novel summation inequalities and their applications to stability analysis for systems with time varying delay the inequality technique plays an important role in stability analysis for time delay systems this technical note presents a new sequence of novel summation inequalities by introducing some free matrices which includes the newly developed wirtinger based and free matrix based summation inequalities as special cases moreover the idea can be easily extended to the multiple summation inequality case based on the proposed inequalities relaxed stability conditions are obtained for systems with time varying delay numerical examples are given to demonstrate the effectiveness of the proposed approach

the method of lyapunov functionals and exponential stability of impulsive systems with time delay abstract this paper studies exponential stability of impulsive systems with time delay by employing the method of lyapunov functionals several exponential stability criteria are established our results have improved and generalized some of the known results found in the literature several examples are also discussed to illustrate our results

augmented zero equality approach to stability for linear systems with time varying delay abstract this work focuses the delay dependent stability problem for linear systems with time varying delays by composing a suitable augmented lyapunov krasovskii functionals using recent developed integral inequality and choosing newly states a set of sufficient conditions for stability condition is induced within framework of linear matrix inequalities lmis to enhance the feasible region of stability single augmented zero equality is established with the augmented state vectors for the first time and the equality constraint is incorporated into a simple stability criterion by utilizing finsler s lemma the comparison of maximum bounds of time delay with various results proposed by recent studies will be conducted in numerical examples to demonstrate the superiority of the theorems presented by this paper

fuzzy model based admissibility analysis and output feedback control for nonlinear discrete time systems with time varying delay abstract this paper is concerned with the admissibility analysis and stabilization problems for singular fuzzy discrete time systems with time varying delay the novelty of this paper comes from the consideration of a new summation inequality which is less conservative than the usual jensen inequality the abel lemma based inequality and the seuret inequality based on the inequality sufficient conditions are established to ensure the systems to be admissible moreover the corresponding conditions for the existence of desired static output feedback controller gains are derived to guarantee that the closed loop system is admissible the conditions can be solved by a modified cone complementarity linearization ccl algorithm examples are given to show the effectiveness of the proposed method

an accelerated exponential time integrator for semi linear stochastic strongly damped wave equation with additive noise abstract this paper is concerned with the strong approximation of a semi linear stochastic wave equation with strong damping driven by additive noise based on a spatial discretization performed by a spectral galerkin method we introduce a kind of accelerated exponential time integrator involving linear functionals of the noise under appropriate assumptions we provide error bounds for the proposed full discrete scheme it is shown that the scheme achieves higher strong order in time direction than the order of temporal regularity of the underlying problem which allows for higher convergence rate than usual time stepping schemes particularly for the space time white noise case in two or three spatial dimensions the scheme still exhibits a good convergence performance another striking finding is that even for the velocity with low regularity the scheme always promises first order strong convergence in time numerical examples are finally reported to confirm our theoretical findings

on delay differential equations with impulses abstract sufficient conditions are obtained respectively for the asymptotic stability of the trivial solution of x t ax t j 1 bjx tj t tj t tj and for the existence of a nonoscillatory solution conditions are also obtained for all solutions to be oscillatory the asymptotic behaviour of an impulsively perturbed delay logistic equation is investigated as an extension to a nonlinear equation

a note on relationship between two classes of integral inequalities this technical note firstly introduces two classes of integral inequalities with and without free matrices respectively and points out that they although in different forms are actually equivalent in the sense of conservatism i e the two corresponding ones produce the same tight upper bounds secondly the relationship between the method of integral inequalities with free matrices and the free weighting matrix technique is intensively investigated it is shown that these two different methods are actually equivalent in assessing the stability of time delay systems

higher order pathwise numerical approximations of spdes with additive noise in this article the pathwise numerical approximation of semilinear parabolic stochastic partial differential equations spdes driven by additive noise is considered a new numerical scheme for the time and space discretization of such spdes is proposed and this scheme is shown to converge for such spdes faster than standard numerical schemes such as the linear implicit euler scheme or the linear implicit crank nicholson scheme the suggested scheme takes advantage of the smoothing effect of the dominant linear operator and of two linear functionals of the noise process of the spde the abstract setting under which the scheme is analyzed includes spdes driven by fractional brownian motions too

high order runge kutta methods for impulsive delay differential equations abstract the purpose of this paper is to obtain high order runge kutta methods for nonlinear impulsive delay differential equations iddes in order to achieve the purpose continuity and smoothness of the exact solutions of iddes are analyzed and then the discontinuous points and non smooth points are chosen as a part of the nodes of the runge kutta methods furthermore it is proved that the pth order runge kutta method for iddes is also convergent of order p and some simple numerical examples are given to demonstrate the theoretical results

