mixed h2 h fuzzy proportional spatial integral control design for a class of nonlinear distributed parameter systems abstract in this paper a fuzzy feedback control design problem with a mixed h 2 h performance is addressed by using the distributed proportional spatial integral p si control approach for a class of nonlinear distributed parameter systems represented by semi linear parabolic partial differential integral equations pdies the objective of this paper is to develop a fuzzy distributed p si controller with a mixed h 2 h performance index for the semi linear parabolic pdie system to do this the semi linear parabolic pdie system is first assumed to be exactly represented by a takagi sugeno t s fuzzy parabolic pdie model in a given local domain of hilbert space then based on the t s fuzzy pdie model a distributed fuzzy p si state feedback controller is proposed such that the closed loop pdie system is locally exponentially stable with a mixed h 2 h performance the sufficient condition on the existence of the fuzzy controller is given by using the lyapunov s direct method the technique of integration by parts and vector valued wirtinger s inequalities and presented in terms of standard linear matrix inequalities lmis moreover by using the existing lmi optimization techniques a suboptimal h fuzzy controller is derived in the sense of minimizing an upper bound of a given h 2 performance function finally the developed design methodology is successfully applied to feedback control of a semi linear reaction diffusion system with spatial integral terms

the average path length for a class of scale free fractal hierarchical lattices rigorous results abstract with the help of the recurrence relations derived from the self similar structure we obtain the closed form solution for the average path length of a class of scale free fractal hierarchical lattices hls with a general parameter q which are simultaneously scale free self similar and disassortative our rigorous solution shows that the average path length of the hls grows logarithmically as d t n t log 2 q 2 in the infinite limit of network size of n t and that they are not small worlds but grow with a power law relationship to the number of nodes

sampled data synchronization of markovian coupled neural networks with mode delays based on mode dependent lkf this paper investigates sampled data synchronization problem of markovian coupled neural networks with mode dependent interval time varying delays and aperiodic sampling intervals based on an enhanced input delay approach a mode dependent augmented lyapunov krasovskii functional lkf is utilized which makes the lkf matrices mode dependent as much as possible by applying an extended jensen s integral inequality and wirtinger s inequality new delay dependent synchronization criteria are obtained which fully utilizes the upper bound on variable sampling interval and the sawtooth structure information of varying input delay in addition the desired stochastic sampled data controllers can be obtained by solving a set of linear matrix inequalities finally two examples are provided to demonstrate the feasibility of the proposed method

recent developments on the stability of systems with aperiodic sampling an overview this article presents basic concepts and recent research directions about the stability of sampled data systems with aperiodic sampling we focus mainly on the stability problem for systems with arbitrary time varying sampling intervals which has been addressed in several areas of research in control theory systems with aperiodic sampling can be seen as time delay systems hybrid systems input output interconnections discrete time systems with time varying parameters etc the goal of the article is to provide a structural overview of the progress made on the stability analysis problem without being exhaustive which would be neither possible nor useful we try to bring together results from diverse communities and present them in a unified manner for each of the existing approaches the basic concepts fundamental results converse stability theorems when available and relations with the other approaches are discussed in detail results concerning extensions of lyapunov and frequency domain methods for systems with aperiodic sampling are recalled as they allow to derive constructive stability conditions furthermore numerical criteria are presented while indicating the sources of conservatism the problems that remain open and the possible directions of improvement at last some emerging research directions such as the design of stabilizing sampling sequences are briefly discussed

estimation of domain of attraction for aperiodic sampled data switched delayed neural networks subject to actuator saturation in this paper for the case of the asynchronous switching caused by that subsystem s switching occuring during a sampling interval the domain of attraction estimation problem is investigated for aperiodic sampled data switched delayed neural networks asdsdnns subject to actuator saturation a parameters dependent time scheduled lyapunov functional consisting of a novel looped functional is constructed using segmentation technology and linear interpolation by employing this novel functional and using an average dwell time adt approach exponential stability criteria are proposed for polytopic uncertain asdsdnns subject to actuator saturation and a relationship between adt and sampling period is revealed for asdsdnns as a corollary exponential stability criteria are proposed for nominal asdsdnns subject to actuator saturation furthermore by describing the domain of attraction as a time varying ellipsoid determined by the time scheduled lyapunov matrix the proposed theoretical conditions are transformed into a linear matrix inequality lmi based multi objective optimization problem the dynamic estimates of the domain of attraction for asdsdnns are solved numerical simulation examples are provided to illustrate the effectiveness of the proposed method

free matrix based integral inequality for stability analysis of systems with time varying delay the free weighting matrix and integral inequality methods are widely used to derive delay dependent criteria for the stability analysis of time varying delay systems because they avoid both the use of a model transformation and the technique of bounding cross terms this technical note presents a new integral inequality called a free matrix based integral inequality that further reduces the conservativeness in those methods it includes well known integral inequalities as special cases using it to investigate the stability of systems with time varying delays yields less conservative delay dependent stability criteria which are given in terms of linear matrix inequalities two numerical examples demonstrate the effectiveness and superiority of the method

