further note on global exponential stability of uncertain cellular neural networks with variable delays for cellular neural networks with time varying delays and uncertainties a recent work for exponential stability with convergence rate k of the networks is extended a new linear matrix inequality criterion for the stability which give information on the delay dependent property is derived

remark on the paper of park this paper considers certain neutral differential equation with the distributed delayddt x t c t x email protected p t x t q t x email protected r t t d tx s ds 0 without imposing a nonnegative restriction on coefficients of the equation we establish a delay dependent asymptotic stability condition for the equation by introducing a new lyapunov function the condition presented here is different from that of park j h park lmi optimization approach to asymptotic stability of certain neutral delay differential equation with time varying coefficients appl math comput 160 2005 355 361 in the sense that it is dependent on all delays of the equation numerical examples illustrate effectiveness and sharpness of our theoretical result

impulsive control in this paper the concept and principles of impulsive control are presented impulsive control can be applied to a class of systems whose state variables are changeable in a very short time period in particular the asymptotic stability of the impulsive control of a nonlinear system is given

stability with respect to part of the variables in systems with impulse effect abstract effective sufficient conditions are found for stability with respect to part of the variables in systems of ordinary differential equations with impulse effect the approach presented is based on the specially introduced piecewise continuous ljapunov functions

techniques for the efficient evaluation of two dimensional autocorrelation functions the evaluation of the autocorrelation of multidimensional sequences using the fft is investigated the bidimensional case is treated in detail not only because it is of special interest for the applications but also because the reasoning used for this case can be applied to higher dimension signals the analysis confirms that the use of the proposed frequency domain techniques leads to significant computation time savings

an efficient algorithm for two dimensional autoregressive spectrum estimation an algorithm similar to the burg algorithm is given for autoregressive estimation in one dimension coefficients of the filter used to decorrelate the signal are found recursively from lower order filters the coefficients needed to get the larger sized filters can be found at each stage of the recursion from the correlations of lower order filter outputs thus the resulting estimate does not assume knowledge of ensemble averages it offers a computational saving of 25 over the commonly used method in which an estimate of the correlation matrix is first computed and then inverted

global exponential stability of cellular neural networks with variable delays for cellular neural networks with time varying delays the problems of determining the exponential stability and estimating the exponential convergence rate are investigated by employing the lyapunov krasovskii functional and linear matrix inequality lmi technique a novel criterion for the stability which give information on the delay dependent property is derived two examples are given to demonstrate the effectiveness of the obtained 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

periodic solutions of delay impulsive differential equations abstract we study the following semilinear impulsive differential equation with delay u t a u t f t u t u t t 0 t t i u s s s r 0 u t i i i u t i i 1 2 0 t 1 t 2 in a banach space x with an unbounded operator a where r 0 is a constant and u t s u t s s r 0 here u t i u t i u t i constitutes an impulsive condition which can be used to model more physical phenomena than the traditional initial value problems we assume that f t u w is t periodic in t and then prove with some compactness conditions that if solutions of the equation are ultimately bounded then the differential equation has a t periodic solution the new results obtained here extend some results in this area for differential equations without impulsive conditions or without delays

global stability of almost periodic solution of multispecies mutualism system with time delays and impulsive effects abstract this paper discusses an almost periodic multispecies lotka volterra mutualism system with time delays and impulsive effects by using the theory of comparison theorem and constructing a suitable lyapunov functional sufficient conditions which guarantee the existence and uniqueness and global asymptotical stability of almost periodic solution of this system are obtained the results of this paper is completed new an suitable example indicates the feasibility of the main results

razumikhin type theorems for time delay systems with persistent impulses abstract the main results of the paper are generalizations of the razumikhin classical theorems for stability analysis of impulsive time delay systems by employing lyapunov razumikhin method and impulsive control theory several razumikhin type theorems for uniform stability and global exponential stability are obtained the significance and novelty of the results lie in that the criteria for stability of impulsive time delay systems admit the existence of persistent impulses and unbounded time varying delays two examples are provided to show the effectiveness of the proposed results