nonlinear discrete time systems with delayed control a reduction in this work the notion of reduction is introduced for discrete time nonlinear input delayed systems the retarded dynamics is reduced to a new system which is free of delays and equivalent in terms of stabilizability to the original one different stabilizing strategies are proposed over the reduced model connections with existing predictor based methods are discussed the methodology is also worked out over particular classes of time delay systems as sampled data dynamics affected by an entire input delay

single multiple integral inequalities with applications to stability analysis of time delay systems this technical note is concerned with the problem of stability analysis for time delay systems a new series of integral inequalities to bound a single integral term is presented by introducing some free matrices which produces tighter bounds than some existing ones similarly based on orthogonal polynomials defined in integral inner spaces new series of multiple integral inequalities are presented as well which include the existing double ones to show the effectiveness of the proposed inequalities their applications to stability analysis of systems with discrete and distributed delays are provided with numerical examples

new finite sum inequalities with applications to stability of discrete time delay systems this paper is concerned with the problem of stability analysis of discrete time delay systems new finite sum inequalities which encompass the ones based on abel lemma or wirtinger type inequality are first proposed the potential capability of the newly derived inequalities is then demonstrated by establishing less conservative stability conditions for some classes of linear discrete time systems with delay the derived stability criteria are theoretically and numerically proved to be less conservative than existing results

technical communique improved stability criterion and its applications in delayed controller design for discrete time systems this paper is concerned with the problem of delay dependent stability analysis for discrete time systems with interval like time varying delays and the problem of stabilization for discrete time linear systems via time delayed controllers the first problem is solved by applying a novel lyapunov functional and an improved delay dependent stability criterion is obtained in terms of a linear matrix inequality based on this a sufficient condition for the solvability of the second problem is presented the reduced conservatism of the proposed stability result is shown through a numerical example while the applicability of the time delayed controller design method is demonstrated by an inverted pendulum system

stochastic finite time h state estimation for discrete time semi markovian jump neural networks with time varying delays in this article the finite time h infty state estimation problem is addressed for a class of discrete time neural networks with semi markovian jump parameters and time varying delays the focus is mainly on the design of a state estimator such that the constructed error system is stochastically finite time bounded with a prescribed h infty performance level via finite time lyapunov stability theory by constructing a delay product type lyapunov functional in which the information of time varying delays and characteristics of activation functions are fully taken into account and using the jensen summation inequality the free weighting matrix approach and the extended reciprocally convex matrix inequality some sufficient conditions are established in terms of linear matrix inequalities to ensure the existence of the state estimator finally numerical examples with simulation results are provided to illustrate the effectiveness of our proposed results

persistent impulsive effects on stability of functional differential equations with finite or infinite delay abstract in this paper the stability problem of impulsive functional differential equations ifdes is considered several criteria ensuring the uniform stability of ifdes with finite or infinite delay are derived by establishing some new razumikhin conditions different with the current existing ones our development results can be applied to delay systems with persistent impulsive effects finally an example and its computer simulation is given to show the effectiveness and advantages of the proposed method

unknown input observer design for one sided lipschitz discrete time systems subject to time delay in this paper we address the problem of unknown input observer design which simultaneously estimates state and unknown input of a class of nonlinear discrete time systems with time delay a novel approach to the state estimation problem of nonlinear systems where the nonlinearities satisfy the one sided lipschitz and quadratically inner bounded conditions is proposed this approach also allows us to reconstruct the unknown inputs of the systems the nonlinear system is first transformed to a new system which can be decomposed into unknown input free and unknown input dependent subsystems the estimation problem is then reduced to designing observer for the unknown input free subsystem rather than full order observer design in this paper we propose observer design of reduced order which is more practical and cost effective by utilizing several mathematical techniques the time delay issue as well as the bilinear terms which often emerge when designing observers for nonlinear discrete time systems are handled and less conservative observer synthesis conditions are derived in the linear matrix inequalities form two numerical examples are given to show the efficiency and high performance of our results

full discretization of semilinear stochastic wave equations driven by multiplicative noise a fully discrete approximation of the semilinear stochastic wave equation driven by multiplicative noise is presented a standard linear finite element approximation is used in space and a stochastic trigonometric method is used for the temporal approximation this explicit time integrator allows for mean square error bounds independent of the space discretization and thus does not suffer from a step size restriction as in the often used stormer verlet leapfrog scheme furthermore it satisfies an almost trace formula i e a linear drift of the expected value of the energy of the problem numerical experiments are presented and confirm the theoretical results

