abel lemma based finite sum inequality and its application to stability analysis for linear discrete time delay systems this paper is concerned with stability of linear discrete time delay systems note that a tighter estimation on a finite sum term appearing in the forward difference of some lyapunov functional leads to a less conservative delay dependent stability criterion by using abel lemma a novel finite sum inequality is established which can provide a tighter estimation than the ones in the literature for the finite sum term applying this abel lemma based finite sum inequality a stability criterion for linear discrete time delay systems is derived it is shown through numerical examples that the stability criterion can provide a larger admissible maximum upper bound than stability criteria using a jensen type inequality approach and a free weighting matrix approach

state estimation for static neural networks with time varying delays based on an improved reciprocally convex inequality this brief is concerned with the problem of neural state estimation for static neural networks with time varying delays notice that a luenberger estimator can produce an estimation error irrespective of the neuron state trajectory this brief provides a method for designing such an estimator for static neural networks with time varying delays first in depth analysis on a well used reciprocally convex approach is made leading to an improved reciprocally convex inequality second the improved reciprocally convex inequality and some integral inequalities are employed to provide a tight upper bound on the time derivative of some lyapunov krasovskii functional as a result a novel bounded real lemma brl for the resultant error system is derived third the brl is applied to present a method for designing suitable luenberger estimators in terms of solutions of linear matrix inequalities with two tuning parameters finally it is shown through a numerical example that the proposed method can derive less conservative results than some existing ones

global exponential periodicity of a class of recurrent neural networks with oscillating parameters and time varying delays in this paper we present the analytical results on the global exponential periodicity of a class of recurrent neural networks with oscillating parameters and time varying delays sufficient conditions are derived for ascertaining the existence uniqueness and global exponential periodicity of the oscillatory solution of such recurrent neural networks by using the comparison principle and mixed monotone operator method the periodicity results extend or improve existing stability results for the class of recurrent neural networks with and without time delays

network based h filtering using a logic jumping like trigger this paper is concerned with the network based h filtering for a stochastic system where data transmission from the stochastic system to a filter is completed via a communication network network induced delays packet dropouts and packet disorders are unavoidable due to the use of the network first a logic zero order hold zoh is designed to discard the disordered packets actively the network induced delays and packet dropouts are modeled as an interval time varying delay by decomposing the delay interval into n subintervals uniformly the filter to be designed is modeled as a markov jumping filter with n modes governed by a markov chain in order to work out the transition rate from one mode to another a logic jumping like trigger is embedded into the logic zoh to simulate the switching of the markov process second based on the markov jumping filter model together with a new integral inequality in the stochastic setting a novel bounded real lemma is presented to ensure that the resultant filtering error system is mean exponentially stable with a prescribed h performance then a sufficient condition on the existence of desired markov jumping filters is provided in terms of a set of linear matrix inequalities finally an air vehicle system is employed to show effectiveness of the proposed design method

generalized levitin polyak well posedness in constrained optimization in this paper we consider levitin polyak type well posedness for a general constrained optimization problem we introduce generalized levitin polyak well posedness and strongly generalized levitin polyak well posedness necessary and sufficient conditions for these types of well posedness are given relations among these types of well posedness are investigated finally we consider convergence of a class of penalty methods and a class of augmented lagrangian methods under the assumption of strongly generalized levitin polyak well posedness

which diameter and angle rule provides optimal flow patterns in a coronary bifurcation the branching angle and diameter ratio in epicardial coronary artery bifurcations are two important determinants of atherogenesis murray s cubed diameter law and bifurcation angle have been assumed to yield optimal flows through a bifurcation in contrast we have recently shown a 7 3 diameter law hk diameter model based on minimum energy hypothesis in an entire tree structure here we derive a bifurcation angle rule corresponding to the hk diameter model and critically evaluate the streamline flow through hk and murray type bifurcations the bifurcations from coronary casts were found to obey the hk diameter model and angle rule much more than murray s model a finite element model was used to investigate flow patterns for coronary artery bifurcations of various types the inlet velocity and pressure boundary conditions were measured by combowire y bifurcation of murray type decreased wall shear stress wss 10 40 and created an increased oscillatory shear index osi in atherosclerosis prone regions as compared with hk type bifurcations the hk type bifurcations were found to have more optimal flow patterns i e higher wss and lower osi than murray type bifurcations which have been traditionally believed to be optimized this study has implications for changes in bifurcation angles and diameters in percutaneous coronary intervention

global exponential synchronization of multiple memristive neural networks with time delay via nonlinear coupling this paper presents theoretical results on the global exponential synchronization of multiple memristive neural networks with time delays a novel coupling scheme is introduced in a general topological structure described by a directed or undirected graph with a linear diffusive term and discontinuous sign term several criteria are derived based on the lyapunov stability theory to ascertain the global exponential stability of synchronization manifold in the coupling scheme simulation results for several examples are given to substantiate the effectiveness of the theoretical results

