synchronization via pinning control on general complex networks this paper studies synchronization via pinning control on general complex dynamical networks such as strongly connected networks networks with a directed spanning tree weakly connected networks and directed forests a criterion for ensuring network synchronization on strongly connected networks is given it is found that the vertices with very small in degrees should be pinned first in addition it is shown that the original condition with controllers can be reformulated such that it does not depend on the form of the chosen controllers which implies that the vertices with very large out degrees may be pinned then a criterion for achieving synchronization on networks with a directed spanning tree which can be composed of many strongly connected components is derived it is found that the strongly connected components with very few connections from other components should be controlled and the components with many connections from other components can achieve synchronization even without controls

shift register synthesis modulo m the berlekamp algorithm takes a sequence of elements from a field and finds the shortest linear recurrence or linear feedback shift register that can generate the sequence we present an algorithm which generalizes berlekamp s to the case when the elements of the sequence are integers modulo m where m is an arbitrary but known integer details will be published elsewhere

mean square h synchronization of coupled stochastic partial differential systems in this paper the criterion and control are considered for the mean square h synchronization of coupled stochastic partial differential systems spdss based on the integral lyapunov like functional and by virtue of completing squares technique a sufficient criterion is provided to guarantee the mean square h synchronization the effect of spatial domain on the mean square h synchronization is also embodied in this criterion when the coupled spdss cannot achieve the mean square h synchronization the adaptive controllers are adopted for the coupled spdss and the effectiveness of the adaptive controllers is verified via a rigorous mathematical analysis when the number of the nodes in the complex networks is large pinning control is a natural choice the adaptive pinning control strategy is also presented and a criterion is obtained which guarantees the mean square h synchronization of coupled spdss numerical experiments are also given to illustrate the correctness of our results

tsallis information dimension of complex networks abstract the fractal and self similarity properties are revealed in many complex networks the information dimension is a useful method to describe the fractal and self similarity properties of the complex networks in order to show the influence of different parts in the complex networks to the information dimension we have proposed a new information dimension based on the tsallis entropy namely the tsallis information dimension the proposed information dimension is changed according to the scale which is described by the nonextensivity parameter q and it is inverse with the nonextensivity parameter q the existing information dimension is a special case of the tsallis information dimension when q 1 the tsallis information dimension is a generalized information dimension of the complex networks

estimating the ultimate bound and positively invariant set for the lorenz system and a unified chaotic system to estimate the ultimate bound and positively invariant set for a dynamic system is an important but quite challenging task in general in this paper we attempt to investigate the ultimate bound and positively invariant set for two specific systems the lorenz system and a unified chaotic system we derive an ellipsoidal estimate of the ultimate bound and positively invariant set for the lorenz system for all the positive values of its parameters a b and c and obtain the minimum value of volume for the ellipsoid comparing with the best results in the current literature d li j lu x wu g chen estimating the bounds for the lorenz family of chaotic systems chaos solitons fractals 23 2005 529 534 x liao on the global basin of attraction and positively invariant set for the lorenz chaotic system and its application in chaos control and synchronization sci china ser e 34 2004 1404 1419 our new results fill up the gap of the estimate for the cases of 0 a 1 and 0 b 2 x liao on the global basin of attraction and positively invariant set for the lorenz chaotic system and its application in chaos control and synchronization sci china ser e 34 2004 1404 1419 furthermore the estimation derived here contains the results given in d li j lu x wu g chen estimating the bounds for the lorenz family of chaotic systems chaos solitons fractals 23 2005 529 534 and x liao on the global basin of attraction and positively invariant set for the lorenz chaotic system and its application in chaos control and synchronization sci china ser e 34 2004 1404 1419 as special cases along the same line we also provide estimates of cylindrical and ellipsoidal bounds for a unified chaotic system for its parameter range 0 129 and obtain the minimum value of volume for the ellipsoid the estimate is more accurate than and also extends the result of d li j lu x wu g chen estimating the bounds for the lorenz family of chaotic systems chaos solitons fractals 23 2005 529 534 and x liao on the global basin of attraction and positively invariant set for the lorenz chaotic system and its application in chaos control and synchronization sci china ser e 34 2004 1404 1419

