equilibrium and stability analysis of delayed neural networks under parameter uncertainties abstract this paper proposes new results for the existence uniqueness and global asymptotic stability of the equilibrium point for neural networks with multiple time delays under parameter uncertainties by using lyapunov stability theorem and applying homeomorphism mapping theorem new delay independent stability criteria are obtained the obtained results are in terms of network parameters of the neural system only and therefore they can be easily checked we also present some illustrative numerical examples to demonstrate that our result are new and improve corresponding results derived in the previous literature

state estimation for discrete time dynamical networks with time varying delays and stochastic disturbances under the round robin protocol this paper is concerned with the state estimation problem for a class of nonlinear dynamical networks with time varying delays subject to the round robin protocol the communication between the state estimator and the nodes of the dynamical networks is implemented through a shared constrained network in which only one node is allowed to send data at each time instant the round robin protocol is utilized to orchestrate the transmission order of nodes by using a switch based approach the dynamics of the estimation error is modeled by a periodic parameter switching system with time varying delays the purpose of the problem addressed is to design an estimator such that the estimation error is exponentially ultimately bounded with a certain asymptotic upper bound in mean square subject to the process noise and exogenous disturbance furthermore such a bound is subsequently minimized by the designed estimator parameters a novel lyapunov like functional is employed to deal with the dynamics analysis issue of the estimation error sufficient conditions are established to guarantee the ultimate boundedness of the estimation error in mean square by applying the stochastic analysis approach then the desired estimator gains are characterized by solving a convex problem finally a numerical example is given to illustrate the effectiveness of the estimator design scheme

an improved global asymptotic stability criterion for delayed cellular neural networks a new lyapunov krasovskii functional is constructed for delayed cellular neural networks and the s procedure is employed to handle the nonlinearities an improved global asymptotic stability criterion is also derived that is a generalization of and an improvement over previous results numerical examples demonstrate the effectiveness of the criterion

a study on h state estimation of static neural networks with time varying delays this paper studies the problem of h state estimation for static neural networks with time varying delay by construction of a suitable lyapunov krasovskii functional some improved delay dependent conditions are established such that the error system is globally exponentially stable with a decay rate and a prescribed h performance is guaranteed in order to get less conservative results of the state estimation condition zero equalities and reciprocally convex approach are employed the estimator gain matrix can be obtained in terms of the solution to linear matrix inequalities numerical examples are provided to illustrate the effectiveness and performance of the developed method

state estimation for fuzzy cellular neural networks with time delay in the leakage term discrete and unbounded distributed delays this paper deals with the problem of state estimation for fuzzy cellular neural networks fcnns with time delay in the leakage term discrete and unbounded distributed delays in this paper leakage delay in the leakage term is used to unstable the neuron states it is challenging to develop a delay dependent condition to estimate the unstable neuron states through available output measurements such that the error state system is globally asymptotically stable by constructing the lyapunov krasovskii functional which contains a triple integral term an improved delay dependent stability criterion is derived in terms of linear matrix inequalities lmis however by using the free weighting matrices method a simple and efficient criterion is derived in terms of lmis for estimation the restriction such as the time varying delay which was required to be differentiable or even its time derivative which was assumed to be smaller than one are removed instead the time varying delay is only assumed to be bounded finally numerical examples and its simulations are given to demonstrate the effectiveness of the derived results

global stability analysis in delayed cellular neural networks in this paper the author analyzes further problems of global stability for a class of cellular neural networks with delays by means of the lyapunov functional method inequalities a 2 b 2 g 2ab and a 3 b 3 c 3 g 3abc a b cg 0 analysis technique some stability criteria are obtained under more general conditions these criteria can be applied to design globally stable networks and thus have important significance in both theory and applications

a domain attraction criterion for interval fuzzy neural networks in this paper we study qualitative properties of equilibrium points in a class of interval fuzzy neural networks and obtain an estimate on the domain of robust attraction of locally exponentially stable equilibrium points both the conditions and the estimate are formulated in terms of the parameter intervals so they are easily verifiable the result can be used for the evaluation of fault tolerance capability for interval fuzzy neural networks

periodic bidirectional associative memory neural networks with distributed delays some sufficient conditions are obtained for the existence and global exponential stability of a periodic solution to the general bidirectional associative memory bam neural networks with distributed delays by using the continuation theorem of mawhin s coincidence degree theory and the lyapunov functional method and the young s inequality technique these results are helpful for designing a globally exponentially stable and periodic oscillatory bam neural network and the conditions can be easily verified and be applied in practice an example is also given to illustrate our results

on iterative learning algorithms for the formation control of nonlinear multi agent systems this paper deals with formation control problems for multi agent systems with nonlinear dynamics and switching network topologies using the nearest neighbor knowledge a distributed algorithm is constructed by employing the iterative learning control approach sufficient conditions are given to obtain the desired relative formations of agents which benefits from the strict positiveness of products of stochastic matrices it is shown that the derived results can effectively work although the network topologies dynamically change along both time and iteration axes and the corresponding directed graphs may not have spanning trees such result is also illustrated via numerical simulations

