further results on exponential stability of neural networks with time varying delay this paper investigates the problem of the exponential stability for a class of neural networks with time varying delay a triple integral term and a term considering the delay information in a new way are introduced to the lyapunov krasovskii functional lkf the obtained criterion show advantages over the existing ones since not only a novel lkf is constructed but also several techniques such as wirtinger based inequality and convex combination technique are used to estimate the upper bound of the derivative of the lkf finally a numerical example is provided to verify the effectiveness and benefit of the proposed criterion

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

technical communique new conditions for delay derivative dependent stability two recent lyapunov based methods have significantly improved the stability analysis of time delay systems the delay fractioning approach of gouaisbaut and peaucelle 2006 for systems with constant delays and the convex analysis of systems with time varying delays of park and ko 2007 in this paper we develop a convex optimization approach to stability analysis of linear systems with interval time varying delay by using the delay partitioning based lyapunov krasovskii functionals lkfs novel lkfs are introduced with matrices that depend on the time delays these functionals allow the derivation of stability conditions that depend on both the upper and lower bounds on delay derivatives

global asymptotic stability of recurrent neural networks with multiple time varying delays in this paper several sufficient conditions are established for the global asymptotic stability of recurrent neural networks with multiple time varying delays the lyapunov krasovskii stability theory for functional differential equations and the linear matrix inequality lmi approach are employed in our investigation the results are shown to be generalizations of some previously published results and are less conservative than existing results the present results are also applied to recurrent neural networks with constant time delays

an improved algebraic criterion for global exponential stability of recurrent neural networks with time varying delays this brief paper presents an m matrix based algebraic criterion for the global exponential stability of a class of recurrent neural networks with decreasing time varying delays the criterion improves some previous criteria based on m matrix and is easy to be verified with the connection weights of the recurrent neural networks with decreasing time varying delays in addition the rate of exponential convergence can be estimated via a simple computation based on the criterion herein

the complexity of fault detection problems for combinational logic circuits in this correspondence we analyze the computational complexity of fault detection problems for combinational circuits and propose an approach to design for testability although major fault detection problems have been known to be in general np complete they were proven for rather complex circuits in this correspondence we show that these are still np complete even for monotone circuits and thus for unate circuits we show that for k level k 3 monotone unate circuits these problems are still np complete but that these are solvable in polynomial time for 2 level monotone unate circuits a class of circuits for which these fault detection problems are solvable in polynomial time is presented ripple carry adders decoder circuits linear circuits etc belong to this class a design approach is also presented in which an arbitrary given circuit is changed to such an easily testable circuit by inserting a few additional test points

sampled data synchronization analysis of markovian neural networks with generally incomplete transition rates this paper investigates the problem of sampled data synchronization for markovian neural networks with generally incomplete transition rates different from traditional markovian neural networks each transition rate can be completely unknown or only its estimate value is known in this paper compared with most of existing markovian neural networks our model is more practical because the transition rates in markovian processes are difficult to precisely acquire due to the limitations of equipment and the influence of uncertain factors in addition the time dependent lyapunov krasovskii functional is proposed to synchronize drive system and response system by applying an extended jensen s integral inequality and wirtinger s inequality new delay dependent synchronization criteria are obtained which fully utilize the upper bound of variable sampling interval and the sawtooth structure information of varying input delay moreover the desired sampled data controllers are obtained finally two examples are provided to illustrate the effectiveness of the proposed method

an augmented lkf approach involving derivative information of both state and delay an augmented lyapunov krasovskii functional lkf approach is presented to derive sufficient conditions for the existence uniqueness and globally exponential stability of the equilibrium point of a class of cellular neural networks with time varying delays by dividing the variation interval of the time delay into several subintervals with equal length a novel vector lkf is introduced and new conditions are obtained based on the homeomorphism mapping principle free weighting matrix method and linear matrix inequality techniques since the criteria are involving derivative information of both state and delay the obtained results are less conservative than some previous ones two examples are also given to show the effectiveness of the presented criteria

stability of markovian jump generalized neural networks with interval time varying delays this paper examines the problem of asymptotic stability for markovian jump generalized neural networks with interval time varying delays markovian jump parameters are modeled as a continuous time and finite state markov chain by constructing a suitable lyapunov krasovskii functional lkf and using the linear matrix inequality lmi formulation new delay dependent stability conditions are established to ascertain the mean square asymptotic stability result of the equilibrium point the reciprocally convex combination technique jensen s inequality and the wirtinger based double integral inequality are used to handle single and double integral terms in the time derivative of the lkf the developed results are represented by the lmi the effectiveness and advantages of the new design method are explained using five numerical examples

delay dependent global exponential stability for delayed recurrent neural networks this paper deals with the global exponential stability for delayed recurrent neural networks drnns by constructing an augmented lyapunov krasovskii functional and adopting the reciprocally convex combination approach and wirtinger based integral inequality delay dependent global exponential stability criteria are derived in terms of linear matrix inequalities meanwhile a general and effective method on global exponential stability analysis for drnns is given through a lemma where the exponential convergence rate can be estimated with this lemma some global asymptotic stability criteria of drnns acquired in previous studies can be generalized to global exponential stability ones finally a frequently utilized numerical example is carried out to illustrate the effectiveness and merits of the proposed theoretical results