finite time semistability and consensus for nonlinear dynamical networks this paper focuses on semistability and finite time stability analysis and synthesis of systems having a continuum of equilibria semistability is the property whereby the solutions of a dynamical system converge to lyapunov stable equilibrium points determined by the system initial conditions in this paper we merge the theories of semistability and finite time stability to develop a rigorous framework for finite time semistability in particular finite time semistability for a continuum of equilibria of continuous autonomous systems is established continuity of the settling time function as well as lyapunov and converse lyapunov theorems for semistability are also developed in addition necessary and sufficient conditions for finite time semistability of homogeneous systems are addressed by exploiting the fact that a homogeneous system is finite time semistable if and only if it is semistable and has a negative degree of homogeneity unlike previous work on homogeneous systems our results involve homogeneity with respect to semistable dynamics and require us to adopt a geometric description of homogeneity finally we use these results to develop a general framework for designing semistable protocols in dynamical networks for achieving coordination tasks in finite time

state space realizations and monomial equivalence for convolutional codes we will study convolutional codes with the help of state space realizations it will be shown that two such minimal realizations belong to the same code if and only if they are equivalent under the full state feedback group this result will be used in order to prove that two codes with positive forney indices are monomially equivalent if and only if they share the same adjacency matrix the adjacency matrix is an invariant of the code obtained via a minimal state space realization and counts in a detailed way the weights of all possible outputs it contains full information about the weights of the codewords in the given code

symmetrizing the kullback leibler distance we define a new distance measure the resistor average distance between two probability distributions that is closely related to the kullback leibler distance while the kullbackleibler distance is asymmetric in the two distributions the resistor average distance is not it arises from geometric considerations similar to those used to derive the chernoff distance determining its relation to well known distance measures reveals a new way to depict how commonly used distance measures relate to each other

cluster synchronization in directed networks of partial state coupled linear systems under pinning control this paper investigates the cluster synchronization for network of linear systems via a generalized pinning control strategy which allows the network of each cluster to take relaxed topological structure for the case with fixed topology it is shown that a feasible feedback controller can be designed to achieve the given cluster synchronization pattern if the induced network topology of each cluster has a directed spanning tree and further compared to the couplings among different clusters the couplings within the each cluster are sufficiently strong an extra balanced condition is imposed on the network topology of each cluster to allow for the cluster synchronization under arbitrary switching network topologies such a balanced condition can be removed via the use of dwell time technique for all the cases the lower bounds for such strengths of couplings within each cluster that secure the synchronization as well as cluster synchronization rate are explicitly specified finally some illustrative examples are provided to demonstrate the effectiveness of the theoretical findings

calibrated steganalysis of mp3stego in multi encoder scenario abstract experimenting with different mp3 encoders shows subtle differences in their outputs indicating they have been implemented differently if this characteristic is not addressed properly it could degrade performance of mp3 steganalysis additionally calibration is a powerful technique which has not found its true potential in mp3 steganalysis this paper tries to fill these gaps first we propose a new set of calibrated features based on quantization step to that end we show that quantization steps of mp3 bit stream and steganography induced noise are respectively band limited and wide band signals we use this observation and apply a low pass filter on quantization steps of mp3 bit stream and then use the result for calibrating of features then we present our analysis on different encoders and show that their statistical properties are quite dissimilar for all fields of mp3 bitstream we use this observation and propose an encoder classifier that have near perfect accuracy this accuracy is achieved after testing a wide range of feature selection methods and finally using genetic algorithm due to its superior performance our simulations show that the proposed method achieved accuracy of 95 8 and 95 2 at 3 12 of maximum embedding rate in the single and multi encoder scenarios respectively

