stability analysis of the telegrapher s equations with dynamic boundary condition abstract this paper is concerned with the stability analysis of a distributed parameter circuit with dynamic boundary condition the distributed parameter circuit is written by the telegrapher s equations whose boundary condition is described by an ordinary differential equation first of all it is shown that for any physical parameters of the circuit the system operator generates an exponentially stable c 0 semigroup on a hilbert space however it is not clear whether the decay rate of the semigroup is the most precise one in this paper the spectral analysis is conducted for the system satisfying the distortionless condition and it is shown that the semigroup satisfies the spectrum determined growthcondition

graph theoretical clustering based on limited neighbourhood sets abstract a method for clustering data according to a visual model of clusters is proposed the method uses either of two graphs which are defined according to relative distance and based on the gabriel graph and the relative neighbourhood graph respectively the method is locally sensitive hierarchic and based on the concept of limited neighbourhood sets clusters that are either disjoint or homogeneous and separable by sharp changes in point density may be detected

brief paper distributed h consensus filtering in sensor networks with multiple missing measurements the finite horizon case this paper is concerned with a new distributed h consensus filtering problem over a finite horizon for sensor networks with multiple missing measurements the so called h consensus performance requirement is defined to quantify bounded consensus regarding the filtering errors agreements over a finite horizon a set of random variables are utilized to model the probabilistic information missing phenomena occurring in the channels from the system to the sensors a sufficient condition is first established in terms of a set of difference linear matrix inequalities dlmis under which the expected h consensus performance constraint is guaranteed given the measurements and estimates of the system state and its neighbors the filter parameters are then explicitly parameterized by means of the solutions to a certain set of dlmis that can be computed recursively subsequently two kinds of robust distributed h consensus filters are designed for the system with norm bounded uncertainties and polytopic uncertainties finally two numerical simulation examples are used to demonstrate the effectiveness of the proposed distributed filters design scheme

a complex networks approach for data clustering abstract this work proposes a method for data clustering based on complex networks theory a data set is represented as a network by considering different metrics to establish the connection between each pair of objects the clusters are obtained by taking into account five community detection algorithms the network based clustering approach is applied in two real world databases and two sets of artificially generated data the obtained results suggest that the exponential of the minkowski distance is the most suitable metric to quantify the similarities between pairs of objects in addition the community identification method based on the greedy optimization provides the best cluster solution we compare the network based clustering approach with some traditional clustering algorithms and verify that it provides the lowest classification error rate

statistical mechanics and phase transitions in clustering a new approach to clustering based on statistical physics is presented the problem is formulated as fuzzy clustering and the association probability distribution is obtained by maximizing the entropy at a given average variance the corresponding lagrange multiplier is related to the temperature and motivates a deterministic annealing process where the free energy is minimized at each temperature critical temperatures are derived for phase transitions when existing clusters split it is a hierarchical clustering estimating the most probable cluster parameters at various average variances

fuzzy classifier design using genetic algorithms a new method for design of a fuzzy rule based classifier using genetic algorithms gas is discussed the optimal parameters of the fuzzy classifier including fuzzy membership functions and the size and structure of fuzzy rules are extracted from the training data using gas this is done by introducing new representation schemes for fuzzy membership functions and fuzzy rules an effectiveness measure for fuzzy rules is developed that allows for systematic addition or deletion of rules during the ga optimization process a clustering method is utilized for generating new rules to be added when additions are required the performance of the classifier is tested on two real world databases iris and wine and a simulated gaussian database the results indicate that highly accurate classifiers could be designed with relatively few fuzzy rules the performance is also compared to other fuzzy classifiers tested on the same databases

brief paper fault tolerant control for singular systems with actuator saturation and nonlinear perturbation in this paper the problem of robust fault tolerant control for a class of singular systems subject to both time varying state dependent nonlinear perturbation and actuator saturation is investigated a sufficient condition for the existence of a fixed gain controller is first proposed which guarantees the regularity impulse free and stability of the closed loop system under all possible faults an optimization problem with lmi constraints is formulated to determine the largest contractively invariant ellipsoid an adaptive fault tolerant controller is then developed to compensate for the failure effects on the system by estimating the fault and updating the design parameter matrices online both of these two controllers are in the form of a saturation avoidance feedback with the advantage of relatively small actuator capacities compared with the high gain counterpart an example is included to illustrate the proposed procedures and their effectiveness