radial basis function neural network for approximation and estimation of nonlinear stochastic dynamic systems this paper presents a means to approximate the dynamic and static equations of stochastic nonlinear systems and to estimate state variables based on radial basis function neural network rbfnn after a nonparametric approximate model of the system is constructed from a priori experiments or simulations a suboptimal filter is designed based on the upper bound error in approximating the original unknown plant with nonlinear state and output equations the procedures for both training and state estimation are described along with discussions on approximation error nonlinear systems with linear output equations are considered as a special case of the general formulation finally applications of the proposed rbfnn to the state estimation of highly nonlinear systems are presented to demonstrate the performance and effectiveness of the method

sampled data state estimation for markovian jumping fuzzy cellular neural networks with mode dependent probabilistic time varying delays in this paper the problem of state estimation for markovian jumping fuzzy cellular neural networks fcnns using sampled data with mode dependent probabilistic time varying delays is investigated by developing a delay decomposition approach the information of the delayed states can be taken into full consideration by introducing a stochastic variable with a bernoulli distribution the information of probability distribution of the time varying delay is considered and transformed into one with deterministic time varying delay the main purpose of this paper is to estimate the neuron states through available output measurements such that the dynamics of the estimation error is globally asymptotically stable in the mean square based on the lyapunov krasovskii functional including triple integral terms and decomposed integral intervals delay distribution dependent stability criteria are obtained in terms of linear matrix inequalities lmis finally two numerical examples are given to illustrate the effectiveness of the proposed theoretical results

saturated finite interval iterative learning for tracking of dynamic systems with hnn structural output this brief investigates the interval iterative learning problem for dynamic systems with hierarchical neural network hnn structural output the first objective is to design the output of a dynamic system with hnn structure a sufficient condition is obtained to achieve the interval tracking in a finite interval by applying iterative learning control ilc then the saturated ilc is considered into the discussed system and a less conservative criterion is obtained to achieve the tracking in a finite interval using a network structure decomposition technique finally simulation results are given to illustrate the usefulness of the developed criteria

on the period of the ikeda lift for u m m let k mathbf q sqrt d be an imaginary quadratic field with discriminant d and chi the dirichlet character corresponding to the extension k mathbf q let m 2n or 2n 1 with n a positive integer let f be a primitive form of weight 2k 1 and character chi for vargamma 0 d or a primitive form of weight 2k for sl 2 mathbf z according as m 2n or m 2n 1 for such an f let i m f be the lift of f to the space of modular forms of weight 2k 2n and character det k n for the hermitian modular group vargamma k m constructed by ikeda we then express the period langle i m f i m f rangle of i m f in terms of special values of the adjoint l function of f and its twist by the character chi this proves the conjecture concerning the period of the hermitian ikeda lift proposed by ikeda

improved approach to robust stability and h performance analysis for systems with an interval time varying delay abstract an improved delay and range dependent robust stability and h performance analysis criterion for systems with an interval time varying delay is investigated a novel lyapunov krasovskii functional containing triple integral terms is established and an extended free weighting matrix method double integral inequality method is subsequently proposed numerical examples validate the effectiveness of the proposed double integral inequality method and show that our approach is less conservative than existing methods

new exponential stability results for delayed neural networks with time varying delays abstract this paper presents new sufficient conditions for the uniqueness and exponential stability of the equilibrium point for delayed neural networks with time varying delays by employing a more general type of lyapunov krasovskii functional and using lmi linear matrix inequality we derive new results for exponential stability of the equilibrium point for delayed neural networks the results establish a relation between the delay time and the parameters of the network the results are compared with the previous results derived in the literature

observer design for switched recurrent neural networks an average dwell time approach this paper is concerned with the problem of observer design for switched recurrent neural networks with time varying delay the attention is focused on designing the full order observers that guarantee the global exponential stability of the error dynamic system based on the average dwell time approach and the free weighting matrix technique delay dependent sufficient conditions are developed for the solvability of such problem and formulated as linear matrix inequalities the error state decay estimate is also given then the stability analysis problem for the switched recurrent neural networks can be covered as a special case of our results finally four illustrative examples are provided to demonstrate the effectiveness and the superiority of the proposed methods

event triggered h_ infty state estimation for delayed stochastic memristive neural networks with missing measurements the discrete time case in this paper the event triggered h infty state estimation problem is investigated for a class of discrete time stochastic memristive neural networks dsmnns with time varying delays and missing measurements the dsmnn is subject to both the additive deterministic disturbances and the multiplicative stochastic noises the missing measurements are governed by a sequence of random variables obeying the bernoulli distribution for the purpose of energy saving an event triggered communication scheme is used for dsmnns to determine whether the measurement output is transmitted to the estimator or not the problem addressed is to design an event triggered h infty estimator such that the dynamics of the estimation error is exponentially mean square stable and the prespecified h infty disturbance rejection attenuation level is also guaranteed by utilizing a lyapunov krasovskii functional and stochastic analysis techniques sufficient conditions are derived to guarantee the existence of the desired estimator and then the estimator gains are characterized in terms of the solution to certain matrix inequalities finally a numerical example is used to demonstrate the usefulness of the proposed event triggered state estimation scheme