lower bounds on the proportion of leaders needed for expected consensus of 3 d flocks this paper considers the consensus behavior of a spatially distributed 3 d dynamical network composed of heterogeneous agents leaders and followers in which the leaders have the preferred information about the destination while the followers do not have all followers move in a 3 d euclidean space with a given speed and with their headings updated according to the average velocity of the corresponding neighbors compared with the 2 d model a key point lies in how to analyze the dynamical behavior of a linear nonhomogeneous equation where the nonhomogeneous term strongly nonlinearly depends on the states of all agents using the network structure and the estimation of some characteristics for the initial states we present a proper decaying rate for the nonhomogeneous term and then establish lower bounds on the ratio of the number of leaders to the number of followers that is needed for the expected consensus by considering two cases 1 fixed speed and neighborhood radius and 2 variable speed and neighborhood radius with respect to the population size some simulation examples are given to justify the theoretical results

sliding mode control based algorithms for consensus in connected swarms in this article finite time consensus algorithms for a swarm of self propelling agents based on sliding mode control and graph algebraic theories are presented algorithms are developed for swarms that can be described by balanced graphs and that are comprised of agents with dynamics of the same order agents with first and higher order dynamics are considered for consensus the agents inputs are chosen to enforce sliding mode on surfaces dependent on the graph laplacian matrix the algorithms allow for the tuning of the time taken by the swarm to reach a consensus as well as the consensus value as an example the case when a swarm of first order agents is in cyclic pursuit is considered

synchronization and transient stability in power networks and nonuniform kuramoto oscillators motivated by recent interest for multiagent systems and smart grid architectures we discuss the synchronization problem for the network reduced model of a power system with nontrivial transfer conductances our key insight is to exploit the relationship between the power network model and a first order model of coupled oscillators assuming overdamped generators possibly due to local excitation controllers a singular perturbation analysis shows the equivalence between the classic swing equations and a nonuniform kuramoto model here nonuniform kuramoto oscillators are characterized by multiple time constants nonhomogeneous coupling and nonuniform phase shifts extending methods from transient stability synchronization theory and consensus protocols we establish sufficient conditions for synchronization of nonuniform kuramoto oscillators these conditions reduce to necessary and sufficient tests for the standard kuramoto model combining our singular perturbation and kuramoto analyses we derive

consensus for networks with unknown but bounded disturbances we consider stationary consensus protocols for networks of dynamic agents the measure of the neighbors states is affected by unknown but bounded disturbances here the main contribution is the formulation and solution of what we call the epsilon consensus problem where the states are required to converge in a target set of radius epsilon asymptotically or in finite time we introduce as a solution a dead zone policy that we denote as the lazy rule

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

pinning synchronization of delayed complex dynamical networks with nonlinear coupling abstract in this paper we find that complex networks with the watts strogatz or scale free ba random topological architecture can be synchronized more easily by pin controlling fewer nodes than regular systems theoretical analysis is included by means of lyapunov functions and linear matrix inequalities lmi to make all nodes reach complete synchronization numerical examples are also provided to illustrate the importance of our theoretical analysis which implies that there exists a gap between the theoretical prediction and numerical results about the minimum number of pinning controlled nodes

analysis and control of output synchronization in directed and undirected complex dynamical networks this research focuses on the problem of output synchronization in undirected and directed complex dynamical networks respectively by applying barbalat s lemma first to ensure the output synchronization several sufficient criteria are established for these network models based on some mathematical techniques such as the lyapunov functional method and matrix theory furthermore some adaptive schemes to adjust the coupling weights among network nodes are developed to achieve the output synchronization by applying the designed adaptive laws several criteria for output synchronization are deduced for the network models in addition a design procedure of the adaptive law is shown finally two simulation examples are used to show the effectiveness of the previous results

paradigms and puzzles in the theory of dynamical systems a self contained exposition is given of an approach to mathematical models in particular to the theory of dynamical systems the basic ingredients form a triptych with the behavior of a system in the center and behavioral equations with latent variables as side panels the author discusses a variety of representation and parametrization problems in particular questions related to input output and state models the proposed concept of a dynamical system leads to a new view of the notions of controllability and observability and of the interconnection of systems in particular to what constitutes a feedback control law the final issue addressed is that of system identification it is argued that exact system identification leads to the question of computing the most powerful unfalsified model

