this paper, we deal with weighted pseudo almost automorphic behavior of hyperbolic semilinear integro-differential equations in intermediate Banach spaces, where the nonlinear perturbation is weighted pseudo almost automorphic type or weighted Stepanov-like pseudo almost automorphic type. As applications, some interesting examples are presented to illustrate the main findings.

In this work, the propagation of higher-dimensional nonlinear Rossby waves under the generalized beta effect is considered. Using the methods of weak nonlinear perturbation expansions and the multiple scales, we obtain a new (2 + 1)-dimensional generalized Boussinesq equation from the barotropic potential vorticity equation for the first time. Furthermore, a new dispersion relation for the linear Rossby waves is given corresponding to the linearized Boussinesq equation. More importantly, based on the methods of the traveling wave setting and the Jacobi elliptic function expansions, several kinds of exact traveling wave solutions for the higher-dimensional nonlinear Rossby waves, including the periodic solutions, solitary solutions and others are obtained. Finally, we simulate the solitary solutions obtained by using the method of the Jacobi elliptic function. The numerical results show that the amplitude of the Rossby solitary waves is decreasing with the increase of generalized beta effect.

This paper studies delay-dependent robust stability analysis for uncertain linear systems with constant delay, time-varying delay and nonlinear perturbations. The restriction on the derivative of time-varying delay is removed, which means that the fast time-varying delays are allowed. Combined with Leibniz-Newton formula, integral inequalities, Wirtinger-based integral inequality, Peng-Park’s integral inequality, utilization of zero equation and new Lyapunov-Krasovskii functional have been adopted to study. New delay-dependent robust stability criteria for uncertain time-delay systems are established in terms of linear matrix inequalities (LMIs). Numerical examples and simulation suggest that the results given to illustrate the effectiveness and improvement over some existing methods.

This work deal with asymptotic almost-periodicity of mild solutions for a class of difference equations with a Weyl-like fractional difference in Banach space. Based on a combination of a decomposition technique and the Krasnoselskii&rsquo, s fixed point theorem, we establish some new existence theorems of mild solutions with asymptotic almost-periodicity. Our results extend some related conclusions, since (locally) Lipschitz assumption on the nonlinear perturbation is not needed and with Lipschitz assumption becoming a special case. An example is presented to validate the application of our results.

We prove the existence of solution for a class of p(x)-Laplacian equations where the nonlinearity has a critical growth. Here, we consider two cases: the first case involves the situation where the variable exponents are periodic functions. The second one involves the case where the variable exponents are nonperiodic perturbations.

Incorporating the ITS in traffic flow, two lattice hydrodynamic models considering the following lattice are proposed to study the influence of the following lattice on traffic flow stability. The results from the linear stability theory show that considering the following lattice could lead to the improvement of the traffic flow stability. The modified Korteweg-de Vries equations (the mKdV equation, for short) near the critical point are derived by using the nonlinear perturbation method to show that the traffic jam could be described by the kink-antikink soliton solutions for the mKdV equations.

This paper focuses on the issue of robustly exponential stability for uncertain neutral systems with mixed time-varying delays and nonlinear perturbations. Some new sufficient conditions dependent on the delays are derived in terms of Lyapunov-Krasovskii functionals combined with free-weighting matrices. Two numerical examples are given to show the effectiveness of the proposed method.

The problem of mean square bounded-input-bounded-output (BIBO) stability for the stochastic delay systems with nonlinear perturbations is investigated in this paper. Using the Razumikhin technique combined with comparison principle, several novel BIBO mean square stability criteria are established. A numerical example is given to illustrate the effectiveness of our result.

Alexseev`s formula generalizes the variation of constants formula and permits the study of a nonlinear perturbation of a system with certain stability properties. In recent years M. Pinto introduced the notion of -stability. S.K. Choi et al. investigated -stability for the nonlinear differential systems using the notion of -similarity. Applying these two notions, we study bounds for solutions of the perturbed differential systems.

This paper is concerned with nonlinear nonlocal differential inclusion of evolution type in Frechet spaces, defined on right half-line. The underlying feature of the inclusion under consideration is that it is non-autonomous. We obtain some compactness characterizations of integral solution sets for the inclusion without nonlinear perturbations. Then, making use of these characterizations, we derive a new existence result of global integral solutions for the original inclusion. No invariance condition on the nonlinearity is involved. The results we obtained here extend the semilinear case of the previous related ones such as [I.I. Vrabie, Existence in the large for nonlinear delay evolution inclusions with nonlocal initial conditions, J. Funct. Anal. 262 (2012) 1363–1391] and are new even for the case of the nonlinearity being a single-valued function.