h_ infty state estimation for discrete time complex networks with randomly occurring sensor saturations and randomly varying sensor delays in this paper the state estimation problem is investigated for a class of discrete time delay nonlinear complex networks with randomly occurring phenomena from sensor measurements the randomly occurring phenomena include randomly occurring sensor saturations rosss and randomly varying sensor delays rvsds that result typically from networked environments a novel sensor model is proposed to describe the rosss and the rvsds within a unified framework via two sets of bernoulli distributed white sequences with known conditional probabilities rather than employing the commonly used lipschitz type function a more general sector like nonlinear function is used to describe the nonlinearities existing in the network the purpose of the addressed problem is to design a state estimator to estimate the network states through available output measurements such that for all probabilistic sensor saturations and sensor delays the dynamics of the estimation error is guaranteed to be exponentially mean square stable and the effect from the exogenous disturbances to the estimation accuracy is attenuated at a given level by means of an h norm in terms of a novel lyapunov krasovskii functional and the kronecker product sufficient conditions are established under which the addressed state estimation problem is recast as solving a convex optimization problem via the semidefinite programming method a simulation example is provided to show the usefulness of the proposed state estimation conditions

robust stability of delayed fuzzy cohen grossberg neural networks in this paper using a linear matrix inequality and a differential inequality we obtain an exponentially robust stability criterion for interval fuzzy cohen grossberg type neural networks with time varying delays the criterion can be easily applied to the design of fuzzy general neural networks

existence and stability of almost periodic solution for bam neural networks with delays by using the banach fixed point theorem and constructing suitable lyapunov function some sufficient conditions are obtained ensuring existence uniqueness and global stability of almost periodic solution of the bam neural networks with variable coefficients and delays these results are helpful to design global exponential stable bam networks and almost periodic oscillatory bam networks

a new result on h_ infty state estimation of delayed static neural networks this brief presents a new guaranteed h infty performance state estimation criterion for delayed static neural networks to facilitate the use of the slope information about activation function the estimation error of activation function is separated into two parts for the first time then a novel lyapunov krasovskii functional lkf is constructed which has fully captured the slope information of the activation based on the new lkf a less conservative design criterion of estimator is derived to ensure the asymptotic stability of estimation error system with h infty performance the desired estimator gain matrices and the performance index are obtained by solving a convex optimization problem the simulation results show that the proposed method has much better performance than the most recent results

asymptotic behaviors of stochastic cohen grossberg neural networks with mixed time delays asymptotic behaviors of stochastic cohen grossberg neural networks with mixed time delays are investigated where the mixed time delays comprise both the discrete time varying delays and the distributed time delays the theory of stochastic functional differential equations is applied to establish two sets of novel criteria on asymptotic stability and ultimate boundedness finally two examples are given to illustrate our theoretical results and to indicate that two sets of criteria do not include each other

design of state estimator for bam fuzzy cellular neural networks with leakage and unbounded distributed delays in this paper the state estimation problem is studied for the bidirectional associative memory bam fuzzy cellular neural networks fcnns with delays where the delays include leakage and unbounded distributed delays the problem addressed is to estimate the neuron states through available output measurements such that for all admissible leakage and unbounded distributed delays the dynamics of the estimation error is globally asymptotically stable a delay dependent linear matrix inequality lmi criterion for the existence of the estimator is proposed by using the lyapunovkrasovskii functional method in addition the unknown gain matrix is determined by solving a delay dependent lmi finally numerical examples and simulations are provided to illustrate the effectiveness of the theoretical results

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

some novel approaches on state estimation of delayed neural networks this paper studies the issue of state estimation for a class of neural networks nns with time varying delay a novel lyapunov krasovskii functional lkf is constructed where triple integral terms are used and a secondary delay partition approach sdpa is employed compared with the existing delay partition approaches the proposed approach can exploit more information on the time delay intervals by taking full advantage of a modified wirtinger s integral inequality mwii improved delay dependent stability criteria are derived which guarantee the existence of desired state estimator for delayed neural networks dnns a better estimator gain matrix is obtained in terms of the solution of linear matrix inequalities lmis in addition a new activation function dividing method is developed by bringing in some adjustable parameters three numerical examples with simulations are presented to demonstrate the effectiveness and merits of the proposed methods