stability analysis for neural networks with time varying interval delay this letter is concerned with the stability analysis of neural networks nns with time varying interval delay the relationship between the time varying delay and its lower and upper bounds is taken into account when estimating the upper bound of the derivative of lyapunov functional as a result some improved delay interval dependent stability criteria for nns with time varying interval delay are proposed numerical examples are given to demonstrate the effectiveness and the merits of the proposed method

dissipativity analysis for neural networks with two delay components using an extended reciprocally convex matrix inequality abstract this paper focuses on the problem of strictly q s r dissipativity analysis for neural networks with two delay components based on the dynamic delay interval method a lyapunov krasovskii functional is constructed by solving its self positive definite and derivative negative definite conditions via an extended reciprocally convex matrix inequality several new sufficient conditions that guarantee the neural networks strictly q s r dissipative are derived furthermore the dissipativity analysis of neural networks with two delay components is extended to the stability analysis finally two numerical examples are employed to illustrate the advantages of the proposed method

bounds for different spreads of line and total graphs abstract in this paper we explore some results concerning the spread of the line and the total graph of a given graph a sufficient condition for the spread of a unicyclic graph with an odd girth to be at most the spread of its line graph is presented additionally we derive an upper bound for the spread of the line graph of graphs on n vertices having a vertex edge connectivity at most a positive integer k combining techniques of interlacing of eigenvalues we derive lower bounds for the laplacian and signless laplacian spread of the total graph of a connected graph moreover for a regular graph an upper and lower bound for the spread of its total graph is given

signless laplacians of finite graphs we survey properties of spectra of signless laplacians of graphs and discuss possibilities for developing a spectral theory of graphs based on this matrix for regular graphs the whole existing theory of spectra of the adjacency matrix and of the laplacian matrix transfers directly to the signless laplacian and so we consider arbitrary graphs with special emphasis on the non regular case the results which we survey old and new are of two types a results obtained by applying to the signless laplacian the same reasoning as for corresponding results concerning the adjacency matrix b results obtained indirectly via line graphs among other things we present eigenvalue bounds for several graph invariants an interpretation of the coefficients of the characteristic polynomial a theorem on powers of the signless laplacian and some remarks on star complements

robust point pattern matching based on spectral context finding correspondences between two related feature point sets is a basic task in computer vision and pattern recognition in this paper we present a novel method for point pattern matching via spectral graph analysis in particular we aim to render the spectral matching algorithm more robust for positional jitter and outlier a local structural descriptor namely the spectral context is proposed to describe the attribute domain of point sets which is fundamentally different from the previous methods furthermore the approximate distance order is defined and employed as the metric for geometric consistency of neighboring points in this work by combining these two novel ingredients we formulate feature point set matching as an optimization problem with one to one constraints the correspondences are then obtained by maximizing the given objective function via the technique of probabilistic relaxation comparative experiments conducted on both synthetic and real data demonstrate the effectiveness of the proposed method especially in the presence of positional jitter and outliers a novel spectral method is proposed for the problem of point pattern matching we propose a local structural descriptor via spectral graph analysis we define a metric of geometric consistency by using the quantity of order

exponential stability analysis for delayed neural networks with switching parameters average dwell time approach this paper is concerned with the problem of exponential stability analysis of continuous time switched delayed neural networks by using the average dwell time approach together with the piecewise lyapunov function technique and by combining a novel lyapunov krasovskii functional which benefits from the delay partitioning method with the free weighting matrix technique sufficient conditions are proposed to guarantee the exponential stability for the switched neural networks with constant and time varying delays respectively moreover the decay estimates are explicitly given the results reported in this paper not only depend upon the delay but also depend upon the partitioning which aims at reducing the conservatism numerical examples are presented to demonstrate the usefulness of the derived theoretical results

robust stability analysis for stochastic neural networks with time varying delay this brief investigates the problem of mean square exponential stability of uncertain stochastic delayed neural networks dnns with time varying delay a novel lyapunov functional is introduced with the idea of the discretized lyapunov krasovskii functional lkf method then a new delay dependent mean square exponential stability criterion is derived by applying the free weighting matrix technique and by equivalently eliminating time varying delay through the idea of convex combination numerical examples illustrate the effectiveness of the proposed method and the improvement over some existing methods

delay dependent stability criteria for generalized neural networks with two delay components this paper investigates the delay dependent stability for generalized continuous neural networks with time varying delays a novel lyapunov krasovskii functional lkf that considers more information on activation functions of delayed neural networks and delay upper bounds is developed simultaneously most commonly used techniques for treating the derivative of the lkf are reviewed and compared with each other with the way of introducing slack matrices those techniques are classified into two categories including free weighting matrix fwm based techniques and reciprocally convex combination based techniques it is found that the introduced slack matrices play an important role in conservatism reducing and those four types of fwm based methods lead to same results and are equivalent moreover the obtained criteria are extended to the system with a single time varying delay two numerical examples are given to verify the effectiveness of the proposed method