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

single experiment observability decomposition of discrete time analytic systems this paper addresses the single experiment observability decomposition of discrete time analytic systems unlike the continuous time case there exist systems which cannot be decomposed into observable and unobservable subsystems due to the fact that the observable space is not integrable in this paper a necessary and sufficient condition for integrability of observable space is given as a corollary of this condition it is proven that if the system is reversible the observability decomposition can be always achieved moreover integrability of observable space is also addressed for delta domain models of non uniformly sampled systems

brief transfer equivalence and realization of nonlinear higher order input output difference equations two fundamental modelling problems in nonlinear discrete time control systems are studied using the language of differential forms the discrete time nonlinear single input single output systems to be studied are described by input output i o difference equations i e a high order difference equation relating the input the output and a finite number of their time shifts a new definition of equivalence is introduced which generalizes the notion of transfer equivalence well known for the linear case our definition is based upon the notion of an irreducible differential form of the system and was inspired by the analogous definition for continuous time systems the second problem to be addressed is the realization problem the i o difference equation is assumed to be in the irreducible form so that one can obtain an accessible and observable realization necessary and sufficient conditions are given for the existence of a local state space realization of the irreducible i o difference equation these conditions are formulated in terms of the integrability of certain subspaces of one forms classified according to their relative degree the sufficiency part of the proof gives a constructive procedure up to finding the integrating factors and integration of the set of one forms for obtaining a locally observable and accessible state space system if the system is not in the irreducible form one has first to apply the reduction procedure to transform the system into the irreducible form

statistical mechanics of community detection starting from a general ansatz we show how community detection can be interpreted as finding the ground state of an infinite range spin glass our approach applies to weighted and directed networks alike it contains the ad hoc introduced quality function from j reichardt and s bornholdt phys rev lett 93 218701 2004 and the modularity q as defined by newman and girvan phys rev e 69 026113 2004 as special cases the community structure of the network is interpreted as the spin configuration that minimizes the energy of the spin glass with the spin states being the community indices we elucidate the properties of the ground state configuration to give a concise definition of communities as cohesive subgroups in networks that is adaptive to the specific class of network under study further we show how hierarchies and overlap in the community structure can be detected computationally efficient local update rules for optimization procedures to find the ground state are given we show how the ansatz may be used to discover the community around a given node without detecting all communities in the full network and we give benchmarks for the performance of this extension finally we give expectation values for the modularity of random graphs which can be used in the assessment of statistical significance of community structure

non fragile finite time l 2 l state estimation for discrete time markov jump neural networks with unreliable communication links this paper is concerned with the problem of finite time l 2 l non fragile state estimation for discrete time markov jump neural networks with unreliable communication links the simultaneous occurrences of packet dropouts time delays and the sensor nonlinearity stemmed from the unreliable communication links are considered the focus is on the design of non fragile state estimator such that the augmented estimation error system is mean square stochastically finite time stable with a prescribed level of l 2 l performance by employing lyapunov krasovskii approach and finite time analysis theory some sufficient conditions have been obtained for the existence of an admissible state estimator finally a numerical example is employed to demonstrate the effectiveness of our proposed approach

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

exponential synchronization of lure complex dynamical networks with uncertain inner coupling and pinning impulsive control this paper is concerned with the exponential synchronization of lure type complex dynamical networks with uncertain coupling strength a novel pinning impulsive controller is designed to achieve synchronization in which only selection of nodes are chosen to control instead of the whole network in addition the proposed control scheme is digital and it can lead to low installation cost and less time in order to realize synchronization of lure type complex dynamical networks crucial delay dependent stability conditions are derived by utilizing lyapunov functional together with information of the time varying delay and convex combination technique the resulting stability conditions are formulated in the form of linear matrix inequalities lmis and by solving the obtained lmis desired impulsive control gain matrices are calculated which are capable to guarantee the exponential stability of error system finally the effectiveness of the proposed method is demonstrated through numerical simulations

distributed parameter estimation in unreliable wsns motivated by the application of wireless sensor networks we study a class of distributed learning algorithms for estimating an unknown deterministic parameter in such networks each sensor activates in an unreliable network environment which admits new nodes joining and old nodes leaving the network and can tolerate link failures and noisy interference additionally sensors operate under limited computational bandwidth and energy resources in order to overcome these constraints we propose a novel algorithm to reliably estimate the unknown parameter associated with a linear measurement function based on its noisy samples occasionally made at local sensors each local sensor processes its observation updates its estimate through local information exchange and sends its quantized estimate to its one hop neighbors based on the theory of matrix decomposition and stochastic approximation we show that the studied algorithm converges almost surely to the unknown parameter with probability one and the sensor estimate is in expectation equal to the unknown parameter specifically we further provide the upper bounds on the mean square error and convergence time finally we present a numerical example to assess and compare the communication cost with several similar scheme algorithms to achieve a given performance