on the lifting of elliptic cusp forms to siegel cusp forms of degree 2n i 1 cf 8 in this paper we will prove that their conjecture is true moreover we obtain a simple fourier coefficient formula for f z ibukiyama 23 also made a similar conjecture which was formulated in terms of the koecher maass series which we will not consider here let us describe our results throughout this paper we fix positive integers k and n such that k n mod 2 and put e 1 k 1 n for any positive rational number n we denote the absolute value of the discriminant of q vn q by dn the primitive dirichlet character corresponding to q v n q is denoted by xn let fn be the positive rational number such that n nf2nlet b e m2n q be a positive definite half integral symmetric matrix put db det 2b db d db fb f db and xb x db note that edb 0 1 mod 4 and that fb is an integer for each prime p let p qp cx be the unique additive character such that bp x exp 27ir ltx for x e z p 1 recall that the siegel series for b is defined by

bounded h_ infty synchronization and state estimation for discrete time varying stochastic complex networks over a finite horizon in this paper new synchronization and state estimation problems are considered for an array of coupled discrete time varying stochastic complex networks over a finite horizon a novel concept of bounded h synchronization is proposed to handle the time varying nature of the complex networks such a concept captures the transient behavior of the time varying complex network over a finite horizon where the degree of bounded synchronization is quantified in terms of the h norm a general sector like nonlinear function is employed to describe the nonlinearities existing in the network by utilizing a timevarying real valued function and the kronecker product criteria are established that ensure the bounded h synchronization in terms of a set of recursive linear matrix inequalities rlmis where the rlmis can be computed recursively by employing available matlab toolboxes the bounded h state estimation problem is then studied for the same complex network where the purpose is to design a state estimator to estimate the network states through available output measurements such that over a finite horizon the dynamics of the estimation error is guaranteed to be bounded with a given disturbance attenuation level again an rlmi approach is developed for the state estimation problem finally two simulation examples are exploited to show the effectiveness of the results derived in this paper

robust consensus for linear multi agent systems with mixed uncertainties abstract this paper studies the robust consensus problem for a class of linear multi agent systems mass with polytopic uncertainties and external disturbances the uncertainties appear in both the dynamics of each agent and the topology of the overall network based on lyapunov stability theory the robust consensus problem is converted to the robust h stabilization of the error system with the aid of the homogeneous parameter dependent hpd lyapunov functions and sum of squares sos technique the robust consensus problem is further formulated as an sos programming sufficient conditions to achieve robust consensus with disturbance rejection capability are presented in terms of sos constraints as an extension the robust consensus problem for discrete time mass is studied in a similar way numerical examples are provided to illustrate the effectiveness of the approach

analysis on robust h performance and stability for linear systems with interval time varying state delays via some new augmented lyapunov krasovskii functional in this paper the problem of h performance and stability analysis for linear systems with interval time varying delays is considered first by constructing a newly augmented lyapunov krasovskii functional which has not been proposed yet an improved h performance criterion with the framework of linear matrix inequalities lmis is introduced next the result and method are extended to the problem of a delay dependent stability criterion finally numerical examples are given to show the superiority of proposed method

congruence of siegel modular forms and special values of their standard zeta functions in this paper we consider the relationship between the congruence of cuspidal hecke eigenforms with respect to sp n z and the special values of their standard zeta functions in particular we propose a conjecture concerning the congruence between saito kurokawa lifts and non saito kurokawa lifts and prove it under certain condition

an explicit formula for siegel series combining induction formulas for local densities with a functional equation for the siegel series we give an explicit formula for the siegel series by this formula we also give an explicit formula for the fourier coefficients of the siegel eisenstein series

formation potential field for trajectory tracking control of multi agents in constrained space abstractin this paper a novel formation potential field method is proposed for the multi agent formation control the objective is to control a group of agents to automatically generate and maintain a specific formation while avoiding internal collisions and collisions with spatial constraints a formation potential field is designed combining multiple local attractive potential fields with multiple local repulsive potential fields to further relax requirements of agents initial positions and enhance the robustness a global attractive potential field is added outside the influence range of the local formation potential field the optimality of the proposed scheme in formation time is analysed as well as illustrated by contrast simulation results following the design of the formation potential field two controllers are proposed accordingly to achieve a stable dynamic formation during the process of trajectory tracking while the saturation effect of input is taken into account furthermore a collisi

stability of asymmetric hopfield networks in this paper we discuss dynamical behaviors of recurrently asymmetrically connected neural networks in detail we propose an effective approach to study global and local stability of the networks many of well known existing results are unified in our framework which gives much better test conditions for global and local stability sufficient conditions for the uniqueness of the equilibrium point and its stability conditions are given too

robust cooperative learning control for directed networks with nonlinear dynamics this paper studies a class of robust cooperative learning control problems for directed networks of agents a with nonidentical nonlinear dynamics that do not satisfy a global lipschitz condition and b in the presence of switching topologies initial state shifts and external disturbances all uncertainties are not only time varying but also iteration varying it is shown that the relative formation of nonlinear agents achieved via cooperative learning can be guaranteed to converge to the desired formation exponentially fast as the number of iterations increases a necessary and sufficient condition for exponential convergence of the cooperative learning process is that at each time step the network topology graph of nonlinear agents can be rendered quasi strongly connected through switching along the iteration axis simulation tests illustrate the effectiveness of our proposed cooperative learning results in refining arbitrary high precision relative formation of nonlinear agents