stability for neural networks with time varying delays via some new approaches this paper considers the problem of delay dependent stability criteria for neural networks with time varying delays first by constructing a newly augmented lyapunov krasovskii functional a less conservative stability criterion is established in terms of linear matrix inequalities second by proposing novel activation function conditions which have not been proposed so far further improved stability criteria are proposed finally three numerical examples used in the literature are given to show the improvements over the existing criteria and the effectiveness of the proposed idea

stability analysis for continuous systems with two additive time varying delay components this paper presents a new result of stability analysis for continuous systems with two additive time varying delay components which represent a general class of delay systems with strong application background in network based control systems this criterion is expressed as a set of linear matrix inequalities which can be readily tested by using standard numerical software a numerical example is provided to show the effectiveness and advantage of the proposed stability condition

extended dissipativity analysis for markovian jump neural networks with time varying delay via delay product type functionals this paper investigates the problem of extended dissipativity for markovian jump neural networks mjnns with a time varying delay the objective is to derive less conservative extended dissipativity criteria for delayed mjnns toward this aim an appropriate lyapunov krasovskii functional lkf with some improved delay product type terms is first constructed then by employing the extended reciprocally convex matrix inequality ercmi and the wirtinger based integral inequality to estimate the derivative of the constructed lkf a delay dependent extended dissipativity condition is derived for the delayed mjnns an improved extended dissipativity criterion is also given via the allowable delay sets method based on the above mentioned results the extended dissipativity condition of delayed nns without markovian jump parameters is directly derived finally three numerical examples are employed to illustrate the advantages of the proposed method

stability analysis of neural networks with two delay components based on dynamic delay interval method in this paper a dynamic delay interval ddi method is proposed to deal with the stability problem of neural networks with two delay components this method extends the fixed interval of a time varying delay to a dynamic one which relaxes the restriction on upper and lower bounds of the delay intervals combining the reciprocally convex combination technique and wirtinger integral inequality the ddi method leads to some much less conservative delay dependent stability criteria based on a linear matrix inequality for neural networks with two delay components furthermore the criteria for the system with a single time varying delay are provided some examples are given to illustrate the effectiveness of the obtained results

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

admissible delay upper bounds for global asymptotic stability of neural networks with time varying delays this paper is concerned with global asymptotic stability of a neural network with a time varying delay where the delay function is differentiable uniformly bounded with delay derivative bounded from above first a general reciprocally convex inequality is presented by introducing some slack vectors with flexible dimensions this inequality provides a tighter bound in the form of a convex combination than some existing ones second by constructing proper lyapunov krasovskii functional global asymptotic stability of the neural network is analyzed for two types of the time varying delays depending on whether or not the lower bound of the delay derivative is known third noticing that sufficient conditions on stability from estimation on the derivative of some lyapunov krasovskii functional are affine both on the delay function and its derivative allowable delay sets can be refined to produce less conservative stability criteria for the neural network under study finally two numerical examples are given to substantiate the effectiveness of the proposed method

brief paper robust h filtering for a class of uncertain linear systems with time varying delay this paper deals with the problem of delay dependent robust h filtering for uncertain linear systems with time varying delay two cases of time varying delays are fully considered one is the time varying delay being continuous uniformly bounded while the other is the time varying delay being differentiable uniformly bounded with delay derivative bounded by a constant a stable linear filter is designed to ensure that the filtering error system is asymptotically stable with a prescribed level of h noise attenuation based on a new integral inequality delay dependent sufficient conditions for the existence of such a filter are established in terms of linear matrix inequalities lmis through deriving these conditions neither model transformation nor bounding technique for cross terms is employed moreover the relationship between the sufficient conditions for the two cases of time varying delay is disclosed finally two examples are also given to illustrate the effectiveness of the proposed methodology

almost sure exponential stability of recurrent neural networks with markovian switching this paper presents new stability results for recurrent neural networks with markovian switching first algebraic criteria for the almost sure exponential stability of recurrent neural networks with markovian switching and without time delays are derived the results show that the almost sure exponential stability of such a neural network does not require the stability of the neural network at every individual parametric configuration next both delay dependent and delay independent criteria for the almost sure exponential stability of recurrent neural networks with time varying delays and markovian switching parameters are derived by means of a generalized stochastic halanay inequality the results herein include existing ones for recurrent neural networks without markovian switching as special cases finally simulation results in three numerical examples are discussed to illustrate the theoretical results

technical communique absolute stability of time delay systems with sector bounded nonlinearity this paper deals with the problem of absolute stability of time delay systems with sector bounded nonlinearity some new delay dependent stability criteria are obtained and formulated in the form of linear matrix inequalities lmis neither model transformation nor bounding technique for cross terms is involved through derivation of the stability criteria numerical examples show that the results obtained in this paper improve the estimate of the stability limit over some existing result