relaxing realizability conditions for discrete time nonlinear systems this paper addresses two related topics first a nonrealizable set of input output equations can be made realizable in the classical state space form by adding a postcompensator whereas this is impossible in the continuous time case construction of such postcompensator of minimal order is presented second a general subclass of discrete time systems is suggested for which the observable subspace is non integrable the construction is based on the nonrealizable system which is realized by adding a postcompensator and then combined with the output of the original system

finite horizon h_ infty filtering with missing measurements and quantization effects in this paper a new h filtering approach is developed for a class of discrete time varying systems subject to missing measurements and quantization effects the missing measurements are modeled via a diagonal matrix consisting of a series of mutually independent random variables satisfying certain probabilistic distributions on the interval 0 1 the measured output is quantized by a logarithmic quantizer attention is focused on the design of a stochastic h filter such that the h estimation performance is guaranteed over a given finite horizon in the simultaneous presence of probabilistic missing measurements quantization effects as well as external non gaussian disturbances a necessary and sufficient condition is first established for the existence of the desired time varying filters in virtue of the solvability of certain coupled recursive riccati difference equations rdes owing to its recursive nature the proposed rde approach is shown to be suitable for online application without the need of increasing the problem size the simulation experiment is carried out for the mobile robot localization problem with non gaussian disturbances missing measurements and quantization effects the effectiveness of the proposed method is demonstrated in the numerical example

static output feedback control of nonhomogeneous markovian jump systems with asynchronous time delays this paper investigates the problem of static output feedback control for a class of nonhomogeneous markovian jump system nmjs with asynchronous time delays atds since the atds subject to uncertain transition probabilities tps are taking into account in a practical phenomenon new approaches are introduced to deal with the atds characterized by nonhomogeneous markov processes it is assumed that the communication links are not perfect due to its detrimental effect on the performance of systems stochastic variables are presented to characterize the data transmission which are depending on operation modes and satisfying the bernoulli distribution sets of slack variables are adopted to decouple the product terms between system matrices and lyapunov matrices based on an extended lyapunov function combined with finsler inequality approach the robust static output feedback controller is designed for the closed loop nmjs finally a numerical example is provided to verify the design method

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

community detection in complex networks using extremal optimization we propose a method to find the community structure in complex networks based on an extremal optimization of the value of modularity the method outperforms the optimal modularity found by the existing algorithms in the literature giving a better understanding of the community structure we present the results of the algorithm for computer simulated and real networks and compare them with other approaches the efficiency and accuracy of the method make it feasible to be used for the accurate identification of community structure in large complex networks

linearization of discrete time systems the algebraic formalism developed in this paper unifies the study of the accessibility problem and various notions of feedback linearizability for discrete time nonlinear systems the accessibility problem for nonlinear discrete time systems is shown to be easy to tackle by means of standard linear algebraic tools whereas this is not the case for nonlinear continuous time systems in which case the most suitable approach is provided by differential geometry the feedback linearization problem for discrete time systems is recasted through the language of differential forms in the event that a system is not feedback linearizable the largest feedback linearizable subsystem is characterized within the same formalism using the notion of derived flag of a pfaffian system a discrete time system may be linearizable by dynamic state feedback though it is not linearizable by static state feedback necessary and sufficient conditions are given for the existence of a so called linearizing output which in turn is a sufficient condition for dynamic state feedback linearizability

finding local community structure in networks although the inference of global community structure in networks has recently become a topic of great interest in the physics community all such algorithms require that the graph be completely known here we define both a measure of local community structure and an algorithm that infers the hierarchy of communities that enclose a given vertex by exploring the graph one vertex at a time this algorithm runs in time o k2d for general graphs when d is the mean degree and k is the number of vertices to be explored for graphs where exploring a new vertex is time consuming the running time is linear o k we show that on computer generated graphs the average behavior of this technique approximates that of algorithms that require global knowledge as an application we use this algorithm to extract meaningful local clustering information in the large recommender network of an online retailer