existence and global attractivity of positive periodic solutions for the impulsive delay nicholson s blowflies model in this paper we shall consider the following nonlinear impulsive delay population model 0 1 x t d t x t p t x t m w e a t x t m w a e t 0 t t k x t k 1 b k x t k k 1 2 where m is a positive integer d t a t and p t are positive periodic continuous functions with period w 0 in the nondelay case m 0 we show that 0 1 has a unique positive periodic solution x t which is globally asymptotically stable in the delay case we present sufficient conditions for the global attractivity of x t our results imply that under the appropriate linear periodic impulsive perturbations the impulsive delay equation 0 1 preserves the original periodic property of the nonimpulsive delay equation in particular our work extends and improves some known results

boundedness and periodicity in impulsive ordinary and functional differential equations abstract in this paper we study the boundedness and periodicity of solutions for impulsive ordinary differential equations odes and functional differential equations fdes by using horn s fixed point theorem hale yoshizawa type criteria for the existence of t periodic solutions are established to use these criteria we also give two new boundedness theorems and establish new existence results for t periodic solutions which show that the impulsive perturbations do contribute to yielding periodic solutions even when the underlying systems do not enjoy periodic solutions

asymptotic properties of the positive equilibrium of a discrete survival model this paper is concerned with the discrete wazewska and lasota model x n 1 x email protected n pe n x n k where email protected 0 1 n email protected 0 and email protected 0 1 2 we show that every positive solution of is persistent and then we provide sufficient conditions for oscillation of all solutions about x finally we give sufficient conditions for x to be stable or attractive

stability of networked control systems with asynchronous renewal links an impulsive systems approach we consider networked control systems in which sensors actuators and controller transmit through asynchronous communication links each introducing independent and identically distributed intervals between transmissions we model these scenarios through impulsive systems with several reset maps triggered by independent renewal processes i e the intervals between jumps associated with a given reset map are identically distributed and independent of the other jump intervals for linear dynamic and reset maps we establish that mean exponential stability is equivalent to the spectral radius of an integral operator being less than one we also prove that the origin of a non linear impulsive system is locally stable with probability one if its local linearization about the zero equilibrium is mean exponentially stable which justifies the importance of studying the linear case the applicability of the results is illustrated through an example using a linearized model of a batch reactor

periodic solution and almost periodic solution of impulsive lasota wazewska model with multiple time varying delays this paper deals with the impulsive lasota wazewska model with multiple time varying delays our results show that the system is uniformly persistent under some appropriate conditions the sufficient condition for global exponential stability of the system is given applying mawhin s continuation theorem of coincidence degree we prove that the periodic system has at least one strictly positive periodic solution by employing hull theory of impulsive almost periodic system the existence and uniqueness of strictly positive almost periodic solution of the almost periodic system is obtained two examples are provided to illustrate our results

almost periodic solutions of lasota wazewska type delay differential equation sufficient conditions are derived for the existence of a globally attractive almost periodic solution of a single species model given by the nonautonomous lasota wazewska type delay differential equations x t txt ptfxt in which 0 p t 0 t are continuous almost periodic functions and f is a decreasing positive c1 function conditions of the uniform asymptotical stability for some associated nonautonomous delay differential equations x t txt ptxt are also discussed

uniform stability of delayed impulsive reaction diffusion systems abstract in this article the stability problem of impulsive reaction diffusion functional differential equations irfdes is discussed applying lyapunov functional method and the comparison principle of irfdes some useful criteria are acquired to assure uniform stability and uniformly asymptotical stability of the equilibrium point of irfdes respectively finally a numerical example is provided to show the validity of our findings

global attractivity for certain impulsive delay differential equations abstract in this paper we study the global attractivity of zero solution of the following impulsive delay differential equation x t a t x t p t f x t t 0 t t k x t k x t k b k x t k k n some sufficient conditions to guarantee every solution of the equation converges to zero are obtained as its applications we apply our results to some well known impulsive delay ecological equations