a trigonometric method for the linear stochastic wave equation a fully discrete approximation of the linear stochastic wave equation driven by additive noise is presented a standard finite element method is used for the spatial discretization and a stochastic trigonometric scheme for the temporal approximation this explicit time integrator allows for error bounds independent of the space discretization and thus does not have a step size restriction as in the often used stormer verlet leap frog scheme moreover it enjoys a trace formula as does the exact solution of our problem these favorable properties are demonstrated with numerical experiments

further results on periodic boundary value problems for nonlinear first order impulsive functional differential equations abstract this paper is concerned with the solvability of periodic boundary value problems for nonlinear impulsive functional differential equations x t a t x t f t x t x 1 t x n t t j t 1 t p x t k x t k i k x t k k 1 2 p x 0 x t we obtain sufficient conditions for the existence of at least one solution of problem at resonance and nonresonance cases respectively examples are presented to illustrate the main results

technical communique improved delay range dependent stability criteria for linear systems with time varying delays this paper is concerned with the stability analysis of linear systems with time varying delays in a given range a new type of augmented lyapunov functional is proposed which contains some triple integral terms in the proposed lyapunov functional the information on the lower bound of the delay is fully exploited some new stability criteria are derived in terms of linear matrix inequalities without introducing any free weighting matrices numerical examples are given to illustrate the effectiveness of the proposed method

further results on h control for discrete time markovian jump time delay systems abstractthis paper studies the problem of h control for a class of discrete time markovian jump systems with time delay the purpose is to improve the existing results on h controller design for markovian jump systems a novel summation inequality is presented and an improved stability criterion for the system is derived by utilising the new inequality which is proved to be less conservative than most results in the literature then the state feedback controller is designed which guarantees the stochastic stability of the closed loop system with a given disturbance attenuation numerical examples are provided to illustrate the effectiveness and advantages of the proposed techniques

an extended reciprocally convex matrix inequality for stability analysis of systems with time varying delay abstract the reciprocally convex combination lemma rccl is an important technique to develop stability criteria for the systems with a time varying delay this note develops an extended reciprocally convex matrix inequality which reduces the estimation gap of the rccl based matrix inequality and reduces the number of decision variables of the recently proposed delay dependent rccl a stability criterion of a linear time delay system is established through the proposed matrix inequality finally a numerical example is given to demonstrate the advantage of the proposed method

an improved summation inequality to discrete time systems with time varying delay the summation inequality plays an important role in developing delay dependent criteria for discrete time systems with time varying delay this note proposes an improved summation inequality to estimate the summation terms appearing in the forward difference of lyapunov krasovskii functional compared with the inequality recently developed by the wirtinger based summation inequality and the reciprocally convex lemma the proposed one reduces the estimation gap while requires the same number of decision variables a relaxed stability criterion of a linear discrete time system with a time varying delay is established by using such novel inequality two numerical examples are given to demonstrate the advantages of the proposed method

a novel lyapunov functional for stability of time varying delay systems via matrix refined function this paper is concerned with the development of novel stability criteria for time varying delayed systems to this end a new function which consisted of two quadratic functions with a special structural matrix is established to be a lyapunov functional candidate the proposed lyapunov functional plays key role to decrease the conservatism of derived conditions which is verified by three numerical examples

finite element approximation of the linear stochastic wave equation with additive noise semidiscrete finite element approximation of the linear stochastic wave equation lswe with additive noise is studied in a semigroup framework optimal error estimates for the deterministic problem are obtained under minimal regularity assumptions these are used to prove strong convergence estimates for the stochastic problem the theory presented here applies to multidimensional domains and spatially correlated noise numerical examples illustrate the theory

higher order strong approximations of semilinear stochastic wave equation with additive space time white noise novel fully discrete schemes are developed to numerically approximate a semilinear stochastic wave equation driven by additive space time white noise a spectral galerkin method is proposed for the

wirtinger based integral inequality application to time delay systems in the last decade the jensen inequality has been intensively used in the context of time delay or sampled data systems since it is an appropriate tool to derive tractable stability conditions expressed in terms of linear matrix inequalities lmis however it is also well known that this inequality introduces an undesirable conservatism in the stability conditions and looking at the literature reducing this gap is a relevant issue and always an open problem in this paper we propose an alternative inequality based on the fourier theory more precisely on the wirtinger inequalities it is shown that this resulting inequality encompasses the jensen one and also leads to tractable lmi conditions in order to illustrate the potential gain of employing this new inequality with respect to the jensen one two applications on time delay and sampled data stability analysis are provided