complete delay decomposing approach to asymptotic stability for neural networks with time varying delays this paper is concerned with the problem of stability of neural networks with time varying delays a novel lyapunov krasovskii functional decomposing the delays in all integral terms is proposed by exploiting all possible information and considering independent upper bounds of the delay derivative in various delay intervals some new generalized delay dependent stability criteria are established which are different from the existing ones and improve upon previous results numerical examples are finally given to demonstrate the effectiveness and the merits of the proposed method

delay slope dependent stability results of recurrent neural networks by using the fact that the neuron activation functions are sector bounded and nondecreasing this brief presents a new method named the delay slope dependent method for stability analysis of a class of recurrent neural networks with time varying delays this method includes more information on the slope of neuron activation functions and fewer matrix variables in the constructed lyapunov krasovskii functional then some improved delay dependent stability criteria with less computational burden and conservatism are obtained numerical examples are given to illustrate the effectiveness and the benefits of the proposed method

new delay dependent stability criteria for neural networks with two additive time varying delay components this brief is concerned with delay dependent stability for neural networks with two additive time varying delay components by constructing a new lyapunov functional and using a convex polyhedron method to estimate the derivative of the lyapunov functional some new delay dependent stability criteria are derived these stability criteria are less conservative than some existing ones an example is given to demonstrate the less conservatism of the stability results

delay dependent stabilization of linear systems with time varying state and input delays the integral inequality method is a new way of tackling the delay dependent stabilization problem for a linear system with time varying state and input delays email protected t ax t a 1x t h 1 t b 1u t b 2u t h 2 t in this paper a new integral inequality for quadratic terms is first established then it is used to obtain a new state and input delay dependent criterion that ensures the stability of the closed loop system with a memoryless state feedback controller finally some numerical examples are presented to demonstrate that control systems designed based on the criterion are effective even though neither a b 1 nor a a 1 b 1 is stabilizable

multistability of recurrent neural networks with time varying delays and the piecewise linear activation function in this brief stability of multiple equilibria of recurrent neural networks with time varying delays and the piecewise linear activation function is studied a sufficient condition is obtained to ensure that n neuron recurrent neural networks can have 4k 1 n equilibrium points and 2k n of them are locally exponentially stable this condition improves and extends the existing stability results in the literature simulation results are also discussed in one illustrative example

new delay dependent stability criteria for neural networks with time varying delay in this letter a new method is proposed for stability analysis of neural networks nns with a time varying delay some less conservative delay dependent stability criteria are established by considering the additional useful terms which were ignored in previous methods when estimating the upper bound of the derivative of lyapunov functionals and introducing the new free weighting matrices numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

stability criteria for recurrent neural networks with time varying delay based on secondary delay partitioning method a secondary delay partitioning method is proposed to study the stability problem for a class of recurrent neural networks rnns with time varying delay the total interval of the time varying delay is first divided into two parts and then each part is further divided into several subintervals to deal with the state variables associated with these subintervals an extended reciprocal convex combination approach and a double integral term with variable upper and lower limits of integral as a lyapunov functional are proposed which help to obtain the stability criterion the main feature of the proposed result is more effective for the rnns with fast time varying delay a numerical example is used to show the effectiveness of the proposed stability result

delay derivative dependent stability for delayed neural networks with unbound distributed delay in this brief based on lyapunov krasovskii functional approach and appropriate integral inequality a new sufficient condition is derived to guarantee the global stability for delayed neural networks with unbounded distributed delay in which the improved delay partitioning technique and general convex combination are employed the lmi based criterion heavily depends on both the upper and lower bounds on time delay and its derivative which is different from the existent ones and has wider application fields than some present results finally three numerical examples can illustrate the efficiency of the new method based on the reduced conservatism which can be achieved by thinning the delay interval

new criteria of stability analysis for generalized neural networks subject to time varying delayed signals abstract this paper focuses on the new criteria of stability analysis for generalized neural networks gnns subject to time varying delayed signals a new methodology is employed with the aids of slack variables by constructing an augmented lyapunov krasovskii functional lkf involving newton leibniz enumerating and triple integral term some less conservative conditions are achieved in terms of linear matrix inequality lmi numerical examples including real time application are given to illustrate the superiority and effectiveness of proposed approach

robustness analysis of global exponential stability of recurrent neural networks in the presence of time delays and random disturbances in recent years the global stability of recurrent neural networks rnns has been investigated extensively it is well known that time delays and external disturbances can derail the stability of rnns in this paper we analyze the robustness of global stability of rnns subject to time delays and random disturbances given a globally exponentially stable neural network the problem to be addressed here is how much time delay and noise the rnn can withstand to be globally exponentially stable in the presence of delay and noise the upper bounds of the time delay and noise intensity are characterized by using transcendental equations for the rnns to sustain global exponential stability moreover we prove theoretically that for any globally exponentially stable rnns if additive noises and time delays are smaller than the derived lower bounds arrived at here then the perturbed rnns are guaranteed to also be globally exponentially stable three numerical examples are provided to substantiate the theoretical results