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

stability analysis for stochastic cohen grossberg neural networks with mixed time delays in this letter the global asymptotic stability analysis problem is considered for a class of stochastic cohen grossberg neural networks with mixed time delays which consist of both the discrete and distributed time delays based on an lyapunov krasovskii functional and the stochastic stability analysis theory a linear matrix inequality lmi approach is developed to derive several sufficient conditions guaranteeing the global asymptotic convergence of the equilibrium point in the mean square it is shown that the addressed stochastic cohen grossberg neural networks with mixed delays are globally asymptotically stable in the mean square if two lmis are feasible where the feasibility of lmis can be readily checked by the matlab lmi toolbox it is also pointed out that the main results comprise some existing results as special cases a numerical example is given to demonstrate the usefulness of the proposed global stability criteria

robust exponential stability of markovian jump impulsive stochastic cohen grossberg neural networks with mixed time delays this paper is concerned with the problem of exponential stability for a class of markovian jump impulsive stochastic cohen grossberg neural networks with mixed time delays and known or unknown parameters the jumping parameters are determined by a continuous time discrete state markov chain and the mixed time delays under consideration comprise both time varying delays and continuously distributed delays to the best of the authors knowledge till now the exponential stability problem for this class of generalized neural networks has not yet been solved since continuously distributed delays are considered in this paper the main objective of this paper is to fill this gap by constructing a novel lyapunov krasovskii functional and using some new approaches and techniques several novel sufficient conditions are obtained to ensure the exponential stability of the trivial solution in the mean square the results presented in this paper generalize and improve many known results finally two numerical examples and their simulations are given to show the effectiveness of the theoretical results

stochastic dissipativity and passivity analysis for discrete time neural networks with probabilistic time varying delays in the leakage term this paper deals with the dissipativity and passivity analysis for discrete time stochastic neural networks with probabilistic time varying delays the main contribution of this paper is to reduce the conservatism of the dissipativity conditions for the considered neural networks by utilizing the reciprocally convex combination approach this approach is proposed to bound the forward differences of the double and triple summable terms taken in the lyapunov functional by introducing a stochastic variable with a bernoulli distribution the information of probability distribution of the time varying delays are considered and transformed into one with deterministic time varying delays by employing lyapunov functional approach sufficient conditions are derived in terms of linear matrix inequalities to guarantee that the considered neural networks to be strictly q s r dissipative and passive finally numerical examples are given to demonstrate the effectiveness of the obtained results

stabilization of singular markovian jump systems with generally uncertain transition rates this note is devoted to investigating the stability and stabilization problems for continuous time singular markovian jump systems smjss with generally uncertain transition rates gutrs in this gutr singular model each transition rate can be completely unknown or only its estimate value is known in terms of a set of coupled linear matrix inequalities lmis a sufficient condition is established to ensure the systems to be regular impulse free and stochastically stable moreover the corresponding sufficient condition on the existence of a mode dependent state feedback controller is derived to guarantee the closed loop systems stochastically admissible by applying the lmi technique finally a numerical example is presented to illustrate the effectiveness and efficiency of the proposed method

stability analysis of sampled data systems via free matrix based time dependent discontinuous lyapunov approach in this paper a new time dependent discontinuous lyapunov functional namely free matrix based time dependent discontinuous fmbtdd lyapunov functional is introduced for stability analysis of sampled data systems first a modified free matrix based integral inequality mfmbii is derived based on the existing free matrix based integral inequality 1 and it is applied to develop a stability criterion for sampled data systems and then inspired by mfmbii fmbtdd term is established that leads to efficient stability conditions four numerical examples are given to demonstrate the effectiveness of the proposed methods

technical communique stability and robust stability for systems with a time varying delay to concern the stability and robust stability criteria for systems with time varying delays this note uses not only the time varying delayed state x t h t but also the delay upper bounded state x email protected to exploit all possible information for the relationship among a current state x t an exactly delayed state x t h t a marginally delayed state x email protected and the derivative of the state email protected t when constructing lyapunov krasovskii functionals and some appropriate integral inequalities originally suggested by park 1999 a delay dependent stability criterion for systems with uncertain time invariant delays ieee transactions on automatic control 44 4 876 877 two fundamental criteria are provided for the cases where no bound of delay derivative is assumed and where an upper bound of delay derivative is assumed examples show the resulting criteria outperform all existing ones in the literature

on design of interval observers with sampled measurement new design of interval observers for continuous time systems with discrete time measurements is proposed for this purpose new conditions of positivity for linear systems with sampled feedbacks are obtained a sampled data stabilizing control is synthesized based on provided interval estimates efficiency of the obtained solution is demonstrated on examples

on backwards and forwards reachable sets bounding for perturbed time delay systems linear systems with interval time varying delay and unknown but bounded disturbances are considered in this paper we study the problem of finding outer bound of forwards reachable sets and inter bound of backwards reachable sets of the system firstly two definitions on forwards and backwards reachable sets where initial state vectors are not necessary to be equal to zero are introduced then by using the lyapunov krasovskii method two sufficient conditions for the existence of i the smallest possible outer bound of forwards reachable sets and ii the largest possible inter bound of backwards reachable sets are derived these conditions are presented in terms of linear matrix inequalities with two parameters need to tuned which therefore can be efficiently solved by combining existing convex optimization algorithms with a two dimensional search method to obtain optimal bounds lastly the obtained results are illustrated by four numerical examples

smallest eigenvalues of hankel matrices for exponential weights abstract we obtain the rate of decay of the smallest eigenvalue of the hankel matrices i t j k w 2 t dt j k 0 n for a general class of even exponential weights w2 exp 2q on an interval i more precise asymptotics for more special weights have been obtained by many authors

exponential stability of impulsive systems with application to uncertain sampled data systems we establish exponential stability of nonlinear time varying impulsive systems by employing lyapunov functions with discontinuity at the impulse times our stability conditions have the property that when specialized to linear impulsive systems the stability tests can be formulated as linear matrix inequalities lmis then we consider lti uncertain sampled data systems in which there are two sources of uncertainty the values of the process parameters can be unknown while satisfying a polytopic condition and the sampling intervals can be uncertain and variable we model such systems as linear impulsive systems and we apply our theorem to the analysis and state feedback stabilization we find a positive constant which determines an upper bound on the sampling intervals for which the stability of the closed loop is guaranteed the control design lmis also provide controller gains that can be used to stabilize the process we also consider sampled data systems with constant sampling intervals and provide results that are less conservative than the ones obtained for variable sampling intervals