generalized jensen inequalities with application to stability analysis of systems with distributed delays over infinite time horizons the jensen inequality has been recognized as a powerful tool to deal with the stability of time delay systems recently a new inequality that encompasses the jensen inequality was proposed for the stability analysis of systems with finite delays in this paper we first present a generalized integral inequality and its double integral extension it is shown how these inequalities can be applied to improve the stability result for linear continuous time systems with gamma distributed delays then for the discrete time counterpart we provide an extended jensen summation inequality with infinite sequences which leads to less conservative stability conditions for linear discrete time systems with poisson distributed delays the improvements obtained by the introduced generalized inequalities are demonstrated through examples

impulsive stabilization of high order hopfield type neural networks with time varying delays this paper studies the problems of global exponential stability for impulsive high order hopfield type neural networks nns with time varying delays by employing the lyapunov razumikhin technique some criteria ensuring global exponential stability are derived our results are then used to obtain some sufficient conditions under which some nns can be forced to converge by impulsive control numerical examples are also discussed to illustrate our results

dissipativity analysis for stochastic memristive neural networks with time varying delays a discrete time case in this paper the dissipativity problem of discrete time memristive neural networks dmnns with time varying delays and stochastic perturbation is investigated a class of logical switched functions are put forward to reflect the memristor based switched property of connection weights and the dmnns are then recast into a tractable model based on the tractable model the robust analysis method and refined jensen based inequalities are applied to establish some sufficient conditions that ensure the mathcal q mathcal s mathcal r gamma text disspativity of dmnns two numerical examples are presented to illustrate the effectiveness of the obtained results

some remarks on the use of time varying delay to model sample and hold circuits this note revises the so called input delay approach to the control of sampled data systems with nonuniform sampling in which the sample and hold circuit is embedded into an analog system with a time varying input delay it is shown that the conservatism in calculating the maximal admissible sampling period is reduced by about 57 if the time varying delay embedding step is omitted

razumikhin type theorems for hybrid system with memory in this paper we address the stability problem of hybrid systems with memory which are newly developed to model hybrid dynamic systems affected by delays for such systems stability criteria are developed based on razumikhin type conditions which are usually applied in the delay systems we prove that the hybrid system with memory is uniformly globally pre asymptotically stable by small gain theorem besides a relaxed razumikhin type stability criterion is also proposed which does not require strict decrease of the lyapunov razumikhin function during jumps several examples are given to illustrate the effectiveness and generality of the proposed results

stability and stabilization of discrete time tźs fuzzy systems with time varying delay via cauchyźschwartz based summation inequality this paper proposes new stability and stabilization conditions for discrete time fuzzy systems with time varying delays by constructing a suitable lyapunov krasovskii functional and introducing a new summation inequality based on the inequality of cauchy schwartz form which enhances the feasible region of the stability criterion for discrete time systems with time varying delay a stability criterion for such systems is established in order to show the effectiveness of the proposed inequality which provides more tight lower bound of a summation term of quadratic form a delay dependent stability criterion for such systems is derived within the framework of linear matrix inequalities which can be easily solved by various effective optimization algorithms going one step forward the proposed inequality is applied to a stabilization problem in discrete time fuzzy systems with time varying delays the advantages of the proposed stability and stabilization criteria are illustrated via two numerical examples

uniform asymptotic stability of impulsive delay differential equations abstract in this paper criteria on uniform asymptotic stability are established for impulsive delay differential equations using lyapunov functions and razumikhin techniques it is shown that impulses do contribute to yield stability properties even when the underlying system does not enjoy any stability behavior some examples are also discussed to illustrate the theorems

new stability criteria for linear discrete time systems with interval like time varying delays this technical note is concerned with stability of linear discrete time systems with interval like time varying delays two new stability criteria are derived by constructing a new lyapunov functional and utilizing two novel techniques for estimating the forward difference of the lyapunov functional the relationship between these stability criteria and some existing ones is established through the relationship it is clear that these stability criteria are less conservative than some existing ones which is confirmed by a numerical example