robust passivity analysis for stochastic impulsive neural networks with leakage and additive time varying delay components the purpose of this paper is to investigate the problem of robust passivity analysis for delayed stochastic impulsive neural networks with leakage and additive time varying delays the novel contribution of this paper lies in the consideration of a new integral inequality proved to be well known jensen s inequality and takes fully the relationship between the terms in the leibniz newton formula within the framework of linear matrix inequalities lmis by constructing a suitable lyapunov krasovskii functional with triple and four integral terms using jensen s inequality integral inequality technique and lmi frame work which guarantees stability for the passivity of addressed neural networks this lmi can be easily solved via convex optimization techniques finally two interesting numerical examples are given to show the effectiveness of the theoretical results

new delay dependent stability results for neural networks with time varying delay this paper studies the problem of stability analysis for neural networks nns with a time varying delay unlike the previous works the activation functions are assumed to be neither monotonic nor differentiable nor bounded by defining a more general type of lyapunov functionals some new less conservative delay dependent stability criteria are established in terms of linear matrix inequalities lmis meanwhile the computational complexity of the newly obtained stability conditions is reduced because less variables are involved numerical examples are given to illustrate the effectiveness and the benefits of the proposed method

on closedness and test complexity of logic circuits the concept of closedness of a set of logic functions under stuck type faults is introduced all sets of logic functions closed under stuck type faults are classified for the sets of logic functions closed under stuck type faults the test complexity and the universal test sets are considered it is shown that for each class of linear functions or functions and and functions both the minimum numbers of multiple fault detection tests and multiple fault location tests are exactly n 1 where n is the number of inputs of the circuits and that there exists universal test sets with n 1 tests to detect and locate all multiple faults in such circuits

selectable and unselectable sets of neurons in recurrent neural networks with saturated piecewise linear transfer function the concepts of selectable and unselectable sets are proposed to describe some interesting dynamical properties of a class of recurrent neural networks rnns with saturated piecewise linear transfer function a set of neurons is said to be selectable if it can be co unsaturated at a stable equilibrium point by some external input a set of neurons is said to be unselectable if it is not selectable i e such set of neurons can never be co unsaturated at any stable equilibrium point regardless of what the input is the importance of such concepts is that they enable a new perspective of the memory in rnns necessary and sufficient conditions for the existence of selectable and unselectable sets of neurons are obtained as an application the problem of group selection is discussed by using such concepts it shows that under some conditions each group is a selectable set and each selectable set is contained in some group thus groups are indicated by selectable sets of the rnns and can be selected by external inputs simulations are carried out to further illustrate the theory

further results on delay dependent stability criteria of neural networks with time varying delays in this brief paper an augmented lyapunov functional which takes an integral term of state vector into account is introduced owing to the functional an improved delay dependent asymptotic stability criterion for delayed neural networks nns is derived in term of linear matrix inequalities lmis it is shown that the obtained criterion can provide less conservative result than some existing ones when linear fractional uncertainties appear in nns a new robust delay dependent stability condition is also given numerical examples are given to demonstrate the applicability of the proposed approach

relaxed stability criteria for neural networks with time varying delay using extended secondary delay partitioning and equivalent reciprocal convex combination techniques this article investigates global asymptotic stability for neural networks nns with time varying delay which is differentiable and uniformly bounded and the delay derivative exists and is upper bounded first we propose the extended secondary delay partitioning technique to construct the novel lyapunov krasovskii functional where both single integral and double integral state variables are considered while the single integral ones are only solved by the traditional secondary delay partitioning second a novel free weight matrix equality fwme is presented to resolve the reciprocal convex combination problem equivalently and directly without schur complement which eliminates the need of positive definite matrices and is less conservative and restrictive compared with various improved reciprocal convex inequalities furthermore by the present extended secondary delay partitioning equivalent reciprocal convex combination technique and bessel legendre inequality two different relaxed sufficient conditions ensuring global asymptotic stability for nns are obtained for time varying delays respectively with unknown and known lower bounds of the delay derivative finally two examples are given to illustrate the superiority and effectiveness of the presented method

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

new results on stability analysis for delayed markovian generalized neural networks with partly unknown transition rates the stability of delayed markovian generalized neural networks is studied where the transition rates of the modes are partly unknown the partly unknown transition rates generalize the traditional works that are with all known transition rates then a lyapunov krasovskii functional lkf with a delay product type dpt term is constructed the dpt term is not only simple but also fully utilizes the information of time delay based on the new dpt lkf stability criteria are presented which are with lower computational complexity and less conservative in the end the validity and superiorities of the analytical results are verified by several examples