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

passivity of switched recurrent neural networks with time varying delays this paper is concerned with the passivity analysis for switched neural networks subject to stochastic disturbances and time varying delays first using the multiple lyapunov functions method a state dependent switching law is designed to present a stochastic passivity condition second a hysteresis switching law involving both the current state and the previous value of the switching signal are presented to avoid chattering resulted from the state dependent switching third based on the average dwell time approach a class of switching signals is determined to guarantee the switched neural network stochastically passive finally three numerical examples are provided to illustrate the characteristics of three proposed switching laws

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

stability analysis of distributed delay neural networks based on relaxed lyapunov krasovskii functionals this paper revisits the problem of asymptotic stability analysis for neural networks with distributed delays the distributed delays are assumed to be constant and prescribed since a positive definite quadratic functional does not necessarily require all the involved symmetric matrices to be positive definite it is important for constructing relaxed lyapunov krasovskii functionals which generally lead to less conservative stability criteria based on this fact and using two kinds of integral inequalities a new delay dependent condition is obtained which ensures that the distributed delay neural network under consideration is globally asymptotically stable this stability criterion is then improved by applying the delay partitioning technique two numerical examples are provided to demonstrate the advantage of the presented stability criteria

event triggered generalized dissipativity filtering for neural networks with time varying delays this paper is concerned with event triggered generalized dissipativity filtering for a neural network nn with a time varying delay the signal transmission from the nn to its filter is completed through a communication channel it is assumed that the network measurement of the nn is sampled periodically an event triggered communication scheme is introduced to design a suitable filter such that precious communication resources can be saved significantly while certain filtering performance can be ensured on the one hand the event triggered communication scheme is devised to select only those sampled signals violating a certain threshold to be transmitted which directly leads to saving of precious communication resources on the other hand the filtering error system is modeled as a time delay system closely dependent on the parameters of the event triggered scheme based on this model a suitable filter is designed such that certain filtering performance can be ensured provided that a set of linear matrix inequalities are satisfied furthermore since a generalized dissipativity performance index is introduced several kinds of event triggered filtering issues such as h infty filtering passive filtering mixed h infty and passive filtering q s r dissipative filtering and mathcal l 2 mathcal l infty filtering are solved in a unified framework finally two examples are given to illustrate the effectiveness of the proposed method

on extended dissipativity of discrete time neural networks with time delay in this brief the problem of extended dissipativity analysis for discrete time neural networks with time varying delay is investigated the definition of extended dissipativity of discrete time neural networks is proposed which unifies several performance measures such as the h infty performance passivity l 2 l infty performance and dissipativity by introducing a triple summable term in lyapunov function the reciprocally convex approach is utilized to bound the forward difference of the triple summable term and then the extended dissipativity criterion for discrete time neural networks with time varying delay is established the derived condition guarantees not only the extended dissipativity but also the stability of the neural networks two numerical examples are given to demonstrate the reduced conservatism and effectiveness of the obtained results

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

synchronization error estimation and controller design for delayed lur e systems with parameter mismatches this paper investigates the problem of master slave synchronization of two delayed lur e systems in the presence of parameter mismatches first by analyzing the corresponding synchronization error system synchronization with an error level which is referred to as quasi synchronization is established some delay dependent quasi synchronization criteria are derived an estimation of the synchronization error bound is given and an explicit expression of error levels is obtained second sufficient conditions on the existence of feedback controllers under a predetermined error level are provided the controller gains are obtained by solving a set of linear matrix inequalities finally a delayed chua s circuit is chosen to illustrate the effectiveness of the derived results