stability theorems and existence results for periodic solutions of nonlinear impulsive delay differential equations with variable coefficients abstract we consider the following nonlinear impulsive delay differential equation with variable coefficients and forcing term x t a t x t f t x e t t 0 t t k x t k x t k i k x t k k n using new methods different from those in tang et al appl math comput 131 2002 373 nieto j comput appl math lett 15 2002 489 franco and nieto j comput appl math 88 1998 144 nieto j math anal appl 205 1997 423 he and yu j math anal appl 272 2002 67 we establish stability theorems for when e t 0 under the assumption that there is bk such that bkx2 x x ik x x2 for k n and x r theorems 2 1 2 4 the existence results for three positive periodic solutions and nonexistence results for periodic solution of when e t 0 under the assumption exp 0 t a u d u 0 t k 1 b k and bk 1 for all k theorems 3 1 3 2 and the existence results for periodic solution of at resonance which is caused by impulses i e exp 0 t a u d u 0 t k 1 b k under the assumption bk 1 for all k theorems 4 2 4 3 some results obtained improve and generalize the known theorems and some other results are new examples are presented to illustrate the main results

reciprocally convex approach to stability of systems with time varying delays whereas the upper bound lemma for matrix cross product introduced by park 1999 and modified by moon park kwon and lee 2001 plays a key role in guiding various delay dependent criteria for delayed systems the jensen inequality has become an alternative as a way of reducing the number of decision variables it directly relaxes the integral term of quadratic quantities into the quadratic term of the integral quantities resulting in a linear combination of positive functions weighted by the inverses of convex parameters this paper suggests the lower bound lemma for such a combination which achieves performance behavior identical to approaches based on the integral inequality lemma but with much less decision variables comparable to those based on the jensen inequality lemma

regional stabilization for discrete time delay systems with actuator saturations via a delay dependent polytopic approach this paper is concerned with the regional stabilization problem for discrete time delay systems with actuator saturations different from some existing delay independent techniques handling the saturation nonlinearity a delay dependent polytopic approach is first proposed in a discrete time framework then by combining with an augmented lyapunov function a discrete wirtinger based inequality and some novel analysis techniques improved delay dependent regional stabilization conditions are established by means of linear matrix inequalities finally it is shown via two numerical examples that the obtained results are less conservative than some existing ones yet providing a larger estimate of an initial condition set

brief paper wirtinger s inequality and lyapunov based sampled data stabilization discontinuous lyapunov functionals appeared to be very efficient for sampled data systems fridman 2010 naghshtabrizi hespanha teel 2008 in the present paper new discontinuous lyapunov functionals are introduced for sampled data control in the presence of a constant input delay the construction of these functionals is based on the vector extension of wirtinger s inequality these functionals lead to simplified and efficient stability conditions in terms of linear matrix inequalities lmis the new stability analysis is applied to sampled data state feedback stabilization and to a novel sampled data static output feedback problem where the delayed measurements are used for stabilization

stochastic exponential integrator for finite element spatial discretization of stochastic elastic equation we investigate the strong convergence of a full discretization for the stochastic elastic equation driven by multiplicative noise finite element method is used for the spatial approximation and an exponential integrator scheme is proposed for the temporal discretization we show that the fully discrete scheme strongly converges to the mild solution of the continuous problem with precise convergence rates given as shown in our result the exponential integrator scheme achieves a higher strong convergence rate than the backward euler method does in the literature

stability analysis of systems with uncertain time varying delays stability of systems in the presence of bounded uncertain time varying delays in the feedback loop is studied the delay parameter is assumed to be an unknown time varying function for which the upper bounds on the magnitude and the variation are given the stability problem is treated in the integral quadratic constraint iqc framework criteria for verifying robust stability are formulated as feasibility problems over a set of frequency dependent linear matrix inequalities the criteria can be equivalently formulated as semi definite programs sdp using kalman yakubovich popov lemma as such checking robust stability can be performed in a computationally efficient fashion

output feedback stabilization for a discrete time system with a time varying delay this study employs the free weighting matrix approach to investigate the output feedback control of a linear discrete time system with an interval time varying delay first the delay dependent stability is analyzed using a new method of estimating the upper bound on the difference of a lyapunov function without ignoring any terms and based on the results a design criterion for a static output feedback sof controller is derived since the conditions thus obtained for the existence of admissible controllers are not expressed strictly in terms of linear matrix inequalities a modified cone complementarity linearization algorithm is employed to solve the nonconvex feasibility sof control problem furthermore the problem of designing a dynamic output feedback controller is formulated as one of designing an sof controller numerical examples demonstrate the effectiveness of the method and its advantage over existing methods

finite element methods and their error analysis for spdes driven by gaussian and non gaussian noises abstract in this paper we investigate the mean square error of numerical methods for spdes driven by gaussian and non gaussian noises the gaussian noise considered here is a hilbert space valued q wiener process and the non gaussian noise is defined through compensated poisson random measure associated to a levy process as the models consider the influences of gaussian and non gaussian noises simultaneously this makes the models more realistic when the models are also influenced by some randomly abrupt factors but more complicated as a consequence the numerical analysis of the problems becomes more involved we first study the regularity for the mild solution next we propose a semidiscrete finite element scheme in space and a fully discrete linear implicit euler scheme for the spdes and rigorously obtain their error estimates both the regularity results of the mild solution and error estimates obtained in the paper are novel