brief paper on the v stability of complex dynamical networks this paper introduces the concept of lyapunov v stability for complex dynamical networks under the new framework each dynamical node is associated with a passivity degree which indicates to what extent an effort is required for stabilizing the node from this approach the network stability problem is converted to measuring the negative definiteness of one simple matrix that characterizes the topology of the network pinning control is then suggested and investigated based on the new v stability formulation as an illustrative example a network with different node dynamics and non uniform coupling strengths is simulated to verify the analytic results moreover a comparison study for three different kinds of networks is provided to further illustrate the novelty and efficacy of the proposed v stability criterion and stabilization scheme

positive realizations of nonlinear input output discrete time systems abstract the problem of realization of a positive nonlinear input output discrete time system as a positive state space system is investigated the input output system is given by a difference equation of a higher order a necessary and sufficient condition for existence of positive and regularly positively observable realization is provided the state space variables of the realization are found as independent generators of some positive universe associated to the input output system only the single input single output case is studied and all functions describing the systems and their properties are assumed to be continuous

state estimation for stochastic complex networks with switching topology this technical note studies the state estimation problem for stochastic complex networks with switching topology a set of bernoulli random variables are used to describe the switching behavior of the network by using the structure of the extended kalman filter ekf a recursive estimator is developed for each node to guarantee an optimized upper bound on the state estimation error covariance despite the switching coupling and linearization errors compared with the existing results on state estimation for stochastic complex networks a distinct feature for the proposed estimator is that the estimation errors for all nodes are not formulated in an augmented vector so that the gain matrix can be determined separately for each node by solving two riccati like difference equations based on the stochastic analysis theory it is shown that the estimation error is bounded in mean square under certain conditions simulation results are provided to verify the effectiveness of the proposed estimator

exponential synchronization of hybrid coupled networks with delayed coupling this paper investigates exponential synchronization of coupled networks with hybrid coupling which is composed of constant coupling and discrete delay coupling there is only one transmittal delay in the delayed coupling the fact is that in the signal transmission process the time delay affects only the variable that is being transmitted from one system to another then it makes sense to assume that there is only one single delay contributing to the dynamics some sufficient conditions for synchronization are derived based on lyapunov functional and linear matrix inequality lmi in particular the coupling matrix may be asymmetric or nondiagonal moreover the transmittal delay can be different from the one in the isolated system a distinctive feature of this work is that the synchronized state will vary in comparison with the conventional synchronized solution especially the degree of the nodes and the inner delayed coupling matrix heavily influence the synchronized state finally a chaotic neural network is used as the node in two regular networks to show the effectiveness of the proposed criteria

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

kinetics of node splitting in evolving complex networks abstract we introduce a collection of complex networks generated by a combination of preferential attachment and a previously unexamined process of splitting nodes of degree k into k nodes of degree 1 four networks are considered each evolves at each time step by either preferential attachment with probability p or splitting with probability 1 p two methods of attachment are considered first attachment of an edge between a newly created node and an existing node in the network and secondly by attachment of an edge between two existing nodes splitting is also considered in two separate ways first by selecting each node with equal probability and secondly selecting the node with probability proportional to its degree exact solutions for the degree distributions are found and scale free structure is exhibited in those networks where the candidates for splitting are chosen with uniform probability those that are chosen preferentially are distributed with a power law with exponential cut off

reduced order filtering for networks with markovian jumping parameters and missing measurements abstractthe problem of reduced order h filters design for markovian jumping complex networks with polytopic time varying transition probability matrices is first addressed in this paper where th

robust synchronization for 2 d discrete time coupled dynamical networks in this paper a new synchronization problem is addressed for an array of 2 d coupled dynamical networks the class of systems under investigation is described by the 2 d nonlinear state space model which is oriented from the well known fornasini marchesini second model for such a new 2 d complex network model both the network dynamics and the couplings evolve in two independent directions a new synchronization concept is put forward to account for the phenomenon that the propagations of all 2 d dynamical networks are synchronized in two directions with influence from the coupling strength the purpose of the problem addressed is to first derive sufficient conditions ensuring the global synchronization and then extend the obtained results to more general cases where the system matrices contain either the norm bounded or the polytopic parameter uncertainties an energy like quadratic function is developed together with the intensive use of the kronecker product to establish the easy to verify conditions under which the addressed 2 d complex network model achieves global synchronization finally a numerical example is given to illustrate the theoretical results and the effectiveness of the proposed synchronization scheme