transformation techniques and fixed point theories to establish the positive solutions of second order impulsive differential equations abstract using a new method for dealing with the impulse term of second impulsive differential equations we are concerned with determining values of for which there exist positive solutions of the following boundary value problems in the form of x t f t x t 0 t j t t k x t k x t k c k x t k k 1 2 n a x 0 b x 0 a x 1 b x 1 0 1 h s x t d t where 0 is a positive parameter c k is a real sequence with c k 1 k 1 2 n the dependence of positive solution x t on the parameter is also studied i e lim x or lim x 0 the proof of our main result is based upon transformation techniques and fixed point theories this is probably the first time the existence of positive solutions of second order impulsive differential equations has been studied by applying this technique

on the practical stability with respect to h manifolds of hybrid kolmogorov systems with variable impulsive perturbations abstract the present paper is devoted to the problems of practical stability with respect to h manifolds for impulsive kolmogorov systems variable impulsive perturbations are considered we will investigate these problems in the light of the vector lyapunov s method of piecewise continuous functions as an example the case of lotka volterra systems is elaborated the effect of uncertain parameters on the stability behavior of the model is also examined the obtained results extend and complement the existing stability results for kolmogorov and related systems

existence of positive periodic solutions for an impulsive differential equation abstract in this paper we consider the impulsive differential equation x t a t x t p t f t x t 0 t x t 1 t x t n t a e t 0 t t k x t k x t k b k x t k k 1 2 by using a fixed point theorem some criteria are established for the existence of a positive periodic solution of the above equation our work extends and improves some known results

lmi optimization approach to asymptotic stability of certain neutral delay differential equation with time varying coefficients in this article a stability criterion for all solutions of a class of neutral equation of the formddt x t c t x t t p t x t q t x t s r t t d tx s ds 0to approach zero at t is presented using the lyapunov method the condition which is expressed in terms of linear matrix inequality is delay dependent and can be easily solved by various efficient convex optimization algorithm

stability of nonlinear differential systems with state dependent delayed impulses we consider nonlinear differential systems with state dependent delayed impulses impulses which involve the delayed state of the system for which the delay is state dependent such systems arise naturally from a number of applications and the stability issue is complex due to the state dependence of the delay we establish general and applicable results for uniform stability uniform asymptotic stability and exponential stability of the systems by using the impulsive control theory and some comparison arguments we show how restrictions on the change rates of states and impulses should be imposed to achieve system s stability in comparison with general impulsive delay differential systems with state dependent delay in the nonlinearity or the differential systems with constant delays in our approach the boundedness of the state dependent delay is not required but derives from the stability result obtained examples are given to demonstrate the sharpness and applicability of our general results and the proposed approach

impulsive control for existence uniqueness and global stability of periodic solutions of recurrent neural networks with discrete and continuously distributed delays in this paper a class of recurrent neural networks with discrete and continuously distributed delays is considered sufficient conditions for the existence uniqueness and global exponential stability of a periodic solution are obtained by using contraction mapping theorem and stability theory on impulsive functional differential equations the proposed method which differs from the existing results in the literature shows that network models may admit a periodic solution which is globally exponentially stable via proper impulsive control strategies even if it is originally unstable or divergent two numerical examples and their computer simulations are offered to show the effectiveness of our new results

on exponential stabilization for a class of neutral type systems with parameter uncertainties an integral sliding mode approach this paper is focused on integral sliding mode control ismc for a class of parameter uncertain neutral type systems with time varying delays ntstd an integral sliding surface functional is firstly constructed for the ntstd then a delay dependent robust stability criterion is established for all admissible uncertainties which can guarantee the sliding mode dynamic system to be robustly exponentially stable under a certain decay rate in addition by solving the generalized eigenvalue problem gevp presented in the subsequent work the global maximal value of the decay rate as well as the condition of exponential stability for the sliding mode system are derived furthermore a sliding mode control smc law is then synthesised to ensure the stability of the closed loop system and the proposed smc law can drive the state of controlled dynamic system into the predefined sliding surface in finite time finally a numerical example is provided to demonstrate the effectiveness of the obtained results

on quasi stability for impulsive differential systems on developpe une theorie de la stabilite relativement a une solution donnee de systemes differentiels impulsifs une telle etude conduit a un mecanisme complique et les notions de stabilite doivent etre modifiees