delay variation dependent stability of delayed discrete time systems this note is concerned with the stability analysis of linear discrete time system with a time varying delay a generalized free weighting matrix gfwm approach is proposed to estimate summation terms in the forward difference of lyapunov functional and theoretical study shows that the gfwm approach encompasses several frequently used estimation approaches as special cases moreover an augmented lyapunov functional with a delay product type term is constructed to take into account delay changing information as a result the proposed gfwm approach together with the augmented lyapunov functional leads to a less conservative delay variation dependent stability criterion finally numerical examples are given to illustrate the advantages of the proposed criterion

exponential stability of linear delay impulsive differential equations for an impulsive delay differential equation with bounded delay and bounded coefficients the following result is established if each solution is bounded on 0 together with its derivative for each bounded right hand side then the equation is exponentially stable an explicit stability theorem is presented

razumikhin type theorems on exponential stability of impulsive infinite delay differential systems in this note we study the exponential stability of impulsive functional differential systems with infinite delays by using the razumikhin technique and lyapunov functions several razumikhin type theorems on exponential stability are obtained which shows that certain impulsive perturbations may make unstable systems exponentially stable some examples are discussed to illustrate our results

lyapunov razumikhin method for impulsive functional differential equations and applications to the population dynamics the present paper deals with the investigation of the stability of the zero solution of impulsive functional differential equations by means of piecewise continuous functions coupled with the razumikhin technique sufficient conditions for stability uniform stability and asymptotic stability of the zero solution of such equations are found

stability of discrete time systems with time varying delays via a novel summation inequality this technical note is concerned with the stability analysis of discrete linear systems with time varying delays the novelty of the technical note comes from the consideration of a new inequality which is less conservative than the celebrated jensen inequality employed in the context of discrete time delay systems this inequality is a discrete time counterpart of the wirtinger based integral inequality that was recently employed for the improved analysis of continuous tine systems with delays however differently from the continuous time case the proof of the new inequality is not based on the wirtinger inequality the method is also combined with an efficient representation of the improved reciprocally convex combination inequality in order to reduce the conservatism induced by the lmis optimization setup the effectiveness of the proposed result is illustrated by some classical examples from the literature

the euler scheme and its convergence for impulsive delay differential equations this paper presents a fixed stepsize euler scheme for linear impulsive delay differential equations and considers its convergence we propose a method to take the partition nodes for the euler scheme employing the induction and the technique of inequality we obtain the order of convergence for euler scheme an example is given to illustrate the efficiency of our result

stability and passivity analysis of discrete time linear systems with time varying delay abstract this paper focuses on the stability and passivity analysis for a class of discrete time linear systems a novel general free matrix based summation inequality is proposed and two improved stability criteria in terms of linear matrix inequalities lmis are derived by employing the new summation inequality furthermore when an external disturbance appears a sufficient condition is established to ensure the considered linear system to be passive three numerical examples are provided to demonstrate the improvement of the proposed method

brief paper new delay dependent stability criteria for systems with interval delay this paper provides a new delay dependent stability criterion for systems with a delay varying in an interval with a different lyapunov functional defined a tight upper bound of its derivative is given the resulting criterion has advantages over some previous ones in that it involves fewer matrix variables but has less conservatism which is established theoretically examples are provided to demonstrate the advantage of the stability result

impulsive continuous runge kutta methods for impulsive delay differential equations abstract the classical continuous runge kutta methods are widely applied to compute the numerical solutions of delay differential equations without impulsive perturbations however the classical continuous runge kutta methods cannot be applied directly to impulsive delay differential equations because the exact solutions of the impulsive delay differential equations are not continuous in this paper impulsive continuous runge kutta methods are constructed for impulsive delay differential equations with the variable delay based on the theory of continuous runge kutta methods convergence of the constructed numerical methods is studied and some numerical examples are given to confirm the theoretical results

exponential stability of the exact solutions and the numerical solutions for a class of linear impulsive delay differential equations this paper is concerned with exponential stability of a class of linear impulsive delay differential equations iddes exponential stability of this kind of equations is studied by the properties of delay differential equations ddes without impulsive perturbations when different delay differential equations ddes without impulsive perturbations are chosen different sufficient conditions for exponential stability of the linear impulsive delay differential equations iddes are provided numerical methods for this kind of equations are constructed the convergence and exponential stability of the numerical solutions are studied and some experiments are given