state estimation for coupled uncertain stochastic networks with missing measurements and time varying delays the discrete time case this paper is concerned with the problem of state estimation for a class of discrete time coupled uncertain stochastic complex networks with missing measurements and time varying delay the parameter uncertainties are assumed to be norm bounded and enter into both the network state and the network output the stochastic brownian motions affect not only the coupling term of the network but also the overall network dynamics the nonlinear terms that satisfy the usual lipschitz conditions exist in both the state and measurement equations through available output measurements described by a binary switching sequence that obeys a conditional probability distribution we aim to design a state estimator to estimate the network states such that for all admissible parameter uncertainties and time varying delays the dynamics of the estimation error is guaranteed to be globally exponentially stable in the mean square by employing the lyapunov functional method combined with the stochastic analysis approach several delay dependent criteria are established that ensure the existence of the desired estimator gains and then the explicit expression of such estimator gains is characterized in terms of the solution to certain linear matrix inequalities lmis two numerical examples are exploited to illustrate the effectiveness of the proposed estimator design schemes

explicit formulas for the twisted koecher maas series of the duke imamoglu ikeda lift and their applications we give an explicit formula for the twisted koecher maas series of the duke imamoglu ikeda lift as an application we prove a certain algebraicity result for the values of twisted rankin selberg series at integers of half integral weight modular forms which was not treated by shimura j math soc japan 33 649 672 1981

parameter dependent lyapunov functional for stability of time delay systems with polytopic type uncertainties this note concerns the problem of the robust stability of a linear system with a time varying delay and polytopic type uncertainties in order to construct a parameter dependent lyapunov functional for the system we first devised a new method of dealing with a time delay system without uncertainties in this method the derivative terms of the state which is in the derivative of the lyapunov functional are retained and some free weighting matrices are used to express the relationships among the system variables and among the terms in the leibniz newton formula as a result the lyapunov matrices are not involved in any product terms of the system matrices in the derivative of the lyapunov functional this method is then easily extended to a system with polytopic type uncertainties numerical examples demonstrate the validity of the proposed criteria

estimator design for discrete time switched neural networks with asynchronous switching and time varying delay this brief deals with the estimator design problem for discrete time switched neural networks with time varying delay one main problem is the asynchronous mode switching between the neuron state and the estimator our goal is to design a mode dependent estimator for the switched neural networks under average dwell time switching such that the estimation error system is exponentially stable with a prescribed l2 gain in the h sense from the noise signal to the estimation error a new lyapunov functional is constructed that may increase during the mismatched switchings new results on the stability and l2 gain analysis are then obtained the admissible estimator gains are computed by solving a set of linear matrix inequalities the relations among the switching law the maximal delay upper bound and the optimal h disturbance attenuation level are established the effectiveness of the proposed design method is finally illustrated by a numerical example

delay dependent state estimation for delayed neural networks in this letter the delay dependent state estimation problem for neural networks with time varying delay is investigated a delay dependent criterion is established to estimate the neuron states through available output measurements such that the dynamics of the estimation error is globally exponentially stable the proposed method is based on the free weighting matrix approach and is applicable to the case that the derivative of a time varying delay takes any value an algorithm is presented to compute the state estimator finally a numerical example is given to demonstrate the effectiveness of this approach and the improvement over existing ones

boundedness and stability for cohen grossberg neural network with time varying delays abstract in this paper a model is considered to describe the dynamics of cohen grossberg neural network with variable coefficients and time varying delays uniformly ultimate boundedness and uniform boundedness are studied for the model by utilizing the hardy inequality combining with the halanay inequality and the lyapunov functional method some new sufficient conditions are derived for the model to be globally exponentially stable the activation functions are not assumed to be differentiable or strictly increasing moreover no assumption on the symmetry of the connection matrices is necessary these criteria are important in signal processing and the design of networks

boundedness and global exponential stability for generalized cohen grossberg neural networks with variable delay abstract a generalized halanay inequality is established and the boundedness of generalized cohen grossberg neural networks is investigated by applying the generalized halanay inequality and lyapunov functional method new sufficient conditions are obtained ensuring the global exponential stability of the solution of the generalized cohen grossberg neural networks with variable delay three examples are also given for illustration

stability in delayed cohen grossberg neural networks lmi optimization approach in this paper stability problems are further discussed for a class of delayed cohen grossberg neural networks on the basis of the linear matrix inequality lmi optimization approach and also the lyapunov krasovskii functional method combined with the halanay inequality technique several new sufficient criteria are given for ascertaining the global asymptotic stability and exponential stability of the equilibrium point for this system the proposed results are less restrictive than those given in the earlier literature and are easier to verify in practice in addition four examples and their numerical simulations are given two of them are used to demonstrate the effectiveness of the proposed results and another two show that there exist stable bifurcating periodic solutions if the given conditions do not hold