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

random walks in modular scale free networks with multiple traps extensive empirical investigation has shown that a plethora of real networks synchronously exhibit scale free and modular structure and it is thus of great importance to uncover the effects of these two striking properties on various dynamical processes occurring on such networks in this paper we examine two cases of random walks performed on a class of modular scale free networks with multiple traps located at several given nodes we first derive a formula of the mean first passage time mfpt for a general network which is the mean of the expected time to absorption originating from a specific node averaged over all nontrap starting nodes although the computation is complex the expression of the formula is exact moreover the computational approach and procedure are independent of the number and position of the traps we then determine analytically the mfpt for the two random walks being considered the obtained analytical results are in complete agreement with the numerical ones our results show that the number and location of traps play an important role in the behavior of the mfpt since for both cases the mfpt grows as a power law function of the number of nodes but their exponents are quite different we demonstrate that the root of the difference in the behavior of mfpt is attributed to the modular and scale free topologies of the networks this work can deepen the understanding of diffusion on networks with modular and scale free architecture and motivate relevant studies for random walks running on complex random networks with multiple traps

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

griffiths singularities and algebraic order in the exact solution of an ising model on a fractal modular network we use an exact renormalization group transformation to study the ising model on a complex network composed of tightly knit communities nested hierarchically with the fractal scaling recently discovered in a variety of real world networks varying the ratio k j of intercommunity to intracommunity couplings we obtain an unusual phase diagram at high temperatures or small k j we have a disordered phase with a griffiths singularity in the free energy due to the presence of rare large clusters which we analyze through the yang lee zeros in the complex magnetic field plane as the temperature is lowered true long range order is not seen but there is a transition to algebraic order where pair correlations have power law decay with distance reminiscent of the xy model the transition is infinite order at small k j and becomes second order above a threshold value k j m the existence of such slowly decaying correlations is unexpected in a fat tailed scale free network where correlations longer than nearest neighbor are typically suppressed

renormalization group solution of the chutes ladder model abstract we analyze a semi infinite one dimensional random walk process with a biased motion that is incremental in one direction and long range in the other on a network with a fixed hierarchy of long range jumps we find with exact renormalization group calculations that there is a dynamical transition between a localized adsorption phase and an anomalous diffusion phase in which the mean square displacement exponent depends non universally on the bernoulli coin we relate these results to similar findings of unconventional phase behavior in hierarchical networks

a new looped functional for stability analysis of sampled data systems abstract in this paper a new two sided looped functional is introduced for stability analysis of sampled data systems the functional fully utilizes the information on both the intervals x t to x t k and x t to x t k 1 based on the two sided functional an improved stability condition is derived in the form of linear matrix inequality lmi numerical examples show that the result computed by the presented condition approximates nearly the theoretical bound bound obtained by eigenvalue analysis and outperforms substantially others in the existing literature

exponential stabilization for sampled data neural network based control systems this paper investigates the problem of sampled data stabilization for neural network based control systems with an optimal guaranteed cost using time dependent lyapunov functional approach some novel conditions are proposed to guarantee the closed loop systems exponentially stable which fully use the available information about the actual sampling pattern based on the derived conditions the design methods of the desired sampled data three layer fully connected feedforward neural network based controller are established to obtain the largest sampling interval and the smallest upper bound of the cost function a practical example is provided to demonstrate the effectiveness and feasibility of the proposed techniques

a robust stability framework for lti systems with time varying sampling this work aims at enlarging the sampling intervals in several state feedback control situations by designing a sampling map in the state space we consider the case of linear time invariant lti systems with state bounded perturbations and guarantee their exponential stability for a chosen decay rate the approach is based on linear matrix inequalities lmis obtained thanks to lyapunov razumikhin stability conditions and convexification arguments first it enables to optimize the lower bound of the sampling maps by computing the adequate lyapunov razumikhin function this result can be interpreted as a robust stability analysis with respect to arbitrary time varying sampling intervals which may be useful in the case of uncontrolled sampling or in the presence of phenomenon such as sampling jitter then the obtained results are extended to design the sampling map in three dynamic sampling control situations event triggered control self triggered control and state dependent sampling the results are illustrated with a numerical example from the literature