on integrability of observable space for discrete time polynomial control systems the goal of the technical note is to extend the results on the observability decomposition of continuous time nonlinear systems into the discrete time polynomial systems in general the observable space related to the concept of single experiment observability of the discrete time nonlinear systems cannot always be locally spanned by exact one forms whose integrals would define the observable state coordinates in this technical note we show that for the special subclass of reversible polynomial systems the observable space is integrable like in the continuous time case

brief paper set membership filtering for systems with sensor saturation this paper addresses the set membership filtering problem for a class of discrete time varying systems with sensor saturation in the presence of unknown but bounded process and measurement noises a sufficient condition for the existence of set membership filter is derived a convex optimisation method is proposed to determine a state estimation ellipsoid that is a set of states compatible with sensor saturation and unknown but bounded process and measurement noises a recursive algorithm is developed for computing the ellipsoid that guarantees to contain the true state by solving a time varying linear matrix inequality simulation results are provided to demonstrate the effectiveness of the proposed method

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

event based h_ infty filter design for a class of nonlinear time varying systems with fading channels and multiplicative noises in this paper a general event triggered framework is developed to deal with the finite horizon h infty filtering problem for discrete time varying systems with fading channels randomly occurring nonlinearities and multiplicative noises an event indicator variable is constructed and the corresponding event triggered scheme is proposed such a scheme is based on the relative error with respect to the measurement signal in order to determine whether the measurement output should be transmitted to the filter or not the fading channels are described by modified stochastic rice fading models some uncorrelated random variables are introduced respectively to govern the phenomena of state multiplicative noises randomly occurring nonlinearities as well as fading measurements the purpose of the addressed problem is to design a set of time varying filter such that the influence from the exogenous disturbances onto the filtering errors is attenuated at the given level quantified by a h infty norm in the mean square sense by utilizing stochastic analysis techniques sufficient conditions are established to ensure that the dynamic system under consideration satisfies the h infty filtering performance constraint and then a recursive linear matrix inequality rlmi approach is employed to design the desired filter gains simulation results demonstrate the effectiveness of the developed filter design scheme

extended dissipative state estimation for markov jump neural networks with unreliable links this paper is concerned with the problem of extended dissipativity based state estimation for discrete time markov jump neural networks nns where the variation of the piecewise time varying transition probabilities of markov chain is subject to a set of switching signals satisfying an average dwell time property the communication links between the nns and the estimator are assumed to be imperfect where the phenomena of signal quantization and data packet dropouts occur simultaneously the aim of this paper is to contribute with a markov switching estimator design method which ensures that the resulting error system is extended stochastically dissipative in the simultaneous presences of packet dropouts and signal quantization stemmed from unreliable communication links sufficient conditions for the solvability of such a problem are established based on the derived conditions an explicit expression of the desired markov switching estimator is presented finally two illustrated examples are given to show the effectiveness of the proposed design method

boundary feedback stabilization of the telegraph equation decay rates for vanishing damping term abstract we study a semilinear mildly damped wave equation that contains the telegraph equation as a special case we consider neumann velocity boundary feedback and prove the exponential stability of the closed loop system we show that for vanishing damping term in the partial differential equation the decay rate of the system approaches the rate for the system governed by the wave equation without damping term in particular this implies that arbitrarily large decay rates can occur if the velocity damping in the partial differential equation is sufficiently small

event triggered state estimation for discrete time multidelayed neural networks with stochastic parameters and incomplete measurements in this paper the event triggered state estimation problem is investigated for a class of discrete time multidelayed neural networks with stochastic parameters and incomplete measurements in order to cater for more realistic transmission process of the neural signals we make the first attempt to introduce a set of stochastic variables to characterize the random fluctuations of system parameters in the addressed neural network model the delays among the interconnections are allowed to be different which are more general than those in the existing literature the incomplete information under consideration includes randomly occurring sensor saturations and quantizations for the purpose of energy saving an event triggered state estimator is constructed and a sufficient condition is given under which the estimation error dynamics is exponentially ultimately bounded in the mean square it is worth noting that the ultimate boundedness of the error dynamics is explicitly estimated the characterization of the desired estimator gain is designed in terms of the solution to a certain matrix inequality finally a numerical simulation example is presented to illustrate the effectiveness of the proposed event triggered state estimation scheme