further improvement of free weighting matrices technique for systems with time varying delay a novel method is proposed in this note for stability analysis of systems with a time varying delay appropriate lyapunov functional and augmented lyapunov functional are introduced to establish some improved delay dependent stability criteria less conservative results are obtained by considering the additional useful terms which are ignored in previous methods when estimating the upper bound of the derivative of lyapunov functionals and introducing the new free weighting matrices the resulting criteria are extended to the stability analysis for uncertain systems with time varying structured uncertainties and polytopic type uncertainties numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

summation inequalities to bounded real lemmas of discrete time systems with time varying delay summation inequality is an important technique for analysis of discrete time systems with a time varying delay it seems that from the literature a tighter inequality usually leads to a less conservative criterion based on h infty performance analysis problem this note presents different findings on the relationship between the conservatism of bounded real lemma brl and the tightness of summation inequality firstly the brl obtained by the wirtinger based inequality wbi is not always less conservative than the one by the jensen based inequality although the wbi is tighter secondly the wbi is tighter than a general free matrix based inequality gfmbi developed in this note while the brl obtained via the gfmbi is less conservative than the wbi based brl finally a numerical example is given to demonstrate those findings

exponential stability for impulsive delay differential equations by razumikhin method abstract in this paper we study exponential stability for impulsive delay differential equation of the form x t f t x t t t k x t i k t x t t t k k n by employing the razumikhin technique and lyapunov functions several exponential stability criteria are established some examples are also discussed to illustrate our results

exponential stability of impulsive cellular neural networks with time delay via lyapunov functionals this paper investigates the problem of exponential stability for a class of impulsive cellular neural networks with time delay by dividing the network state variables into subgroups according to the characters of the neural networks some sufficient conditions for exponential stability are derived by lyapunov functionals and the method of variation of parameters these conditions are given in terms of some blocks of the interconnection matrix which extend and improve some of the known results in the literature our results show that impulses may be used to stabilize the cellular neural networks with time delay if they are not stable or exponentially stable on the other hand if impulses are input disturbances criteria on the magnitude and frequency of the impulses are also established to maintain the stability property of the original system our results generalize and improve some known results two examples with numerical simulations are given to illustrate our results

note on stability of linear systems with time varying delay this note considers the stability of linear systems with a time varying delay we are interested in a simple lyapunov krasovskii functional lkf approach without delay decomposition in this category all recent tractable results had a fixed bound on the allowable maximum size of the delay for years we propose a new simple lkf including the cross terms of variables and quadratic terms multiplied by a higher degree scalar function and present a new result expressed in the form of lmis we show by two well known examples that our result overcomes the previous allowable maximum size of delay and it is less conservative than the previous results having a relatively small upper bound in the derivative of time delay

new admissibility analysis for discrete singular systems with time varying delay in this paper the issue of admissibility for discrete singular systems with time varying delay is addressed the main contribution of this paper is to reduce the conservatism of the considered system by adopting an improved reciprocally convex combination approach to bound the forward difference of the double summation term and utilizing the reciprocally convex combination approach to bound the forward difference of the triple summation term in the lyapunov function without employing decomposition and equivalent transformation of the considered system a strict delay dependent linear matrix inequality lmi criterion is built to guarantee the considered system to be regular causal and stable a numerical example is given to illustrate the effectiveness of this proposed method

general impulsive control of chaotic systems based on a ts fuzzy model in this paper a time delayed impulsive controller is constructed and the uniformly asymptotic stability of chaotic systems based on a takagi sugeno ts fuzzy model is investigated and some new and useful criteria are derived in addition the uniformly asymptotic synchronization of chaotic systems based on the ts fuzzy model is discussed using similar techniques finally some numerical simulations are presented to illustrate the effectiveness and feasibility of the derived results

extended dissipativity analysis for discrete time delayed neural networks based on an extended reciprocally convex matrix inequality abstract in this paper the extended dissipativity analysis for discrete time neural networks with a time varying delay is investigated first a novel lyapunov krasovskii functional lkf is constructed with a delay product type term introduced then in the forward difference of the lkf the sum terms are bounded via an extended reciprocally convex matrix inequality as a result an extended dissipativity criterion is established in terms of linear matrix inequalities meanwhile this criterion is extended to the stability analysis of the counterpart system without disturbance finally two numerical examples are given to demonstrate the effectiveness and improvements of the presented criterion