In this paper, we study the relationship between calmness and exact penalization for vector optimization problems under nonlinear perturbations. Some sufficient conditions for the problem calmness are also derived.

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.

This paper studies the global asymptotic stability for uncertain systems with mixed delays. The mixed delays include constant delay in the leakage term (i.e., leakage delay) and time-varying delays. The uncertainties under consideration are nonlinear time-varying parameter perturbations and norm-bounded uncertainties. Based on a appropriate Lyapunov–Krasovskii functional with triple integral terms, some integral inequalities and convex combination technique, a novel delay-dependent stability criterion is derived in terms of linear matrix inequalities (LMIs). Finally, three numerical examples are included to show the superiority of the proposed method.

In this paper, we consider the problem of delay-dependent robust stability of a class of uncertain discrete-time systems with time-varying delay using Lyapunov functional approach. Two categories of time-varying uncertainties are considered for the robust stability analysis: viz., (i) nonlinear perturbations and (ii) norm-bounded uncertainties. In the proposed stability analysis, by exploiting a candidate Lyapunov functional, and using minimal number of slack matrix variables, less conservative stability criteria are developed in terms of linear matrix inequalities (LMIs) for computing the maximum allowable bound of the delay-range, within which, the uncertain system under consideration remains asymptotically stable in the sense of Lyapunov. The effectiveness of the proposed stability criteria is demonstrated using standard numerical examples.

This paper is concerned with the finite-time stability problem for switched systems subject to both nonlinear perturbation and impulse effects. The average dwell time approach, combined with the algebraic matrix theory, is utilized to derive a criterion guaranteeing that the state trajectory does not exceed a certain threshold over a pre-specified finite-time interval. The requirement that at least one subsystem should be stable to ensure asymptotic stability is no longer necessary. Moreover, the finite-time stability degree could be positive, which is a relaxed condition for asymptotic stability. A numerical example is presented to illustrate the effectiveness of the proposed method.

We construct stable invariant manifolds for semiflows generated by the nonlinear impulsive differential equation with parameters x′ = A(t)x + f(t, x, λ), t ≠ τi and x(τi+) = Bix(τi) + gi(x(τi), λ), i ∈ ℕ in Banach spaces, assuming that the linear impulsive differential equation x′ = A(t)x, t ≠ τi and x(τi+) = Bix(τi), i ∈ ℕ admits a nonuniform (µ, ν)-dichotomy. It is shown that the stable invariant manifolds are Lipschitz continuous in the parameter λ and the initial values provided that the nonlinear perturbations f, g are sufficiently small Lipschitz perturbations.

We provide easily verifiable sufficient conditions for the existence of solutions to non- linear ordinary differential equations subject to nonlocal boundary conditions. These conditions are based on the solution space of the corresponding linear, homogeneous problem and on the size of the nonlinear perturbation. The results presented here are more general nonlinearities than those in (17) and (26).

In this paper, the robust exponential stability problem is investigated for a class of neutral systems with interval time-varying delay and nonlinear perturbations. Based on the Lyapunov-Krasovskii functionals in conjunction with Leibniz-Newton formula, novel LMI-based delay-dependent and delay-independent criteria are proposed to guarantee the robust exponential stability with a convergence rate for our considered systems. Finally, numerical examples are illustrated to show the improved results from using the proposed method.

This paper is concerned with the problem of robust exponential stability for linear parameter-dependent (LPD) neutral systems with mixed time-varying delays and nonlinear perturbations. Based on a new parameter-dependent Lyapunov-Krasovskii functional, Leibniz-Newton formula, decomposition technique of coefficient matrix, free-weighting matrices, Cauchy’s inequality, modified version of Jensen’s inequality, model transformation, and linear matrix inequality technique, new delay-dependent robust exponential stability criteria are established in terms of linear matrix inequalities (LMIs). Numerical examples are given to show the effectiveness and less conservativeness of the proposed methods.

This paper deals with a class of uncertain Takagi–Sugeno fuzzy delayed systems with nonlinear perturbations. Based on the Gronwall–Bellman inequality, we present the norm equivalent conditions of robust exponential stability for such systems. Namely, if the delay terms and the nonlinear terms can be controlled by the norm of system states, then the robust exponential stability can be achieved. Finally, an example is provided to verify technical feasibility and operability of the developed results.

We treat nonresonance of quasilinear elliptic equations with nonlinear boundary con- ditions via Friedrichs constant c� . Here we give a sensitivity result for nonlinear perturbations of the right hand side and provide an explicit estimate for cin convex domains. Finally, to illustrate our results we discuss the p-Laplacian case.