the predictable degree property and row reducedness for systems over a finite ring motivated by applications in communications we consider linear discrete time systems over the finite ring z p r we solve the open problem of deriving a theory of row reduced representations for these systems we introduce a less restrictive form of representation than the adapted form introduced by fagnani and zampieri we call this form the composed form we define the concept of p predictable degree property and p row reduced we demonstrate that these concepts coupled with the composed form provide a natural setting that extends several classical results from the field case to the ring case in particular the classical rank test on the leading row coefficient matrix is generalized we show that any annihilator of a behavior mathfrak b of a pre specified degree is uniquely parametrized with finitely many coefficients in terms of a kernel representation in p row reduced composed form the underlying theory is the theory of reduced p basis for submodules of z q p r xi that is developed in this paper we show how to construct a p row reduced kernel representation in composed form by constructing a reduced p basis for the module mathfrak b perp

new list decoding algorithms for reed solomon and bch codes in this paper we devise a rational curve fitting algorithm and apply it to the list decoding of reed solomon and bose chaudhuri hocquenghen bch codes the resulting list decoding algorithms exhibit the following significant properties

synchronization control for discrete time delayed dynamical networks with switching topology under actuator saturations this article is concerned with the synchronization control problem for a class of discrete time dynamical networks with mixed delays and switching topology the saturation phenomenon of physical actuators is specifically considered in designing feedback controllers by exploring the mixed delay dependent sector conditions in combination with the piecewise lyapunov like functional and the average dwell time switching a sufficient condition is first established under which all trajectories of the error dynamics are bounded for admissible initial conditions and nonzero external disturbances while the l l performance constraint is satisfied furthermore the exponential stability of the error dynamics is ensured for admissible initial conditions in the absence of disturbances second by using some congruence transformations the explicit condition guaranteeing the existence of desired controller gains is obtained in terms of the feasibility of a set of linear matrix inequalities then three convex optimization problems are formulated regarding the disturbance tolerance the l l performance and the initial condition set respectively finally two simulation examples are given to show the effectiveness and merits of the proposed results

synchronization control for nonlinear stochastic dynamical networks pinning impulsive strategy in this paper a new control strategy is proposed for the synchronization of stochastic dynamical networks with nonlinear coupling pinning state feedback controllers have been proved to be effective for synchronization control of state coupled dynamical networks we will show that pinning impulsive controllers are also effective for synchronization control of the above mentioned dynamical networks some generic mean square stability criteria are derived in terms of algebraic conditions which guarantee that the whole state coupled dynamical network can be forced to some desired trajectory by placing impulsive controllers on a small fraction of nodes an effective method is given to select the nodes which should be controlled at each impulsive constants the proportion of the controlled nodes guaranteeing the stability is explicitly obtained and the synchronization region is also derived and clearly plotted numerical simulations are exploited to demonstrate the effectiveness of the pinning impulsive strategy proposed in this paper

finite time information consensus for multi agent systems with fixed and switching topologies in this paper we study the consensus problems for a group of interacting agents first we analytically establish the explicit expression of the consensus state for the entire group second we prove that the agents of the group under a particular type of nonlinear interaction can reach the consensus state in finite time in the scenarios with fixed and switching undirected topologies the results are also extended to the case where the topology of the group is directed and satisfies a detailed balance condition on coupling weights third some numerical examples are provided to analyze the influencing factors of the convergence time that is the parameter of the particular interaction function and the algebraic connectivity of graphs finally an application of the theoretical results in sensor networks is given namely computing the maximum likelihood estimate of unknown parameters

reed solomon list decoding from a system theoretic perspective in this paper the sudan guruswami approach to list decoding of reed solomon rs codes is cast in a system theoretic framework with the data a set of trajectories or time series is associated which is then modeled as a so called behavior in this way a connection is made with the behavioral approach to system theory it is shown how a polynomial representation of the modeling behavior gives rise to the bivariate interpolating polynomials of the sudan guruswami approach the concept of weighted row reduced is introduced and used to achieve minimality two decoding methods are derived and a parametrization of all bivariate interpolating polynomials is given