sufficient stability conditions of nonlinear differential systems under impulsive control with state dependent delay in this technical note we study the delayed impulsive control of nonlinear differential systems where the impulsive control involves the delayed state of the system for which the delay is state dependent since the state dependence of the delay makes the impulsive transients dependent on the historical information of the states which means that it is hard to know exactly a priori how far in the history the information is needed the main challenge is how to determine the historical states we resolve this challenge and establish some sufficient conditions for local stability of nonlinear differential systems with state dependent delayed impulsive control based on impulsive control theory two examples are given to show the effectiveness of the proposed approach

existence and global attractivity of positive periodic solution for an impulsive lasota wazewska model abstract sufficient conditions are obtained for the existence and global attractivity of periodic positive solution of an impulsive lasota wazewska model for the survival of red blood cells

positive almost periodic solution for a class of lasota wazewska model with multiple time varying delays in this paper we study the existence and global exponential convergence of positive almost periodic solutions for the generalized lasota wazewska model with multiple time varying delays under proper conditions we employ a novel proof to establish some criteria to ensure that all solutions of this model converge exponentially to a positive almost periodic solution moreover we give an example to illustrate our main results

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

on the stability of invariant sets of systems with impulse effect abstract a system of differential equations with impulse effect is considered it is assumed that this system has an invariant set m by means of the direct lyapunov method the necessary and sufficient conditions of its uniform asymptotic stability are obtained the conditions on the perturbations of right hand sides of differential equations and impulse effects under which the uniform asymptotic stability of the invariant set m of the nonperturbed system implies the uniform asymptotic stability of the invariant set of the perturbed system are obtained the stability properties of invariant sets of periodic systems are also studied

periodic solutions of a class of impulsive neutral delay differential equation abstract a class of impulsive neutral delay differential equation is studied by using fixed point theorem in cone some sufficient conditions of the existence for multiple periodic solutions are obtained some known results are generalized two examples are also given to support our main results

positive solutions of a nonlinear impulsive equation with periodic boundary conditions abstract in this paper we investigate nonlinear second order differential equations subject to linear impulse conditions and periodic boundary conditions sign properties of an associated green s function are exploited to get existence results for positive solutions of the nonlinear boundary value problem with impulse upper and lower bounds for positive solutions are also given the results obtained yield periodic positive solutions of the corresponding periodic impulsive nonlinear differential equation on the whole real axis

oscillation and stability of linear impulsive delay differential equations the main results of this paper are that the oscillation and the stability of a linear impulsive delay differential equation are equivalent respectively to the oscillation and the stability of a corresponding linear delay differential equation without impulses the results of this paper can be used to improve and derive some of the known results in the literature

an invariance principle for nonlinear hybrid and impulsive dynamical systems in this paper we develop an invariance principle for dynamical systems possessing left continuous flows specifically we show that left continuity of the system trajectories in time for each fixed state point and continuity of the system trajectory in the state for every time in some dense subset of the semi infinite interval are sufficient for establishing an invariance principle for hybrid and impulsive dynamical systems as a special case of this result we state and prove new invariant set stability theorems for a class of nonlinear impulsive dynamical systems namely state dependent impulsive dynamical systems these results provide less conservative stability conditions for impulsive systems as compared to classical results in the literature and allow us to address the stability of limit cycles and periodic orbits of impulsive systems

existence and global attractivity of positive periodic solutions of functional differential equations with impulses abstract sufficient and realistic conditions are obtained for the existence and global attractivity of positive periodic solutions of the delay differential system with impulses d y t d t y t f t y t 1 t y t n t a e t 0 t t k y t k y t k b k y t k k 1 2 the method involves the application of the gaines and mawhin s coincidence degree theory the constructing suitable lyapunov functionals and estimations of uniform upper bounds on solutions when these results are applied to some special delay population models some new results are obtained and some known results are generalized in particular our results indicate that under the appropriate linear periodic impulsive perturbations the above impulsive delay differential equation preserves the original periodicity and global attractivity of the nonimpulsive delay differential equation d y t d t y t f t y t 1 t y t n t