In this paper, we consider the problem of mu-stability of unbounded time-varying delays neural systems with nonlinear perturbations. Some mu-stability criterias are derived by using Lyapunov- Krasovski functional method . Those criteria are expressed in the form of linear matrix inequalities (LMIs).

Published version of a paper from the journal:Abstract and Applied Analysis. Also available from Hindawi:http://dx.doi.org/10.1155/2013/738653 The problem of bounded-input bounded-output ( BIBO) stability is investigated for a class of delay switched systems with mixed time-varying discrete and constant neutral delays and nonlinear perturbation. Based on the Lyapunov-Krasovskii functional theory, new BIBO stabilization criteria are established in terms of delay-dependent linear matrix inequalities. The numerical simulation is carried out to demonstrate the effectiveness of the results obtained in the paper.

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.

This paper is concerned with finite-time state estimation for Markovian jump systems with quantizations and randomly occurring nonlinearities under event-triggered scheme. The event triggered scheme and the quantization effects are used to reduce the data transmission and ease the network bandwidth burden. The randomly occurring nonlinearities are taken into account, which are governed by a Bernoulli distributed stochastic sequence. Based on stochastic analysis and linear matrix inequality techniques, sufficient conditions of stochastic finite-time boundedness and stochastic H∞ finite-time boundedness are firstly derived for the existence of the desired estimator. Then, the explicit expression of the gain of the desired estimator are developed in terms of a set of linear matrix inequalities. Finally, a numerical example is employed to demonstrate the usefulness of the theoretical results.

We provide a concise review on multi-field inflation and cosmological perturbations. We discuss convenient and physically meaningful bases in terms of which perturbations can be systematically studied. We give formal accounts on the gauge fixing conditions and present the perturbation action in two gauges. We also briefly review non-linear perturbations., (v1) 59 pages, 8 figures, invited review for International Journal of Modern Physics D; (v2) 60 pages, typos corrected and references added

We study the local exponential stability of evolution difference systems with slowly varying coefficients and nonlinear perturbations. We establish the robustness of the exponential stability in infinite-dimensional Banach spaces, in the sense that the exponential stability for a given pseudolinear equation persists under sufficiently small perturbations. The main methodology is based on a combined use of new norm estimates for operator-valued functions with the “freezing” method.

This paper addresses impulsive switched singular systems with nonlinear perturbation term. The main theme is to establish exponential stability of the systems where the impulses are of fixed time type and treated as perturbation. We first establish the exponential stability of a single-mode impulsive systems using the Lyapunov method . We have observed that if the underlying continuous system is stable and the impulses are applied slowly, then it is guaranteed that the impulsive system maintains the stability property. Later, a switched system with impulsive effects is considered. The method of multiple Lyapunov function and average dwell time switching signal are used. We have noticed that if all subsystems are exponentially stable and the average dwell time is sufficiently large, then the impulsive switched system is exponentially stable. Numerical examples with simulations are given to illustrate the effectiveness of the proposed theoretical results.

SUMMARY This paper is concerned with the problem of robust stability of Markovian jump singularly perturbed descriptor systems with uncertain switchings and nonlinear perturbations for any , where is a pre-defined positive scalar. A linear matrix inequality (LMI) condition is firstly established to guarantee the existence and uniqueness of a solution. Then, an e-independent condition in terms of LMI related to is derived via using an e-dependent Lyapunov function, where the solution exists uniquely and is globally exponentially mean-square stable simultaneously. Finally, numerical examples are used to show the feasibility and effectiveness of the given theoretical results. Copyright © 2012 John Wiley & Sons, Ltd.

This paper considers exponential stability in mean-square of singular Markovian jump systems. The systems under consideration involve nonlinear perturbation and time-varying delays. By using the Lyapunov–Krasovskii functional, delay-dependent stability conditions in terms of linear matrix inequality (LMI) are addressed, which guarantee exponential mean-square stability and a prescribed H ∞ performance index for the considered systems. Two numerical examples are given to illustrate the effectiveness of the proposed main results.

This paper is concerned with the problem of μ-stability of impulsive differential systems with unbounded time-varying delays and nonlinear perturbations. Some μ-stability criteria, which depend on the range of distributed delay and the decay rate of discrete delay (not the range), are derived by using Lyapunov–Krasovski functional method. Those criteria are expressed in the form of linear matrix inequalities and they can easily be checked. Two numerical examples are provided to demonstrate the effectiveness of the obtained results. Copyright © 2012 John Wiley & Sons, Ltd.