stability and synchronization of discrete time markovian jumping neural networks with mixed mode dependent time delays in this paper we introduce a new class of discrete time neural networks dnns with markovian jumping parameters as well as mode dependent mixed time delays both discrete and distributed time delays specifically the parameters of the dnns are subject to the switching from one to another at different times according to a markov chain and the mixed time delays consist of both discrete and distributed delays that are dependent on the markovian jumping mode we first deal with the stability analysis problem of the addressed neural networks a special inequality is developed to account for the mixed time delays in the discrete time setting and a novel lyapunov krasovskii functional is put forward to reflect the mode dependent time delays sufficient conditions are established in terms of linear matrix inequalities lmis that guarantee the stochastic stability we then turn to the synchronization problem among an array of identical coupled markovian jumping neural networks with mixed mode dependent time delays by utilizing the lyapunov stability theory and the kronecker product it is shown that the addressed synchronization problem is solvable if several lmis are feasible hence different from the commonly used matrix norm theories such as the m matrix method a unified lmi approach is developed to solve the stability analysis and synchronization problems of the class of neural networks under investigation where the lmis can be easily solved by using the available matlab lmi toolbox two numerical examples are presented to illustrate the usefulness and effectiveness of the main results obtained

further robust stability analysis for uncertain takagi sugeno fuzzy systems with time varying delay via relaxed integral inequality abstract this paper focuses on robust stability analysis for uncertain takagi sugeno fuzzy systems with time varying delays two delay product type terms are introduced for constructing a new lyapunov krasovskii functional which contains more information of time varying delay and a novel relaxed integral inequality is applied to estimate the derivative of lkf for achieving reduction of estimation gap as a result several further robust stability criteria with less conservativeness are proposed finally three numerical examples and an application to control of a truck trailer are provided to show the effectiveness and advantages of the presented methods

global asymptotic stability and stabilization of neural networks with general noise neural networks nns in the stochastic environment were widely modeled as stochastic differential equations which were driven by white noise such as brown or wiener process in the existing papers however they are not necessarily the best models to describe dynamic characters of nns disturbed by nonwhite noise in some specific situations in this paper general noise disturbance which may be nonwhite is introduced to nns since nns with nonwhite noise cannot be described by ito integral equation a novel modeling method of stochastic nns is utilized by a framework in light of random field approach and lyapunov theory the global asymptotic stability and stabilization in probability or in the mean square of nns with general noise are analyzed respectively criteria for the concerned systems based on linear matrix inequality are proposed some examples are given to illustrate the effectiveness of the obtained results

lmi based approach for global asymptotic stability analysis of recurrent neural networks with various delays and structures global asymptotic stability problem is studied for a class of recurrent neural networks with distributed delays satisfying lebesgue stieljies measures on the basis of linear matrix inequality the concerned network model includes many neural network models with various delays and structures as its special cases such as the delays covering the discrete delays and distributed delays and the network structures containing the neutral type networks and high order networks therefore many new stability criteria for the above neural network models have also been derived from the present stability analysis method all the obtained stability results have similar matrix inequality structures and can be easily checked three numerical examples are used to show the effectiveness of the obtained results

maximizing signless laplacian or adjacency spectral radius of graphs subject to fixed connectivity in this paper we characterize the graphs with maximum signless laplacian or adjacency spectral radius among all graphs with fixed order and given vertex or edge connectivity we also discuss the minimum signless laplacian or adjacency spectral radius of graphs subject to fixed connectivity consequently we give an upper bound of signless laplacian or adjacency spectral radius of graphs in terms of connectivity in addition we confirm a conjecture of aouchiche and hansen involving adjacency spectral radius and connectivity

on the complexity of estimating the size of a test set most np completeness results for test generation problems involve a reduction to the redundancy problem which explicitly encodes the satisfiability problem in this correspondence we investigate the complexity of a more modest problem that of estimating the size of a test set under the constraint that the circuit is irredundant we show that even this constrained problem is np hard in the strong sense

new lyapunov krasovskii functionals for global asymptotic stability of delayed neural networks this brief deals with the problem of global asymptotic stability for a class of delayed neural networks some new lyapunov krasovskii functionals are constructed by nonuniformly dividing the delay interval into multiple segments and choosing proper functionals with different weighting matrices corresponding to different segments in the lyapunov krasovskii functionals then using these new lyapunov krasovskii functionals some new delay dependent criteria for global asymptotic stability are derived for delayed neural networks where both constant time delays and time varying delays are treated these criteria are much less conservative than some existing results which is shown through a numerical example

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

improved delay dependent stability condition of discrete recurrent neural networks with time varying delays this brief investigates the problem of global exponential stability analysis for discrete recurrent neural networks with time varying delays in terms of linear matrix inequality lmi approach a novel delay dependent stability criterion is established for the considered recurrent neural networks via a new lyapunov function the obtained condition has less conservativeness and less number of variables than the existing ones numerical example is given to demonstrate the effectiveness of the proposed method

a new criterion of delay dependent asymptotic stability for hopfield neural networks with time delay in this brief the problem of global asymptotic stability for delayed hopfield neural networks hnns is investigated a new criterion of asymptotic stability is derived by introducing a new kind of lyapunov krasovskii functional and is formulated in terms of a linear matrix inequality lmi which can be readily solved via standard software this new criterion based on a delay fractioning approach proves to be much less conservative and the conservatism could be notably reduced by thinning the delay fractioning an example is provided to show the effectiveness and the advantage of the proposed result