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

nonfragile exponential synchronization of delayed complex dynamical networks with memory sampled data control this paper considers nonfragile exponential synchronization for complex dynamical networks cdns with time varying coupling delay the sampled data feedback control which is assumed to allow norm bounded uncertainty and involves a constant signal transmission delay is constructed for the first time in this paper by constructing a suitable augmented lyapunov function and with the help of introduced integral inequalities and employing the convex combination technique a sufficient condition is developed such that the nonfragile exponential stability of the error system is guaranteed as a result for the case of sampled data control free of norm bound uncertainties some sufficient conditions of sampled data synchronization criteria for the cdns with time varying coupling delay are presented as the formulations are in the framework of linear matrix inequality these conditions can be easily solved and implemented two illustrative examples are presented to demonstrate the effectiveness and merits of the proposed feedback control

predictor based sampled data exponential stabilization through continuous discrete observers the problem of stabilizing a linear continuous time system with discrete time measurements and a sampled input with a pointwise constant delay is considered in a first part we design a continuous discrete observer which converges when the maximum time interval between two consecutive measurements is sufficiently small in a second part we construct a dynamic output feedback by using a technique which is strongly reminiscent of the reduction model approach it stabilizes the system when the maximal time between two consecutive sampling instants is sufficiently small no limitation on the size of the delay is imposed and an iss property with respect to additive disturbances is established

static output feedback stabilization necessary conditions for multiple delay controllers this note focuses on the static output feedback stabilization problem for a class of single input single output systems when the control law includes multiple distinct delays we are interested in giving necessary conditions for the existence of such stabilizing controllers illustrative examples second order system chain of integrators or chain of oscillators are presented and discussed

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

multiple integral inequalities and stability analysis of time delay systems abstract this paper is devoted to stability analysis of continuous time delay systems based on a set of lyapunov krasovskii functionals new multiple integral inequalities are derived that involve the famous jensen s and wirtinger s inequalities as well as the recently presented bessel legendre inequalities of seuret and gouaisbaut 2015 and the wirtinger based multiple integral inequalities of park et al 2015 and lee et al 2015 the present paper aims at showing that the proposed set of sufficient stability conditions can be arranged into a bidirectional hierarchy of lmis establishing a rigorous theoretical basis for comparison of conservatism of the investigated methods numerical examples illustrate the efficiency of the method

sampled data robust h control for t s fuzzy systems with time delay and uncertainties abstract this paper investigates sampled data robust h control for t s fuzzy systems with time delay and uncertainties by introducing the free weighting matrices to deal with the integral items and converting the coupling time varying matrix inequalities into a group of decoupling matrix inequalities an innovative delay dependent stabilization criterion is first presented then a sampled data h controller is designed to stabilize the t s fuzzy system to achieve the prescribed disturbance attenuation level which is dependent on both the size of state delay and upper bound of allowable sampling period since 1 the sawtooth structure of delay is fully considered 2 neither model transformation nor bounding techniques are employed in deriving the delay dependent results and 3 none of the integral items are arbitrarily ignored and magnified the less conservative results can be expected a practical application example is given to demonstrate the effectiveness of the proposed methods

technical communique delay range dependent stability for systems with time varying delay this paper is concerned with the stability analysis for systems with time varying delay in a range an appropriate type of lyapunov functionals is proposed to investigate the delay range dependent stability problem the present results may improve the existing ones due to a method to estimate the upper bound of the derivative of lyapunov functional without ignoring some useful terms and the introduction of additional terms into the proposed lyapunov functional which take into account the range of delay numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

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

on discrete wirtinger northcott problems abstract some discrete wirtinger northcott inequalities are established in this paper let dx and x be the periodic difference and non periodic difference of a vector x r n respectively for 1 p we give the maximum and the minimum of d x x d x and x in the l p ball b p 0 n in particular we prove that for p the result min b 0 n d x 4 n n is even 4 n n 2 1 n is odd is equivalent to the well known discrete first northcott inequality established by fan taussky and todd

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

a note on wirtinger type integral inequalities for time delay systems different integral inequalities play important role when problems of stability analysis and controller synthesis for time delay systems are considered the connection of jensen s inequality and extended jensen s inequality is well understood now to reduce the conservativeness introduced by the application of jensen s inequality several versions of the wirtinger integral inequality have been published recently this note presents a comparison between some of these inequalities

sampled data synchronization of chaotic lur e systems via input delay dependent free matrix zero equality approach abstract this paper focuses on the sampled data synchronization problem of chaotic lur e systems clss by using sampled output of the systems with variable sampling rates one novel approach input delay dependent free matrix zero equality iddfmze approach is proposed for the first time the iddfmze approach can not only fully capture the available information on the actual sampling pattern but deploy more system information at the dynamic partitioning point a new lyapunov krasovskii functional lkf with some new terms is constructed which can use more information of the activation function at the dynamic partitioning point based on the presented iddfmze approach and the constructed lkf developed synchronization criterion is obtained in the form of linear matrix inequalities lmis the desired sampled data controller is designed under larger sampling period finally the superiority of proposed results is shown by two numerical examples

synchronization of chaotic lur e systems with time delays using sampled data control the asymptotical synchronization problem is investigated for two identical chaotic lur e systems with time delays the sampled data control method is employed for the system design a new synchronization condition is proposed in the form of linear matrix inequalities the error system is shown to be asymptotically stable with the constructed new piecewise differentiable lyapunov krasovskii functional lkf different from the existing work the new lkf makes full use of the information in the nonlinear part of the system the obtained stability condition is less conservative than some of the existing ones a longer sampling period is achieved with the new method the numerical examples are given and the simulations are performed on chua s circuit the results show the superiorities and effectiveness of the proposed control method

observer design for a class of parabolic systems with large delays and sampled measurements in this paper we design a novel observer for a class of semilinear heat one dimmensional 1 d equations under the delayed and sampled point measurements the main novelty is that the delay is arbitrary to handle any arbitrary delay the observer is constituted of a chain of subobservers each subobserver handles a fraction of the considered delay the resulting estimation error system is shown to be exponentially stable under a sufficient number of subobservers is used the stability analysis is based on a specific lyapunov krasovskii functional and the stability conditions are expressed in terms of linear matrix inequalities lmis