learning to cooperate motivated by the prototypical problem of a marching band this paper studies a class of multi agent formation problems characterized by two features i the agents attempt to complete a finite duration coordinated formation task with high precision by repeating the task and ii the feedback mechanism by which the agents control their motions is based on relative differences between nearest neighbors but the underlying graph topology can vary both during a repetition and from one repetition to the next adopting the framework of iterative learning control leads to the notion of multi agent networks with switching topologies along two directions a finite time axis and an infinite iteration axis for such systems we present distributed algorithms using nearest neighbor information whose exponential convergence can be demonstrated it is shown that as the number of repetition increases the relative formation between agents approaches the desired formation exponentially fast if and only if at each time step the union of the interaction graphs has a spanning tree frequently enough along the iteration axis that is the agents can learn to cooperate the remarkable point of this result is that it is not necessary to have a spanning tree at any specific time step or iteration in order for the system to converge two examples are given to illustrate the ideas including a general example where through iteration the agents can form a desired formation and a special case of it where an additional agent specifies a reference to regulate the formation shape simultaneously

delay dependent robust stabilization of uncertain state delayed systems this paper concerns a problem of robust stabilization of uncertain state delayed systems a new delay dependent stabilization condition using a memoryless controller is formulated in terms of matrix inequalities an algorithm involving convex optimization is proposed to design a controller guaranteeing a suboptimal maximal delay such that the system can be stabilized for all admissible uncertainties

stability analysis of discrete time recurrent neural networks with stochastic delay this paper is concerned with the stability analysis of discrete time recurrent neural networks rnns with time delays as random variables drawn from some probability distribution by introducing the variation probability of the time delay a common delayed discrete time rnn system is transformed into one with stochastic parameters improved conditions for the mean square stability of these systems are obtained by employing new lyapunov functions and novel techniques are used to achieve delay dependence the merit of the proposed conditions lies in its reduced conservatism which is made possible by considering not only the range of the time delays but also the variation probability distribution a numerical example is provided to show the advantages of the proposed conditions

robust stability for interval hopfield neural networks with time delay the conventional hopfield neural network with time delay is intervalized to consider the bounded effect of deviation of network parameters and perturbations yielding a novel interval dynamic hopfield neural network idhnn model a sufficient condition related to the existence of unique equilibrium point and its robust stability is derived

global stability for cellular neural networks with time delay a sufficient condition related to the existence of a unique equilibrium point and its global asymptotic stability for cellular network networks with delay dcnns is derived it is shown that the condition relies on the feedback matrices and is independent of the delay parameter furthermore this condition is less restrictive than that given in the literature

ikeda s conjecture on the period of the duke imamoḡlu ikeda lift let k and n be positive even integers for a cus pidal hecke eigenform h in the kohnen plus subspace of weight k n 2 1 2 for 0 4 let in h be the duke imamoglu ikeda lift of h in the space of cusp forms of weight k for spn z and f the primitive form of weight 2k n for sl2 z corresponding to h under the shimura correspondence we then express the ratio hin h in h i hh hi of the period of in h to that of h in terms of special values of certain l functions of f this proves the conjecture proposed by ikeda concerning the period of the duke imamoglu ikeda lift one of the fascinating problems in the theory of modular forms is to find the relation between the periods or the petersson products of cuspidal hecke eigenforms which are related with each other through their l functions in particular there are several important results concerning the relation between the period of a cuspidal hecke eigen form g for an elliptic modular group sl2 z and that of its lift bhere by a lift of g we mean a cuspidal hecke eigenform for another modular group 0 e g the symplectic group the orthogonal group the unitary group etc whose certain l function can be expressed in terms of certain l functions related with g thus we propose the following problem problem a express the ratio hbbi hg gi e in terms of arithmetic invariants of g for example the special values of certain l functions related with g for some integer e for instance zagier zag77 solved problem a for the doi naganuma

optimal iterative learning control design for multi agent systems consensus tracking abstract under a repeatable operation environment this paper proposes an iterative learning control scheme that can be applied to multi agent systems to perform consensus tracking under the fixed communication topology the agent dynamics are modeled by time varying nonlinear equations which satisfy the global lipschitz continuous condition in addition the desired consensus trajectory is only accessible to a subset of the followers by using the concept of the graph dependent matrix norm the convergence conditions can be specified at the agent level which depend on a set of eigenvalues that are associated with the communication topology the results are first derived for homogeneous agent systems and then extended to heterogeneous systems next optimal controller gain design methods are proposed in the sense that the norm of tracking error converges at the fastest rate which imposes a tightest bounding function for the actual tracking error in the norm analysis framework in the end an illustrative example of a group of heterogeneous agents is provided to demonstrate the effectiveness of the proposed design methods