extended observer form simple existence conditions the paper focuses on the problem of transforming the discrete time single input single output nonlinear state equations into the extended observer form which besides the input and output also depends on a finite number of their past values the simple necessary and sufficient conditions for the existence of the extended coordinate change and the output transformation allowing to solve the problem are formulated in terms of certain partial derivatives related to the input output equation corresponding to the state equations moreover a certain algorithm for transforming the state equations into the observer form is proposed

finding community structure in very large networks the discovery and analysis of community structure in networks is a topic of considerable recent interest within the physics community but most methods proposed so far are unsuitable for very large networks because of their computational cost here we present a hierarchical agglomeration algorithm for detecting community structure which is faster than many competing algorithms its running time on a network with n vertices and m edges is o md phantom rule 0 2em 0ex mathrm log phantom rule 0 2em 0ex n where d is the depth of the dendrogram describing the community structure many real world networks are sparse and hierarchical with m ensuremath sim n and d ensuremath sim mathrm log phantom rule 0 2em 0ex n in which case our algorithm runs in essentially linear time o n phantom rule 0 2em 0ex mathrm log 2 phantom rule 0 2em 0ex n as an example of the application of this algorithm we use it to analyze a network of items for sale on the web site of a large on line retailer items in the network being linked if they are frequently purchased by the same buyer the network has more than 400 000 vertices and 2 ifmmode times else texttimes fi 10 6 edges we show that our algorithm can extract meaningful communities from this network revealing large scale patterns present in the purchasing habits of customers

event based h_ infty state estimation for time varying stochastic dynamical networks with state and disturbance dependent noises in this paper the event based finite horizon h infty state estimation problem is investigated for a class of discrete time varying stochastic dynamical networks with state and disturbance dependent noises also called x v dependent noises an event triggered scheme is proposed to decrease the frequency of the data transmission between the sensors and the estimator where the signal is transmitted only when certain conditions are satisfied the purpose of the problem addressed is to design a time varying state estimator in order to estimate the network states through available output measurements by employing the completing the square technique and the stochastic analysis approach sufficient conditions are established to ensure that the error dynamics of the state estimation satisfies a prescribed h infty performance constraint over a finite horizon the desired estimator parameters can be designed via solving coupled backward recursive riccati difference equations finally a numerical example is exploited to demonstrate the effectiveness of the developed state estimation scheme

brief paper on the observability of discrete time dynamic systems a geometric approach a coordinate free description for dynamic systems described by explicit nonlinear difference equations in one independent variable via a differential geometric framework is presented based on this covariant approach suitable geometric objects for discrete time dynamics are introduced especially the observability along a trajectory is discussed and transformations to normal forms are derived in addition the obtained local observability criteria can be checked by computer algebra algorithms some examples illustrate the proposed approach

realization of discrete time nonlinear input output equations polynomial approach the aim of this paper is to solve reduction and realization problems for discrete time multi input multi output nonlinear control systems by applying the theory of non commutative polynomials first the necessary and sufficient reducibility condition is presented in terms of the greatest common left divisor of two polynomial matrices associated with the set of the higher order input output i o difference equations of the system the condition also provides a method for system reduction i e for finding the irreducible representation of the set of the i o equations being transfer equivalent to the original system representation second to solve the realization problem a formula is presented for computing the differentials of the state coordinates directly from the polynomial description of the nonlinear system the polynomial approach addressed in this paper is more direct and requires noticeably less computations than earlier methods represented in terms of subspaces of differential one forms

a variance constrained approach to recursive state estimation for time varying complex networks with missing measurements in this paper the recursive state estimation problem is investigated for an array of discrete time varying coupled stochastic complex networks with missing measurements a set of random variables satisfying certain probabilistic distributions is introduced to characterize the phenomenon of the missing measurements where each sensor can have individual missing probability the taylor series expansion is employed to deal with the nonlinearities and the high order terms of the linearization errors are estimated the purpose of the addressed state estimation problem is to design a time varying state estimator such that in the presence of the missing measurements and the random disturbances an upper bound of the estimation error covariance can be guaranteed and the explicit expression of the estimator parameters is given by using the riccati like difference equations approach the estimator parameter is characterized by the solutions to two riccati like difference equations it is shown that the obtained upper bound is minimized by the designed estimator parameters and the proposed state estimation algorithm is of a recursive form suitable for online computation finally an illustrative example is provided to demonstrate the feasibility and effectiveness of the developed state estimation scheme