dwell time based stabilisation of switched linear delay systems using clock dependent lyapunov krasovskii functionals dwell time stability conditions of the switched delay systems are derived using multiple clock dependent lyapunov krasovskii functionals the corresponding conditions are approximated by both using

a geometric growth model interpolating between regular and small world networks we propose a geometric growth model which interpolates between one dimensional linear graphs and small world networks the model undergoes a transition from large to small worlds we study the topological characteristics by both theoretical predictions and numerical simulations which are in good accordance with each other our geometrically growing model is a complementarity for the static ws model

new insights on stability of sampled data systems with time delay abstract this paper analyses the stability of sampled data systems with time delay by employing a two sided looped functional approach some improved conditions are derived to guarantee the stability of the system under consideration then based the conditions some intrinsic relationships between sampled data period and time delay are obtained from the illustrative example being solved by the proposed approach it is observed that the results obtained are significantly better than those obtained by existing methods more importantly from the simulation being carried out it is discovered that contrary to the findings in previous studies time delays in a system may enlarge the interval of sampled data periods and accelerate the rate of convergence of the system states rather than deteriorate the system performance

smallest eigenvalue of large hankel matrices at critical point comparing conjecture with parallelised computation abstract we propose a novel parallel numerical algorithm for calculating the smallest eigenvalues of highly ill conditioned hankel matrices it is based on the ldlt decomposition and involves finding a k k sub matrix of the inverse of the original n n hankel matrix h n 1 the computation involves extremely high precision arithmetic message passing interface and shared memory parallelisation we demonstrate that this approach achieves good scalability on a high performance computing cluster hpcc which constitutes a major improvement of the earlier approaches we use this method to study a family of hankel matrices generated by the weight w x e x supported on 0 and 0 such weight generates a hankel determinant a fundamental object in random matrix theory in the situation where 1 2 the smallest eigenvalue tends to 0 exponentially fast if 1 2 it is conjectured that the smallest eigenvalue tends to 0 algebraically with a precise exponent the algorithm run on the hpcc producing a fantastic match between the theoretical value of 2 and the numerical result

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

new criteria for global robust stability of delayed neural networks with norm bounded uncertainties in this paper we study the global asymptotic robust stability of delayed neural networks with norm bounded uncertainties by employing the lyapunov stability theory and homeomorphic mapping theorem we derive some new types of sufficient conditions ensuring the existence uniqueness and global asymptotic stability of the equilibrium point for the class of neural networks with discrete time delays under parameter uncertainties and with respect to continuous and slope bounded activation functions an important aspect of our results is their low computational complexity as the reported results can be verified by checking some properties of symmetric matrices associated with the uncertainty sets of the network parameters the obtained results are shown to be generalizations of some of the previously published corresponding results some comparative numerical examples are also constructed to compare our results with some closely related existing literature results

event triggered sampling control for stability and stabilization of memristive neural networks with communication delays this paper investigates the global asymptotic stability and stabilization of memristive neural networks mnns with communication delays via event triggered sampling control first based on the novel approach in lemma 1 the concerned mnns are converted into traditional neural networks with uncertain parameters next a discrete event triggered sampling control scheme which only needs supervision of the system state at discrete instants is designed for mnns for the first time thanks to this controller the number of control updates could greatly reduce then by getting utmost out of the usable information on the actual sampling pattern a newly augmented lyapunov krasovskii functional lkf is constructed to formulate stability and stabilization criteria it should be mentioned that the lkf is positive definite only at endpoints of each subinterval of the holding intervals but not necessarily positive definite inside the holding intervals finally the feasibility and effectiveness of the proposed results are tested by two numerical examples

the exact solution of the mean geodesic distance for vicsek fractals vicsek fractals are one of the most interesting classes of fractals and the study of their structural properties is important in this paper the exact formula for the mean geodesic distance of vicsek fractals is found the quantity is computed precisely through the recurrence relations derived from the self similar structure of the fractals considered the obtained exact solution exhibits that the mean geodesic distance approximately increases as a power law function of the number of nodes with the exponent equal to the reciprocal of the fractal dimension the closed form solution is confirmed by extensive numerical calculations

how bad are hankel matrices considered are hankel vandermonde and krylov basis matrices it is proved that for any real positive definite hankel matrix of order n its spectral condition number is bounded from below by 3 cdot 2 n 6 also proved is that the spectral condition number of a krylov basis matrix is bounded from below by 3 frac 1 2 cdot 2 frac n 2 3 for v v x 1 ldots x n a vandermonde matrix with arbitrary but pairwise distinct nodes x 1 ldots x n we show that mbox rm cond 2 v geq 2 n 2 n frac 1 2 if either x j leq 1 or x j geq 1 for all j then mbox rm cond 2 v geq 2 n 2