tracking algorithms for multiagent systems this paper is devoted to the consensus tracking issue on multiagent systems instead of enabling the networked agents to reach an agreement asymptotically as the time tends to infinity the consensus tracking between agents is considered to be derived on a finite time interval as accurately as possible we thus propose a learning algorithm with a gain operator to be determined if the gain operator is designed in the form of a polynomial expression a necessary and sufficient condition is obtained for the networked agents to accomplish the consensus tracking objective regardless of the relative degree of the system model of agents moreover the h analysis approach is introduced to help establish conditions in terms of linear matrix inequalities lmis such that the resulting processes of the presented learning algorithm can be guaranteed to monotonically converge in an iterative manner the established lmi conditions can also enable the iterative learning processes to converge with an exponentially fast speed in addition we extend the learning algorithm to address the relative formation problem for multiagent systems numerical simulations are performed to demonstrate the effectiveness of learning algorithms in achieving both consensus tracking and relative formation objectives for the networked agents

synchronization for complex dynamical networks with time delay and discrete time information the synchronization problem is studied for complex dynamical networks cdns with time delay based on discrete time communication pattern a new lyapunov functional is proposed which is positive definite at communication instants but not necessarily positive definite inside the communication intervals and can make full use of the available information about the discrete time communication pattern based on the lyapunov functional an exponential synchronization criterion is proposed to ensure the synchronization of the considered cdns the effectiveness of the developed results are shown by the numerical simulation

pullback of the lifting of elliptic cusp forms and miyawaki s conjecture we construct a lifting from siegel cusp forms of degree r to siegel cusp forms of degree r 2n for r n 1 our result is a partial solution of a conjecture made by miyawaki 27 page 307 in 1992 in particular we can calculate the standard l function of a cusp form of degree 3 and weight 12 which is in accordance with miyawaki s conjecture we give a conjecture on the petersson inner product of the lifting in terms of certain l values

a generalized lmi based approach to the global asymptotic stability of delayed cellular neural networks a novel linear matrix inequality lmi based criterion for the global asymptotic stability and uniqueness of the equilibrium point of a class of delayed cellular neural networks cnns is presented the criterion turns out to be a generalization and improvement over some previous criteria

lmi based stability criteria for neural networks with multiple time varying delays abstract in this paper the stability of neural networks with multiple time varying delays is studied a new class of lyapunov krasovskii functionals is constructed and the s procedure and free weighting matrix method are employed to derive a delay dependent stability criterion from which a delay independent criterion is obtained as a special case moreover the result is also extended to delay dependent and rate independent stability criteria for multiple unknown time varying delays finally numerical examples are given to illustrate the effectiveness of our methods and improvement over the existing ones

design of state estimator for neural networks with leakage discrete and distributed delays abstract in this paper the design problem of state estimator for neural networks with mixed time varying delays and leakage delays has been investigated by using appropriate model transformation that shifts the considered systems into the neutral type time delay systems adapting a new lyapunov krasovskii functional which takes into account the range of time delay and by making use of some inequality techniques delay dependent criteria are developed to estimate the neuron states through available output measurements such that the estimation error system is globally asymptotically stable the criteria are formulated in terms of a set of linear matrix inequalities lmis which can be checked efficiently by use of some standard numerical packages finally three numerical examples and its simulations are given to demonstrate the usefulness and effectiveness of the presented results

globally exponential stabilization of neural networks with mixed time delays via impulsive control the impulsive stabilization problem of neural networks with discrete time varying delays and unbounded continuously distributed delays is considered by using impulse time dependent lyapunov function based techniques to capture the hybrid structure characteristics of the considered impulsive neural networks two novel global exponential stability criteria are obtained in terms of linear matrix inequalities which are capable of dealing with the case where both the continuous and discrete dynamics are unstable when the original continuous time delayed neural networks are not stable sufficient conditions are developed for the design of exponentially stable linear impulsive state feedback controllers four numerical examples are given to illustrate the less conservatism and effectiveness of the proposed results

robust exponential stability of uncertain fuzzy cohen grossberg neural networks with time varying delays in this paper the takagi sugeno t s fuzzy model representation is extended to the stability analysis for uncertain cohen grossberg neural networks cgnns with time varying delays a novel linear matrix inequality lmi based stability criterion is obtained by using lyapunov functional theory to guarantee the exponential stability of uncertain cgnns with time varying delays which are represented by t s fuzzy models finally the proposed stability conditions are demonstrated with numerical examples

comments on a generalized lmi based approach to the global asymptotic stability of delayed cellular neural networks in this letter we point out that the linear matrix inequality lmi based criterion obtained in the above paper singh ieee trans neural netw vol 15 no 1 p 223 5 2004 for the global exponential stability of the delayed neural networks can be simplified to a simpler but equivalent form and thus show that it is not necessary to have such complex form of condition in the above paper as a result we also answer the question raised by the author of the above paper