reversible linear and nonlinear discrete time dynamics it is shown that any causal discrete time system can be realized with a reversible or invertible state variable representation this bridges the gap with continuous time where flows always satisfy this property and settles an old debate on the relevance of invertibility in nonlinear discrete dynamics as the result applies to the linear case it is shown how the classic approach should be slightly modified and several examples of the benefits that can be obtained are given difference algebra is employed for nonlinear systems it leads to a most elegant characterization of causality which enables reversibility to be demonstrated module theory suffices in the linear case which is supplemented by elementary matrix manipulations

h_ infty state estimation for complex networks with uncertain inner coupling and incomplete measurements in this paper the h state estimation problem is investigated for a class of complex networks with uncertain coupling strength and incomplete measurements with the aid of the interval matrix approach we make the first attempt to characterize the uncertainties entering into the inner coupling matrix the incomplete measurements under consideration include sensor saturations quantization and missing measurements all of which are assumed to occur randomly by introducing a stochastic kronecker delta function these incomplete measurements are described in a unified way and a novel measurement model is proposed to account for these phenomena occurring with individual probability with the measurement model a set of h state estimators is designed such that for all admissible incomplete measurements as well as the uncertain coupling strength the estimation error dynamics is exponentially mean square stable and the h performance requirement is satisfied the characterization of the desired estimator gains is derived in terms of the solution to a convex optimization problem that can be easily solved using the semidefinite program method finally a numerical simulation example is provided to demonstrate the effectiveness and applicability of the proposed design approach

synchronization of nonlinear singularly perturbed complex networks with uncertain inner coupling via event triggered control this study is concerned with the synchronization problem of nonlinear singularly perturbed complex networks with time varying coupling delays in an aim to shrink the treatment of network resources event triggered control strategy is proposed to achieve the synchronization criteria by developing the novel lyapunov krasovskii functional some adequate conditions which ensure the asymptotic synchronization are obtained in the form of linear matrix inequalities besides that synchronization problem of nonlinear singularly perturbed complex networks with uncertain inner coupling are also taken into account the uncertain inner coupling is represented by making use of the interval matrix approach finally simulation results are displayed to show the efficacy of the proposed theoretical results

non augmented state estimation for nonlinear stochastic coupling networks abstract this paper considers the state estimation problem for discrete time nonlinear stochastic coupling networks a non augmented filter is designed for each node to guarantee an optimized upper bound on the state estimation error covariance matrix despite nodes coupling as well as the linearization errors compared with the existing augmented filter the cross covariance matrices between coupling nodes are not required to be computed and the gain matrix can be obtained separately for each node by solving two riccati like difference equations

exponential stabilization of the wave equation by dirichlet integral feedback we consider the problem of boundary feedback stabilization of a vibrating string that is fixed at one end and with control action at the other end in contrast to previous studies that have require

linearization of discrete time systems by exogenous dynamic feedback it is shown that a discrete time system may be linearizable by exogenous dynamic feedback even if it cannot be linearized by endogenous feedback this property is completely unexpected and constitutes a fundamental difference with respect to the continuous time case the notion of exogenous linearizing output is introduced it is shown that existence of an exogenous linearizing output is a sufficient condition for dynamic linearizability necessary and sufficient conditions for the existence of an exogenous linearizing output are provided the results of the paper are obtained using transformal operator matrices the properties of such operators are studied the theory is applied to the exact discrete time model of a mobile robot showing that the above mentioned property concerns not only academic examples but also physical systems

asynchronous filtering of nonlinear markov jump systems with randomly occurred quantization via t s fuzzy models this paper focuses on the dissipativity based asynchronous filtering problem for a class of discrete time takagi sugeno fuzzy markov jump systems subject to randomly occurred quantization considering the random fluctuations of network conditions the randomly occurred quantization is introduced to describe the quantization phenomenon appearing in a probabilistic way to take full advantage of the partial information of system modes for the desired system performance we adopt the asynchronous filter in which mode transition matrix is nonhomogeneous the mode dependent time varying delays are introduced which have different bounds for different system modes via fuzzy mode dependent lyapunov functional approach that can reduce conservatism a sufficient condition on the existence of the asynchronous filter is derived such that the filtering error system is stochastically stable and strictly mathcal q mathcal s mathcal r dissipative then the gains of the filter are obtained by solving a set of linear matrix inequalities lmis an example is utilized to illustrate the validity of the developed filter design technique where the relationships among optimal dissipative performance indices delays quantization parameter and the degree of asynchronous jumps are given