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

stabilization for markovian jump systems with partial information on transition probability based on free connection weighting matrices this paper focuses on stability and stabilization for a class of continuous time markovian jump systems with partial information on transition probability the free connection weighting matrix method is proposed to obtain a less conservative stability criterion of markovian jump systems with partly unknown transition probability or completely unknown transition probability as a result a sufficient condition for the state feedback controller design is derived in terms of linear matrix inequalities finally numerical examples are given to illustrate the effectiveness and the merits of the proposed method

sampled data relay control of diffusion pdes we consider a vector reaction advection diffusion equation on a hypercube the measurements are weighted averages of the state over different subdomains these measurements are asynchronously sampled in time subject to matched disturbances the discrete control signals are applied through shape functions and zero order holds the feature of this work is that we consider generalized relay control the control signals take their values in a finite set this allows for networked control through low capacity communication channels first we derive linear matrix inequalities lmis whose feasibility guarantees the ultimate boundedness with a limit bound proportional to the sampling period then we construct a switching procedure for the controller parameters that ensures semi global practical stability for an arbitrarily large domain of initial conditions the trajectories converge to a set whose size does not depend on the domain size for the disturbance free system this procedure guarantees exponential convergence to the origin the results are demonstrated by two examples 2d catalytic slab and a chemical reactor

stabilization of t s fuzzy system with time delay under sampled data control using a new looped functional this paper investigates the sampled data stabilization problem for a takagi sugeno t s fuzzy system with time delay by taking the information of states within the intervals from t k to t and t to t k 1 into account a new two side delay dependent looped functional is introduced which can not only relax the monotonic constraint of lyapunov krasovskii functional lkf but also make better use of the actual sampling pattern furthermore the sampled data fuzzy controller is designed to contain both the present and delayed state information thereby enhancing the control performance and design flexibility based on the novel augmented lkf and improved bounding technique less conservative stability criteria are derived in the form of linear matrix inequalities the superiority of proposed results is shown by two simulation examples

a novel approach to stability and stabilization of fuzzy sampled data markovian chaotic systems abstract this paper studies the problems of stability and stabilization of a class of markovian chaotic systems via fuzzy sampled data control different from some existing results the markovian jumping with general uncertain transition rates is considered for such systems a novel approach i e input delay dependent vector approach is proposed for the first time based on this approach an input delay dependent lyapunov krasovskii functional lkf with cubic function of input delay is successfully constructed and the convex combination technique is used with ease to derive stability and stabilization criteria compared with some existing stability and stabilization criteria for chaotic systems our results are not only less conservative but also with reduced calculation complexity finally the superiorities of proposed results are illustrated by two numerical examples

analytical solution of average path length for apollonian networks with the help of recursion relations derived from the self similar structure we obtain the solution of average path length overline d t for apollonian networks in contrast to the well known numerical result overline d t ensuremath propto text ln text n t 3 4 j s andrade jr et al phys rev lett 94 018702 2005 our rigorous solution shows that the average path length grows logarithmically as overline d t ensuremath propto text ln text n t in the infinite limit of network size n t the extensive numerical calculations completely agree with our closed form solution

structural and spectral properties of a family of deterministic recursive trees rigorous solutions as one of the most significant models the uniform recursive tree urt has found many applications in a variety of fields in this paper we study rigorously the structural features and spectral properties of the adjacency matrix for a family of deterministic uniform recursive trees durts that are deterministic versions of urt firstly from the perspective of complex networks we investigate analytically the main structural characteristics of durts and obtain the accurate solutions for these properties which include degree distribution average path length distribution of node betweenness and degree correlations then we determine the complete eigenvalues and their corresponding eigenvectors of the adjacency matrix for durts our research may shed light on a better understanding of the features for urt also the analytical methods used here are capable of being extended to many other deterministic networks making the precise computation of their properties especially the full spectrum characteristics possible

exponential synchronization of neural networks with discrete and distributed delays under time varying sampling this paper investigates the problem of master slave synchronization for neural networks with discrete and distributed delays under variable sampling with a known upper bound on the sampling intervals an improved method is proposed which captures the characteristic of sampled data systems some delay dependent criteria are derived to ensure the exponential stability of the error systems and thus the master systems synchronize with the slave systems the desired sampled data controller can be achieved by solving a set of linear matrix inequalitys which depend upon the maximum sampling interval and the decay rate the obtained conditions not only have less conservatism but also have less decision variables than existing results simulation results are given to show the effectiveness and benefits of the proposed methods

an improved time delay implementation of derivative dependent feedback abstract we consider an lti system of relative degree r 2 that can be stabilized using r 1 output derivatives the derivatives are approximated by finite differences leading to a time delayed feedback we present a new method of designing and analyzing such feedback under continuous time and sampled measurements this method admits essentially larger time delay sampling period compared to the existing results and for the first time allows to use consecutively sampled measurements in the sampled data case the main idea is to present the difference between the derivative and its approximation in a convenient integral form the kernel of this integral is hard to express explicitly but we show that it satisfies certain properties these properties are employed to construct the lyapunov krasovskii functional that leads to lmi based stability conditions if the derivative dependent control exponentially stabilizes the system then its time delayed approximation stabilizes the system with the same decay rate provided the time delay for continuous time measurements or the sampling period for sampled measurements are small enough

stability analysis of linear systems with interval time varying delays utilizing multiple integral inequalities this paper is devoted to stability analysis of continuous time delay systems with interval time varying delays having known bounds on the delay derivatives a parameterized family of lyapunov krasovskii functionals involving multiple integral terms is introduced and novel multiple integral inequalities are utilized to derive sufficient stability condition for systems with time varying delays the efficiency of the proposed method is illustrated by numerical examples