a class of nonlinear non instantaneous impulsive differential equations involving parameters and fractional order abstract in this article we study asymptotic and smooth properties of solutions to nonlinear non instantaneous impulsive differential equations involving parameters of integer order and fractional order we introduce the concept of continuous dependence and differentiability of solutions and establish sufficient conditions to guarantee the solution depends continuously and is differentiable on the initial condition impulsive parameters and junction parameters finally two models of non instantaneous impulsive logistic equations are given 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

existence and global attractivity of unique positive periodic solution for a lasota wazewska model abstract in this paper we consider the lasota wazewska model x t a t x t i 1 m p i t e q i t x t i t by using a fixed point theorem some criteria are established for the existence of the unique positive periodic solution x of the above equation in particular we not only give the conclusion of convergence of x n to x where x n is a successive sequence but also show that x is a global attractor of all other positive solutions

generalized lyapunov and invariant set theorems for nonlinear dynamical systems in this paper we develop generalized lyapunov and invariant set theorems for nonlinear dynamical systems wherein all regularity assumptions on the lyapunov function and the system dynamics are removed in particular local and global stability theorems are given using lower semicontinuous lyapunov functions furthermore generalized invariant set theorems are derived wherein system trajectories converge to a union of largest invariant sets contained in intersections over finite intervals of the closure of generalized lyapunov level surfaces the proposed results provide transparent generalizations to standard lyapunov and invariant set theorems

a unified framework for hybrid control model and optimal control theory we propose a very general framework that systematizes the notion of a hybrid system combining differential equations and automata governed by a hybrid controller that issues continuous variable commands and makes logical decisions we first identify the phenomena that arise in real world hybrid systems then we introduce a mathematical model of hybrid systems as interacting collections of dynamical systems evolving on continuous variable state spaces and subject to continuous controls and discrete transitions the model captures the identified phenomena subsumes previous models yet retains enough structure to pose and solve meaningful control problems we develop a theory for synthesizing hybrid controllers for hybrid plants in all optimal control framework in particular we demonstrate the existence of optimal relaxed and near optimal precise controls and derive generalized quasi variational inequalities that the associated value function satisfies we summarize algorithms for solving these inequalities based on a generalized bellman equation impulse control and linear programming

the existence of periodic solutions to certain impulsive differential equations abstract for autonomous ordinary differential equations it is shown that there always exist impulsive forcing patterns which permit the existence of periodic solutions however when the differential equation is nonautonomous proving the existence of impulsive periodic solutions appears more complex the authors study here an impulsive differential system which appears to have no periodic solutions continuous manifolds of initial vectors are found for which it is proven that the trajectory emanating from each initial vector is unstable hence nonperiodic it is also established that a particular type of impulsive periodic solution the so called simple periodic motion cannot exist by changing the type of impulse applied some periodic solutions are obtained one of which though not physically meaningful is perhaps mathematically significant

oscillation and global attractivity in hematopoiesis model with delay time in this paper we shall consider the nonlinear delay differential equations with delay time p t bp m t t 1 p n t t cp t that is proposed as a model of hematopoiesis blood cell production where p t denotes the density of mature cells in blood circulation and the time delay t is the time between the production of immature cells in the bone marrow and their maturation for release in the circulating bloodstreams our aim is to give sufficient condition for oscillation of all positive solutions of about the positive steady state and obtain some sufficient conditions for the global attractivity our results extend and improve the well known oscillation results of when m 0

existence and global attractivity of positive periodic solutions of a survival model of red blood cells in this paper we deal with a model for the survival of red blood cells with periodic coefficients x t email protected t x t p t e r t x t r t t 0 some new sufficient conditions are obtained for the existence and global attractivity of positive periodic solutions of the equation

common asymptotic behavior of solutions and almost periodicity for discontinuous delayed and impulsive neural networks the paper considers a general neural network model with impulses at a given sequence of instants discontinuous neuron activations delays and time varying data and inputs it is shown that when the neuron interconnections satisfy an m matrix condition or a dominance condition then the state solutions and the output solutions display a common asymptotic behavior as time t it is also shown via a new technique based on prolonging the solutions of the delayed neural network to that it is possible to select a unique special solution that is globally exponentially stable and can be considered as the unique global attractor for the network finally this paper shows that for almost periodic data and inputs the selected solution is almost periodic moreover it is robust with respect to a large class of perturbations of the data analogous results also hold for periodic data and inputs a by product of the analysis is that a sequence of almost periodic impulses is able to induce in the generic case nonstationary almost periodic solutions in an otherwise globally convergent nonimpulsive neural network to the authors knowledge the results in this paper are the only available results on global exponential stability of the unique periodic or almost periodic solution for a general neural network model combining three main features i e impulses discontinuous neuron activations and delays the results in this paper are compared with several results in the literature dealing with periodicity or almost periodicity of some subclasses of the neural network model here considered and some hints for future work are given