stability analysis of systems with time varying delays via the second order bessel legendre inequality this paper is concerned with the delay dependent stability of systems with time varying delays the novelty relies on the use of the second order bessel legendre integral inequality which is less conservative than the jensen and wirtinger based inequalities unlike similar contributions the features of this inequality are fully integrated into the construction of augmented lyapunov krasovskii functionals leading to novel stability criteria expressed in terms of linear matrix inequalities the stability condition is tested on some classical numerical examples illustrating the efficiency of the proposed method

new delay dependent stability criteria for neural networks with time varying delay using delay decomposition approach this brief is concerned with the problem of asymptotic stability of neural networks with time varying delays the activation functions are monotone nondecreasing with known lower and upper bounds novel stability criteria are derived by employing new lyapunov krasovskii functional and the integral inequality the developed stability criteria have delay dependencies and the results are characterized by linear matrix inequalities new and less conservative solutions to the global stability problem are provided in terms of feasibility testing numerical examples are finally given to demonstrate the effectiveness of the proposed method

brief paper a discrete delay decomposition approach to stability of linear retarded and neutral systems this paper is concerned with stability of linear time delay systems of both retarded and neutral types by using some new simple quadratic lyapunov krasovskii functionals these lyapunov krasovskii functionals consist of two parts one part comes from some existing lyapunov krasovskii functionals employed in han q l 2005a absolute stability of time delay systems with sector bounded nonlinearity automatica 41 2171 2176 han q l 2005b a new delay dependent stability criterion for linear neutral systems with norm bounded uncertainties in all system matrices international journal of systems science 36 469 475 the other part is constructed by uniformly dividing the discrete delay interval into multiple segments and choosing proper functionals with different weighted matrices corresponding to different segments then using these new simple quadratic lyapunov krasovskii functionals some new discrete delay dependent stability criteria are derived for both retarded systems and neutral systems it is shown that these criteria for retarded systems and neutral systems are always less conservative than the ones in han 2005a and han 2005b cited above respectively numerical examples also show that the results obtained in this paper significantly improve the estimate of the discrete delay limit for stability over some other existing results

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

how delays affect neural dynamics and learning we investigate the effects of delays on the dynamics and in particular on the oscillatory properties of simple neural network models we extend previously known results regarding the effects of delays on stability and convergence properties we treat in detail the case of ring networks for which we derive simple conditions for oscillating behavior and several formulas to predict the regions of bifurcation the periods of the limit cycles and the phases of the different neurons these results in turn can readily be applied to more complex and more biologically motivated architectures such as layered networks in general the main result is that delays tend to increase the period of oscillations and broaden the spectrum of possible frequencies in a quantifiable way simulations show that the theoretically predicted values are in excellent agreement with the numerically observed behavior adaptable delays are then proposed as one additional mechanism through which neural systems could tailor their own dynamics accordingly we derive recurrent backpropagation learning formulas for the adjustment of delays and other parameters in networks with delayed interactions and discuss some possible applications

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

global stability of complex valued recurrent neural networks with time delays since the last decade several complex valued neural networks have been developed and applied in various research areas as an extension of real valued recurrent neural networks complex valued recurrent neural networks use complex valued states connection weights or activation functions with much more complicated properties than real valued ones this paper presents several sufficient conditions derived to ascertain the existence of unique equilibrium global asymptotic stability and global exponential stability of delayed complex valued recurrent neural networks with two classes of complex valued activation functions simulation results of three numerical examples are also delineated to substantiate the effectiveness of the theoretical results

new passivity analysis for neural networks with discrete and distributed delays in this brief the problem of passivity analysis is investigated for a class of uncertain neural networks nns with both discrete and distributed time varying delays by constructing a novel lyapunov functional and utilizing some advanced techniques new delay dependent passivity criteria are established to guarantee the passivity performance of nns essentially different from the available results when estimating the upper bound of the derivative of lyapunov functionals we consider and best utilize the additional useful terms about the distributed delays which leads to less conservative results these criteria are expressed in the form of convex optimization problems which can be efficiently solved via standard numerical software numerical examples are provided to illustrate the effectiveness and less conservatism of the proposed results

new and improved results on stability of static neural networks with interval time varying delays abstract in this paper the problem of stability analysis for static neural networks with interval time varying delays is considered by the consideration of new augmented lyapunov functionals new and improved delay dependent stability criteria to guarantee the asymptotic stability of the concerned networks are proposed with the framework of linear matrix inequalities lmis which can be solved easily by standard numerical packages the enhancement of the feasible region of the proposed criteria is shown via two numerical examples by the comparison of maximum delay bounds