mode dependent stochastic synchronization for markovian coupled neural networks with time varying mode delays this paper investigates the stochastic synchronization problem for markovian hybrid coupled neural networks with interval time varying mode delays and random coupling strengths the coupling strengths are mutually independent random variables and the coupling configuration matrices are nonsymmetric a mode dependent augmented lyapunov krasovskii functional lkf is proposed where some terms involving triple or quadruple integrals are considered which makes the lkf matrices mode dependent as much as possible this gives significant improvement in the synchronization criteria i e less conservative results can be obtained in addition by applying an extended jensen s integral inequality and the properties of random variables new delay dependent synchronization criteria are derived the obtained criteria depend not only on upper and lower bounds of mode delays but also on mathematical expectations and variances of the random coupling strengths finally two numerical examples are provided to demonstrate the feasibility of the proposed results

finite time synchronization of sampled data markovian jump complex dynamical networks with additive time varying delays based on dissipative theory abstract this paper is concerned with the problem of finite time synchronization issue of sampled data markovian jump complex dynamical networks mjcdns with additive time varying delays based on dissipative theory sufficient conditions to guarantee the finite time stability of mjcdns with additive time varying delays are presented sampled data control with stochastically varying sampling periods is considered the closed loop system is not just finite time bounded but also satisfies the dissipativity conditions further we handled a nonuniform sampled data controller by utilizing the properties of kronecker product combined with the appropriate lyapunov functionals technique a novel delay dependent finite time stability of dissipativity rule is derived in terms of linear matrix inequalities lmis to ensure that the delayed complex dynamical systems to be dissipative finally numerical examples are given to represent the applicability of the proposed approach

an iqc approach to robust stability of aperiodic sampled data systems conditions for robust stability of sampled data systems with non uniform sampling patterns and structural uncertainties are derived the problem is tackled under the integral quadratic constraint iqc framework where the aperiodic sampling operation is modelled by an delay integration operator characterization based on integral quadratic constrains iqc is identified for this operator and the iqc theory is applied to derive convex stability criteria compared to the dominating lyapunov approach where the candidate lyapunov krasovskii functionals or looped functionals need to be tailored for the systems under consideration and therefore the stability conditions need to be re derived whenever additional uncertainties are considered the proposed approach has the advantage of avoiding such endeavor numerical examples are given to illustrate this main point and effectiveness of the proposed approach

condition numbers of hankel matrices for exponential weights abstract we obtain the rate of growth of the largest eigenvalues and euclidean condition numbers of the hankel matrices i t j k w 2 t d t j k 0 n for a general class of even exponential weights w 2 exp 2 q on an interval i as particular examples we discuss q x x on i r and q x d 2 x 2 on i d d

the condition number of real vandermonde krylov and positive definite hankel matrices we show that the euclidean condition number of any positive definite hankel matrix of order n geq 3 may be bounded from below by gamma n 1 16n with gamma exp 4 cdot it catalan pi approx 3 210 and that this bound may be improved at most by a factor 8 gamma n similar estimates are given for the class of real vandermonde matrices the class of row scaled real vandermonde matrices and the class of krylov matrices with hermitian argument improved bounds are derived for the case where the abscissae or eigenvalues are included in a given real interval our findings confirm that all such matrices including for instance the famous hilbert matrix are ill conditioned already for moderate order as application we describe implications of our results for the numerical condition of various tasks in numerical analysis such as polynomial and rational i nterpolation at real nodes determination of real roots of polynomials computation of coefficients of orthogonal polynomials or the iterative solution of linear systems of equations

small eigenvalues of large hankel matrices in this paper we investigate the smallest eigenvalue denoted as n of a n 1 n 1 hankel or moments matrix associated with the weight w x exp x x 0 0 in the large n limit using a previous result the asymptotics for the polynomials pn z z 0 orthonormal with respect to w which are required in the determination of n are found adopting an argument of szegothe asymptotic behaviour of n for where the related moment problem is determinate is derived this generalizes the result given by szegofor 1 it is shown that for the smallest eigenvalue of the infinite hankel matrix is zero while for 0 it is greater then a positive constant this shows a phase transition in the corresponding hermitian random matrix model as the parameter varies with identified as the critical point the smallest eigenvalue at this point is conjectured

further results on stabilization of chaotic systems based on fuzzy memory sampled data control this note investigates sampled data control for chaotic systems a memory sampled data control scheme that involves a constant signal transmission delay is employed for the first time to tackle the stabilization problem for takagi sugeno fuzzy systems the advantage of the constructed lyapunov functional lies in the fact that it is neither necessarily positive on sampling intervals nor necessarily continuous at sampling instants by introducing a modified lyapunov functional that involves the state of a constant signal transmission delay a delay dependent stability criterion is derived so that the closed loop system is asymptotically stable the desired sampled data controller can be achieved by solving a set of linear matrix inequalities compared with the existing results a larger sampling period is obtained by this new approach a simulation example is presented to illustrate the effectiveness and conservatism reduction of the proposed scheme

trapping in scale free networks with hierarchical organization of modularity a wide variety of real life networks share two remarkable generic topological properties scale free behavior and modular organization and it is natural and important to study how these two features affect the dynamical processes taking place on such networks in this paper we investigate a simple stochastic process trapping problem a random walk with a perfect trap fixed at a given location performed on a family of hierarchical networks that exhibit simultaneously striking scale free and modular structure we focus on a particular case with the immobile trap positioned at the hub node having the largest degree using a method based on generating functions we determine explicitly the mean first passage time mfpt for the trapping problem which is the mean of the node to trap first passage time over the entire network the exact expression for the mfpt is calculated through the recurrence relations derived from the special construction of the hierarchical networks the obtained rigorous formula corroborated by extensive direct numerical calculations exhibits that the mfpt grows algebraically with the network order concretely the mfpt increases as a power law function of the number of nodes with the exponent much less than 1 we demonstrate that the hierarchical networks under consideration have more efficient structure for transport by diffusion in contrast with other analytically soluble media including some previously studied scale free networks we argue that the scale free and modular topologies are responsible for the high efficiency of the trapping process on the hierarchical networks