the complexity of generating minimum test sets for pla s and monotone combinational circuits the authors show that the problem of obtaining a minimum complete test set is np complete for monotone plas even when each product term of the pla contains at most two literals using the ideas developed in the proof of this result they resolve an open question due to b krishnamurthy and s b akers 1984 the authors also show that given a complete test set t the problem of obtaining a minimum test set contained in t is np complete even for two level monotone circuits

lower bounds for the spread of a hermitian matrix abstract some simple lower bounds for the spread of a hermitian matrix are derived these bounds are explicit functions of the entries of the matrix one of which is sharper than a recent result due to e r barnes and a j hoffman comparisons are made with several known results

improved delay dependent asymptotic stability criteria for delayed neural networks this brief is concerned with asymptotic stability of neural networks with uncertain delays two types of uncertain delays are considered one is constant while the other is time varying the discretized lyapunov krasovskii functional lkf method is integrated with the technique of introducing the free weighting matrix between the terms of the leibniz newton formula the integrated method leads to the establishment of new delay dependent sufficient conditions in form of linear matrix inequalities for asymptotic stability of delayed neural networks dnns a numerical simulation study is conducted to demonstrate the obtained theoretical results which shows their less conservatism than the existing stability criteria

stability analysis for delayed neural networks considering both conservativeness and complexity this paper investigates delay dependent stability for continuous neural networks with a time varying delay this paper aims at deriving a new stability criterion considering tradeoff between conservativeness and calculation complexity a new lyapunov krasovskii functional with simple augmented terms and delay dependent terms is constructed and its derivative is estimated by several techniques including free weighting matrix and inequality estimation methods then the influence of the techniques used on the conservativeness and the complexity is analyzed one by one moreover useful guidelines for improving criterion and future work are briefly discussed finally the advantages of the proposed criterion compared with the existing ones are verified based on three numerical examples

exponential stability on stochastic neural networks with discrete interval and distributed delays this brief addresses the stability analysis problem for stochastic neural networks snns with discrete interval and distributed time varying delays the interval time varying delay is assumed to satisfy 0 d1 d t d2 and is described as d t d 1 h t with 0 h t d 2 d 1 based on the idea of partitioning the lower bound d 1 new delay dependent stability criteria are presented by constructing a novel lyapunov krasovskii functional which can guarantee the new stability conditions to be less conservative than those in the literature the obtained results are formulated in the form of linear matrix inequalities lmis numerical examples are provided to illustrate the effectiveness and less conservatism of the developed results

improved stability criteria for linear systems with two additive time varying delays via a novel lyapunov functional abstract this paper consider the stability problem of linear systems with two additive time varying delays a novel lyapunov krasovskii functional lkf is constructed which consists of the delay dependent non integral items and the single integral items based on the newly developed lkf a stability criterion is derived which is less conservative than some recent existing ones furthermore to obtain a tighter bound of the integral term quadratic generalized free weighting matrix inequality qgfmi is used finally a numerical example and an application of the load frequency control for a single area power system are presented to show the effectiveness of the proposed approach

characterizations and lower bounds for the spread of a normal matrix abstract the spread of an n n matrix a with eigenvalues 1 n is defined by spr a max j k j k we prove that if a is normal then spr a max x ax y ay x y c n x y 1 max x ay y ax x y c n x y 1 re x y 0 max x ay y ax x y c n x y 1 x y 0 max spr z a z a 2 z c z 1 2 max x a 2 x x ax 2 x a ax x ax 2 1 2 x c n x 1 we also present several lower bounds for spr a given by these characterizations

proof of conjecture involving the second largest signless laplacian eigenvalue and the index of graphs abstract let g v e be a simple graph denote by d g the diagonal matrix of its vertex degrees and by a g its adjacency matrix then the signless laplacian matrix of g is q g d g a g in 5 cvetkovic et al have given the following conjecture involving the second largest signless laplacian eigenvalue q 2 and the index 1 of graph g see also aouchiche and hansen 1 1 n 1 q 2 1 n 2 2 n 4 with equality if and only if g is the star k 1 n 1 for the lower bound and if and only if g is the complete bipartite graph k n 2 2 for the upper bound in this paper we prove the lower bound and characterize the extremal graphs

stability and l_ 2 performance analysis of stochastic delayed neural networks this brief focuses on the robust mean square exponential stability and l2 performance analysis for a class of uncertain time delay neural networks perturbed by both additive and multiplicative stochastic noises new mean square exponential stability and l2 performance criteria are developed based on the delay partition lyapunov krasovskii functional method and generalized finsler lemma which is applicable to stochastic systems the analytical results are established without involving any model transformation estimation for cross terms additional free weighting matrices or tuning parameters numerical examples are presented to verify that the proposed approach is both less conservative and less computationally complex than the existing ones

a further refinement of discretized lyapunov functional method for the stability of time delay systems the discretized lyapunov functional method for the stability problem of time delay systems is further refined using a combination of integral inequality and variable elimination technique as a result the computational requirement is further reduced for the same discretization mesh for systems without uncertainty the convergence to the analytical solution is greatly accelerated for uncertain systems the new method is much less conservative numerical examples are presented to illustrate the effectiveness of the method