criteria for global pinning controllability of complex networks in this paper we study pinning controllability of networks of coupled dynamical systems in particular we study the problem of asymptotically driving a network of coupled identical oscillators onto some desired common reference trajectory by actively controlling only a limited subset of the whole network the reference trajectory is generated by an exogenous independent oscillator and pinned nodes are coupled to it through a linear state feedback we describe the time evolution of the complex dynamical system in terms of the error dynamics thereby we reformulate the pinning controllability problem as a global asymptotic stability problem by using lyapunov stability theory and algebraic graph theory we establish tractable sufficient conditions for global pinning controllability in terms of the network topology the oscillator dynamics and the linear state feedback

probability guaranteed set membership filtering for systems with incomplete measurements in this note the probability guaranteed set membership filtering problem is investigated for a class of time varying systems with incomplete measurements the uniform distribution over known finite ranges is assumed for mutually independent stochastic variables existing in the functions of system matrices the process noise and measurement noise are unknown bounded and confined to a specified ellipsoidal set respectively which is handled by transformation to the inequality constraints the purpose is to design a set membership filter for all the admissible unknown but bounded noises known deterministic input and incomplete measurements such that the ellipsoidal set including all possible states can be determined by a convex optimization approach with probability constraint a recursive linear matrix inequality rlmi approach is proposed to address the probability guaranteed set membership filtering problem finally a simulation example demonstrates the effectiveness of the proposed filtering scheme

h_ infty state estimation for discrete time delayed systems of the neural network type with multiple missing measurements this paper investigates the h infty state estimation problem for a class of discrete time nonlinear systems of the neural network type with random time varying delays and multiple missing measurements these nonlinear systems include recurrent neural networks complex network systems lur e systems and so on which can be described by a unified model consisting of a linear dynamic system and a static nonlinear operator the missing phenomenon commonly existing in measurements is assumed to occur randomly by introducing mutually individual random variables satisfying certain kind of probability distribution throughout this paper first a luenberger like estimator based on the imperfect output data is constructed to obtain the immeasurable system states then by virtue of lyapunov stability theory and stochastic method the h infty performance of the estimation error dynamical system augmented system is analyzed based on the analysis the h infty estimator gains are deduced such that the augmented system is globally mean square stable in this paper both the variation range and distribution probability of the time delay are incorporated into the control laws which allows us to not only have more accurate models of the real physical systems but also obtain less conservative results finally three illustrative examples are provided to validate the proposed control laws

finite time state estimation for coupled markovian neural networks with sensor nonlinearities this paper investigates the issue of finite time state estimation for coupled markovian neural networks subject to sensor nonlinearities where the markov chain with partially unknown transition probabilities is considered a luenberger type state estimator is proposed based on incomplete measurements and the estimation error system is derived by using the kronecker product by using the lyapunov method sufficient conditions are established which guarantee that the estimation error system is stochastically finite time bounded and stochastically finite time stable respectively then the estimator gains are obtained via solving a set of coupled linear matrix inequalities finally a numerical example is given to illustrate the effectiveness of the proposed new design method

comments on on the discrete time normal form this paper shows briefly that the necessary and sufficient algebraic conditions for transforming the discrete time nonlinear system into the special case of the normal form given in the above paper by califano et al see ibid vol 43 1998 can be restated in a more transparent way

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

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

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

on the discrete time normal form necessary and sufficient conditions under which the discrete time normal form exists are set both in geometric and in algebraic frameworks leading to equivalent conditions the results are therefore extended to generic nonlinear nonaffine continuous time systems

mixed h_2 h_ infty state estimation for discrete time switched complex networks with random coupling strengths through redundant channels this article investigates the mixed h 2 h infty state estimation problem for a class of discrete time switched complex networks with random coupling strengths through redundant communication channels a sequence of random variables satisfying certain probability distributions is employed to describe the stochasticity of the coupling strengths a redundant channel based data transmission mechanism is adopted to enhance the reliability of the transmission channel from the sensor to the estimator the purpose of the addressed problem is to design a state estimator for each node such that the error dynamics achieves both the stochastic stability with probability 1 and the prespecified mixed h 2 h infty performance requirement by using the switched system theory an extensive stochastic analysis is carried out to derive the sufficient conditions ensuring the stochastic stability as well as the mixed h 2 h infty performance index the desired state estimator is also parameterized by resorting to the solutions to certain convex optimization problems a numerical example is provided to illustrate the validity of the proposed estimation scheme