stability analysis of uncertain sampled data systems with incremental delay using looped functionals the robust stability analysis of asynchronous and uncertain sampled data systems with constant incremental input delay is addressed in the looped functional framework these functionals have been shown to be suitable for the analysis of impulsive systems as they allow one to express discrete time stability conditions in an affine way enabling then the consideration of uncertain and time varying systems the stability conditions are obtained by first reformulating the sampled data system as an impulsive system and by then considering a tailored looped functional along with wirtinger s inequality a recently introduced inequality that has been shown to be less conservative than jensen s inequality several examples are given for illustration

on stability of systems with aperiodic sampling devices this technical note is concerned with stability analysis of aperiodic sampled data systems the stability problem is tackled from a pure discrete time point of view where the at sampling behavior of the system is modelled as the response of a nominal discrete time lti system in feedback interconnection with a structured uncertainty conditions under which the uncertainty is positive real pr are identified based on the pr property a number of integral quadratic constraints iqc are derived and the iqc theory is applied to derive stability conditions numerical examples are given to illustrate the effectiveness of the proposed approach

global h_ infty pinning synchronization of complex networks with sampled data communications this paper investigates the global h infty pinning synchronization problem for a class of complex networks with aperiodic samplings combined with the writinger based integral inequality a new less conservative criterion is presented to guarantee the global pinning synchronization of the complex network furthermore a novel condition is proposed under which the complex network is globally pinning synchronized with a given h infty performance index it is shown that the h infty performance index gamma has a positive correlation with the upper bound of the sampling intervals finally the validity and the advantage of the theoretic results obtained are verified by means of the applications in chua s circuit and pendulum

robust estimation for neural networks with randomly occurring distributed delays and markovian jump coupling this paper studies the issue of robust state estimation for coupled neural networks with parameter uncertainty and randomly occurring distributed delays where the polytopic model is employed to describe the parameter uncertainty a set of bernoulli processes with different stochastic properties are introduced to model the randomly occurrences of the distributed delays novel state estimators based on the local coupling structure are proposed to make full use of the coupling information the augmented estimation error system is obtained based on the kronecker product a new lyapunov function which depends both on the polytopic uncertainty and the coupling information is introduced to reduce the conservatism sufficient conditions which guarantee the stochastic stability and the l 2 l infty performance of the augmented estimation error system are established then the estimator gains are further obtained on the basis of these conditions finally a numerical example is used to prove the effectiveness of the 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

stability and stabilization of linear sampled data systems with multi rate samplers and time driven zero order holds in multi rate sampled data systems a continuous time plant is controlled by a discrete time controller which is located in the feedback loop between sensors with different sampling rates and actuators with different refresh rates the main contribution of this paper is to propose sufficient krasovskii based stability and stabilization criteria for linear sampled data systems with multi rate samplers and time driven zero order holds for stability analysis it is assumed that an exponentially stabilizing controller is already designed in continuous time and is implemented as a discrete time controller for each sensor or actuator the problem of finding an upper bound on the lowest sampling frequency or refresh rate that guarantees exponential stability is cast as an optimization problem in terms of linear matrix inequalities lmis furthermore sufficient conditions for controller synthesis are formulated as lmis it is shown through examples that choosing the right sensors or actuators with adequate sampling frequencies or refresh rates has a considerable impact on stability of the closed loop system

from regular to growing small world networks abstract we propose a growing model which interpolates between one dimensional regular lattice and small world networks the model undergoes an interesting phase transition from large to small worlds we investigate the structural properties by both theoretical predictions and numerical simulations our growing model is a complementarity for the important static watts strogatz network model

optimal vertex cover for the small world hanoi networks the vertex cover problem on the hanoi networks hn3 and hn5 is analyzed with an exact renormalization group and parallel tempering monte carlo simulations the grand canonical partition function of the equivalent hard core repulsive lattice gas problem is recast first as an ising like canonical partition function which allows for a closed set of renormalization group equations the flow of these equations is analyzed for the limit of infinite chemical potential at which the vertex cover problem is attained the relevant fixed point and its neighborhood are analyzed and nontrivial results are obtained both for the coverage as well as for the ground state entropy density which indicates the complex structure of the solution space using special hierarchy dependent operators in the renormalization group and monte carlo simulations structural details of optimal configurations are revealed these studies indicate that the optimal coverages or packings are not related by a simple symmetry using a clustering analysis of the solutions obtained in the monte carlo simulations a complex solution space structure is revealed for each system size nevertheless in the thermodynamic limit the solution landscape is dominated by one huge set of very similar solutions

sampled data control for a class of linear time varying systems this paper is concerned with the sampled data control for a class of linear time varying system a classic halanay inequality is first extended to the time varying sampled data system then based on the comparison principle and the extended halanay inequality new criteria for globally uniformly exponential stability and globally uniformly asymptotic stability of the corresponding closed loop system are derived furthermore an algorithm is presented to solve the gain synthesis problem finally one example is given to show the effectiveness of the obtained results

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