on stability of discrete time lti systems with varying time delays this technical note concerns robust stability analysis of discrete time linear time invariant lti systems with varying time delays the stability problem is tackled under the integral quadratic constraint iqc framework the time delay system in question is viewed as feedback interconnection of an lti stable operator and the so called delay difference operator for which iqc characterizations are required in order to apply iqc analysis one of the main contributions of the technical note is to derive novel iqc characterizations for the delay difference operator based on the assumption that the time varying delay parameter and its variation are bounded a set of new stability criteria emerges as the result numerical examples are given to illustrate the effectiveness of the new stability criteria another distinct contribution is the idea of introducing bounds on the so called m step total variation and m step average variation of the time varying delay parameter which is proven to be useful in stability analysis

a comprehensive review of stability analysis of continuous time recurrent neural networks stability problems of continuous time recurrent neural networks have been extensively studied and many papers have been published in the literature the purpose of this paper is to provide a comprehensive review of the research on stability of continuous time recurrent neural networks including hopfield neural networks cohen grossberg neural networks and related models since time delay is inevitable in practice stability results of recurrent neural networks with different classes of time delays are reviewed in detail for the case of delay dependent stability the results on how to deal with the constant variable delay in recurrent neural networks are summarized the relationship among stability results in different forms such as algebraic inequality forms m matrix forms linear matrix inequality forms and lyapunov diagonal stability forms is discussed and compared some necessary and sufficient stability conditions for recurrent neural networks without time delays are also discussed concluding remarks and future directions of stability analysis of recurrent neural networks are given

weak approximation of the stochastic wave equation we investigate the accuracy of approximation of e f u t where u t email protected 0 is the solution of the stochastic wave equation driven by the space time white noise and f is an r valued function defined on the hilbert space l 2 r the approximation is done by the leap frog scheme we show that under certain conditions on f the approximation by the leap frog scheme is of order two

stability criteria for impulsive differential equations in terms of two measures in general the stability notions of a given solution d t of an impulsive differential system cannot be transferred to the stability notions of the trivial solution by change of variables this is because of the fact that moments of impulse effects of 4 t need not be the same as that of a different solution x t and therefore demanding that the difference lx t d t 1 be small for all future time seems unnatural see 4 73 as a result the definitions of stability require suitable changes in the general situations and the corresponding theory has not yet been developed however in the case of impulsive differential systems with fixed moments of impulse effects such a problem does not arise and hence the standard definitions of stability will suffice employing suitable discontinuous lyapunov functions stability theory has recently been developed for such systems 1 2 3 51 in this paper we shall discuss stabiliy theory of impulsive differential systems with fixed moments of impulse effects in terms of two measures since such a theory enables us to unify a variety of stability results found in the literature we shall employ theory of impulsive differential inequalities as well as a direct approach to bring out the advantages of each approach

comments on new finite sum inequalities with applications to stability of discrete time delay systems abstract a recently reported criterion hien and trinh 2016 is reviewed we point out that there may exist typos and errors in the main results proposition 6 and theorem 7 it is also shown that the upper delay bound reported in example 2 could not be re established

overcoming the order barrier in the numerical approximation of stochastic partial differential equations with additive space time noise we consider the numerical approximation of parabolic stochastic partial differential equations driven by additive space time white noise we introduce a new numerical scheme for the time discretization of the finite dimensional galerkin stochastic differential equations which we call the exponential euler scheme and show that it converges in the strong sense faster than the classical numerical schemes such as the linear implicit euler scheme or the crank nicholson scheme for this equation with the general noise in particular we prove that our scheme applied to a semilinear stochastic heat equation converges with an overall computational order 1 3 which exceeds the barrier order 1 6 for numerical schemes using only basic increments of the noise process reported previously by contrast our scheme takes advantage of the smoothening effect of the laplace operator and of a linear functional of the noise and therefore overcomes this order barrier

boundedness for impulsive delay differential equations and applications to population growth models abstract in this paper criteria on uniform ultimate boundedness are derived for impulsive delay differential equations using lyapunov functions and razumikhin techniques it should be noted that the boundedness criteria establish global existence of solutions as well as boundedness without assuming a priori that solutions can necessarily be continued to infinity those criteria are then used to obtain permanence results for population growth models some examples are discussed to illustrate the theorems

random non linear wave equations smoothness of the solutions we show existence and uniqueness for the solution of a onedimensional wave equation with non linear random forcing then we give sufficient conditions for the solution at a given time and a given point to have a density and for this density to be smooth the proof uses the extension of the malliavin calculus to the two parameters wiener functionals