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

delay dependent stability for recurrent neural networks with time varying delays this brief is concerned with the stability for static neural networks with time varying delays delay independent conditions are proposed to ensure the asymptotic stability of the neural network the delay independent conditions are less conservative than existing ones to further reduce the conservatism delay dependent conditions are also derived which can be applied to fast time varying delays expressed in linear matrix inequalities both delay independent and delay dependent stability conditions can be checked using the recently developed algorithms examples are provided to illustrate the effectiveness and the reduced conservatism of the proposed result

state estimation for delayed genetic regulatory networks with reaction diffusion terms this paper addresses the problem of state estimation for delayed genetic regulatory networks dgrns with reaction diffusion terms using dirichlet boundary conditions the nonlinear regulation function of dgrns is assumed to exhibit the hill form the aim of this paper is to design a state observer to estimate the concentrations of mrnas and proteins via available measurement techniques by introducing novel integral terms into the lyapunov krasovskii functional and by employing the wirtinger type integral inequality the convex approach green s identity the reciprocally convex approach and wirtinger s inequality an asymptotic stability criterion of the error system was established in terms of linear matrix inequalities lmis the stability criterion depends upon the bounds of delays and their derivatives it should be noted that if the set of lmis is feasible then the desired observation of dgrns is possible and the state estimation can be determined finally two numerical examples are presented to illustrate the availability and applicability of the proposed scheme design

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

stability and dissipativity analysis of distributed delay cellular neural networks in this brief the problems of delay dependent stability analysis and strict q s dissipativity analysis are investigated for cellular neural networks cnns with distributed delay first by introducing an integral partitioning technique two new forms of lyapunov krasovskii functionals are constructed and improved distributed delay dependent stability conditions are established in terms of linear matrix inequalities based on this criterion a new sufficient delay and dependent condition is given to guarantee that the cnns with distributed delay are strictly q s dissipative the results developed in this brief can tolerate larger allowable delay than existing ones in the literature which is demonstrated by several examples

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

stability analysis of lur e systems with additive delay components via a relaxed matrix inequality abstract this paper is concerned with the stability analysis of lur e systems with sector bounded nonlinearity and two additive time varying delay components in order to accurately understand the effect of time delays on the system stability the extended matrix inequality for estimating the derivative of the lyapunov krasovskii functionals lkfs is employed to achieve the conservatism reduction of stability criteria it reduces estimation gap of the popular reciprocally convex combination lemma rccl combining the extended matrix inequality and two types of lkfs lead to several stability criteria which are less conservative than the rccl based criteria under the same lkfs finally the advantages of the proposed criteria are demonstrated through two examples

bounds on the q spread of a graph the spread s m of an n n complex matrix m is s m maxij i j where the maximum is taken over all pairs of eigenvalues of m i 1 i n 9 and 11 based on this concept gregory et al 7 determined some bounds for the spread of the adjacency matrix a g of a simple graph g and made a conjecture regarding the graph on n vertices yielding the maximum value of the spread of the corresponding adjacency matrix the signless laplacian matrix of a graph g q g d g a g where d g is the diagonal matrix of degrees of g and a g is its adjacency matrix has been recently studied 4 5 the main goal of this paper is to determine some bounds on s q g we prove that for any graph on n 5 vertices 2 s q g 2n 4 and we characterize the equality cases in both bounds further we prove that for any connected graph g with n 5 vertices s q g 2n 4 we conjecture that for n 5 sq g 4n 2 20n 33 and that in this case the upper bound is attained if and only if g is a certain pathcomplete graph

global asymptotic stability for a class of generalized neural networks with interval time varying delays this paper is concerned with global asymptotic stability for a class of generalized neural networks nns with interval time varying delays which include two classes of fundamental nns i e static neural networks snns and local field neural networks lfnns as their special cases some novel delay independent and delay dependent stability criteria are derived these stability criteria are applicable not only to snns but also to lfnns it is theoretically proven that these stability criteria are more effective than some existing ones either for snns or for lfnns which is confirmed by some numerical examples

improved delay dependent stability criteria for generalized neural networks with time varying delays abstract this paper is concerned with the problem of stability analysis for generalized neural networks with time varying delays a novel integral inequality which includes several existing inequalities as special cases is presented by employing a suitable lyapunov krasovskii functional lkf and using the proposed integral inequality to estimate the derivative of the lkf improved delay dependent stability criteria expressed in terms of linear matrix inequalities are derived finally four numerical examples are provided to demonstrate the effectiveness and the improvement of the proposed method

a lower bound on the least signless laplacian eigenvalue of a graph let g be a simple graph with n vertices and m edges and let q n g be the least signless laplacian eigenvalue of g recently guo chen and yu proved that if n ge 6 then begin aligned q n g ge frac 2m n 2 n 1 end aligned which confirms a conjecture proposed by de lima oliveira de abreu and nikiforov in this note we present a new proof for the above inequality where we also completely characterize the case when the equality holds