existence of positive periodic solutions of impulsive functional differential equations with two parameters in this paper we employ a well known fixed point index theorem to study the existence and non existence of positive periodic solutions for the periodic impulsive functional differential equations with two parameters several existence and non existence results are established

design of a stable state feedback controller based on the multirate sampling of the plant output a new type of controller is proposed which detects the ith plant output n sub i times during a period of t sub 0 and changes the plant inputs once during t sub 0 it is shown that an arbitrary state feedback can be realized by such controllers if the plant is observable this implies for instance that arbitrary symmetric pole assignment is possible if the plant is controllable it is also shown that if the plant has no zeros at the origin the state transition matrix of the controller itself can be set arbitrarily without changing the state feedback to be realized that is to say inversely expressed any state feedback can be equivalently realized by a controller with any prescribed degree of stability

lyapunov stability of a class of discrete event systems discrete event systems des are dynamical systems which evolve in time by the occurrence of events at possibly irregular time intervals logical des are a class of discrete time des with equations of motion that are most often nonlinear and discontinuous with respect to event occurrences recently there has been much interest in studying the stability properties of logical des and several definitions for stability and methods for stability analysis have been proposed here the authors introduce a logical des model and define stability in the sense of lyapunov and asymptotic stability for logical des then the authors show that more conventional analysis of stability which employs appropriate lyapunov functions can be used for logical des the authors provide a general characterization of the stability properties of automata theoretic des models petri nets and finite state systems furthermore the lyapunov stability analysis approach is illustrated on a manufacturing system that processes batches of n different types of parts according to a priority scheme to prove properties related to the machine s ability to reorient itself to achieve safe operation and a load balancing problem in computer networks to study the ability of the system to achieve a balanced load to minimize underutilization

periodicity and global dynamics of an impulsive delay lasota wazewska model abstract the periodicity of an impulsive delay lasota wazewska model is discussed sufficient and necessary condition for the existence of a positive periodic solution is established sufficient conditions for its global attractivity are also obtained via the methods of lyapunov function and comparison

existence and multiplicity of positive periodic solutions to functional differential equations with impulse effects abstract this paper deals with a new existence theory for single and multiple positive periodic solutions to a kind of nonautonomous functional differential equations with impulse actions at fixed moments by employing a fixed point theorem in cones easily verifiable sufficient criteria are established the paper extends some previous results and reports some new results about impulsive functional differential equations

impulsive differential equations this paper deals with the periodic solutions problem for impulsive differential equations by using lyapunov s second method and the contraction mapping principle some conditions ensuring the existence and global attractiveness of unique periodic solutions are derived which are given from impulsive control and impulsive perturbation points of view as an application the existence and global attractiveness of unique periodic solutions for hopfield neural networks are discussed finally two numerical examples are provided to demonstrate the effectiveness of the proposed results

event triggered state estimation for markovian jumping impulsive neural networks with interval time varying delays abstractthis paper investigates the event triggered state estimation problem of markovian jumping impulsive neural networks with interval time varying delays the purpose is to design a state estimator to estimate system states through available output measurements in the neural networks there are a set of modes which are determined by markov chain a markovian jumping time delay impulsive neural networks model is employed to describe the event triggered scheme and the network related behaviour such as transmission delay data package dropout and disorder the proposed event triggered scheme is used to determine whether the sampled state information should be transmitted the discrete delays are assumed to be time varying and belong to a given interval which means that the lower and upper bounds of interval time varying delays are available first we design a state observer to estimate the neuron states second based on a novel lyapunov krasovskii functional lkf with triple integral terms and us