extended dissipative synchronization of complex dynamical networks with additive time varying delay and discrete time information abstract the problem of extended dissipativity analysis of complex dynamical networks with additive time varying delays and discrete time information is considered in this article by utilizing the lyapunov functional method jensen s inequality and free weighting matrix analysis techniques we established sufficient criterion such that the complex dynamical networks is synchronized further the extended dissipativity analysis problem which contains h performance passivity performance and l 2 l performance in a unified framework is studied the derived criteria are expressed in terms of linear matrix inequalities that can be easily checked by using the standard numerical softwares illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed results

robust state estimation for uncertain neural networks with time varying delay the robust state estimation problem for a class of uncertain neural networks with time varying delay is studied in this paper the parameter uncertainties are assumed to be norm bounded based on a new bounding technique a sufficient condition is presented to guarantee the existence of the desired state estimator for the uncertain delayed neural networks the criterion is dependent on the size of the time varying delay and on the size of the time derivative of the time varying delay it is shown that the design of the robust state estimator for such neural networks can be achieved by solving a linear matrix inequality lmi which can be easily facilitated by using some standard numerical packages finally two simulation examples are given to demonstrate the effectiveness of the developed approach

an iterative learning approach to formation control of multi agent systems abstract in this paper an efficient framework is proposed to the formation control problem of multiple agents with unknown nonlinear dynamics by means of the iterative learning approach in particular a distributed d type iterative learning scheme is developed for the multi agent system with switching topology whose switching time and sequence are allowed to be varied at different iterations according to the actual trajectories of agents and a sufficient condition is derived to ensure that the desired formation can be always preserved from the initial starting location to the final one after some iterations simulation results are provided to verify the effectiveness of the proposed approach

improved stability analysis of uncertain neutral type neural networks with leakage delays and impulsive effects this paper focuses on the stability analysis for neural networks of neutral type with leakage delays and impulsive effects 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 by utilizing the lyapunov functional method jensen s integral inequality and introducing some free weighting matrices some new delay derivative dependent stability criteria are established for the neutral type neural network the obtained stability criteria are stated in terms of linear matrix inequalities finally numerical examples are given to illustrate the effectiveness and reduced conservatism of the proposed results over the existing ones

lagrange exponential stability for fuzzy cohen grossberg neural networks with time varying delays this paper focuses on the globally exponential stability in lagrange sense for takagi sugeno t s fuzzy cohen grossberg neural networks with time varying delays by employing lyapunov method and delay inequality technique we analyze two different types of activation functions which include both lipschitz function and general activation functions several easily verifiable sufficient criteria about linear matrix inequality form are obtained to guarantee the lagrange exponential stability of cohen grossberg neural networks with time varying delays which are represented by t s fuzzy models meanwhile the estimations of the globally exponentially attractive sets are given here the existence and uniqueness of the equilibrium points need not be considered finally two numerical examples with simulations are given to illustrate the effectiveness of the theoretical results

state estimation for delayed neural networks in this letter the state estimation problem is studied for neural networks with time varying delays the interconnection matrix and the activation functions are assumed to be norm bounded the problem addressed is to estimate the neuron states through available output measurements such that for all admissible time delays the dynamics of the estimation error is globally exponentially stable an effective linear matrix inequality approach is developed to solve the neuron state estimation problem in particular we derive the conditions for the existence of the desired estimators for the delayed neural networks we also parameterize the explicit expression of the set of desired estimators in terms of linear matrix inequalities lmis finally it is shown that the main results can be easily extended to cope with the traditional stability analysis problem for delayed neural networks numerical examples are included to illustrate the applicability of the proposed design method

consensus based formation control laws for systems on lie groups this paper designs the consensus based formation control laws for multi agent systems defined on lie groups the specific results are illustrated on se 2 and se 3 the special euclidean groups of rigid body motions and each of which shares the geometric structure of a lie group the paper develops the control laws for the problem concerned under the assumption that the communication topologies of the multi agent systems are spanning tree shaped ring shaped and complete respectively at last several examples are included in the numerical simulations to verify the theoretical results

an analysis of global asymptotic stability of delayed cellular neural networks in this paper a new sufficient condition is given for the uniqueness and global asymptotic stability of the equilibrium point for delayed cellular neural networks dcnns this condition imposes constraints on the feedback and delayed feedback matrices of a dcnn independently of the delay parameter this result is also compared with the previous results derived in the literature

delay fractioning approach to robust exponential stability of fuzzy cohen grossberg neural networks abstract in this paper the problem of robust exponential stability analysis for a class of takagi sugeno ts fuzzy cohen grossberg neural networks with uncertainties and time varying delays is investigated a generalized activation function is used and the assumptions such as boundedness monotony and differentiability of the activation functions are removed by using a lyapunov krasovskii functional and employing the delay fractioning approach a set of sufficient conditions are established for achieving the required result the obtained conditions are proposed in terms of linear matrix inequalities lmis so its feasibility can be checked easily via standard numerical toolboxs the main advantage of the proposed criteria lies in its reduced conservatism which is mainly based on the time delay fractioning technique in addition to that a numerical example with simulation results is given to show the effectiveness of the obtained lmi conditions