projective cluster synchronization of fractional order coupled delay complex network via adaptive pinning control abstract this paper investigates the projective cluster synchronization of fractional order coupled delay complex network via adaptive pinning control the pinning control method is employed in designing controllers for guaranteeing projective cluster synchronization based on the lyapunov stability theory and well known barbalat s lemma some new sufficient conditions are derived to guarantee the projective cluster synchronization of the fractional order complex network a numerical simulation is given to verify the effectiveness of the theoretical results

a parametric approach to list decoding of reed solomon codes using interpolation in this paper we present a minimal list decoding algorithm for reed solomon rs codes minimal list decoding for a code c refers to list decoding with radius l where l is the minimum of the distances between the received word r and any codeword in c we consider the problem of determining the value of l as well as determining all the codewords at distance l our approach involves a parametrization of interpolating polynomials of a minimal grobner basis g we present two efficient ways to compute g we also show that so called re encoding can be used to further reduce the complexity we then demonstrate how our parametric approach can be solved by a computationally feasible rational curve fitting solution from a recent paper by wu besides we present an algorithm to compute the minimum multiplicity as well as the optimal values of the parameters associated with this multiplicity which results in overall savings in both memory and computation

pinning synchronization of discrete dynamical networks with delay coupling abstract the purpose of this paper is to investigate the pinning synchronization analysis for nonlinear coupled delayed discrete dynamical networks with the identical or nonidentical topological structure based on the lyapunov stability theory pinning control method and linear matrix inequalities several adaptive synchronization criteria via two kinds of pinning control method are obtained two examples based on rulkov chaotic system are included to illustrate the effectiveness and verification of theoretical analysis

toward synchronization in networks with nonlinear dynamics a submodular optimization framework synchronization underlies phenomena including memory and perception in the brain coordinated motion of animal flocks and stability of the power grid these synchronization phenomena are often modeled through networks of phase coupled oscillating nodes heterogeneity in the node dynamics however may prevent such networks from achieving the required level of synchronization in order to guarantee synchronization external inputs can be used to pin a subset of nodes to a reference frequency while the remaining nodes are steered toward synchronization via local coupling in this paper we present a submodular optimization framework for selecting a set of nodes to act as external inputs in order to achieve synchronization from a desired set of initial states we derive threshold based sufficient conditions for synchronization and then prove that these conditions are equivalent to constraints on monotone submodular functions over partition matroids based on this connection we map the sufficient conditions for synchronization to constraints on submodular functions leading to efficient algorithms with provable optimality bounds for selecting input nodes we illustrate our approach via numerical studies of synchronization in power systems

finite time consensus with disturbance rejection by discontinuous local interactions in directed graphs in this technical note we propose a decentralized discontinuous interaction rule which allows to achieve consensus in a network of agents modeled by continuous time first order integrator dynamics affected by bounded disturbances the topology of the network is described by a directed graph the proposed discontinuous interaction rule is capable of rejecting the effects of the disturbances and achieving consensus after a finite transient time an upper bound to the convergence time is explicitly derived in the technical note simulation results referring to a network of coupled kuramoto like oscillators are illustrated to corroborate the theoretical analysis

synchronization in complex delayed dynamical networks with nonsymmetric coupling abstract a new general complex delayed dynamical network model with nonsymmetric coupling is introduced and then we investigate its synchronization phenomena several synchronization criteria for delay independent and delay dependent synchronization are provided which generalize some previous results the matrix jordan canonical formalization method is used instead of the matrix diagonalization method so in our synchronization criteria the coupling configuration matrix of the network does not required to be diagonalizable and may have complex eigenvalues especially we show clearly that the synchronizability of a delayed dynamical network is not always characterized by the second largest eigenvalue even though all the eigenvalues of the coupling configuration matrix are real furthermore the effects of time delay on synchronizability of networks with unidirectional coupling are studied under some typical network structures the results are illustrated by delayed networks in which each node is a two dimensional limit cycle oscillator system consisting of a two cell cellular neural network numerical simulations show that these networks can realize synchronization with smaller time delay and will lose synchronization when the time delay increase larger than a threshold

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

homogeneous finite time consensus tracking of high order integrator agents by parametric approach abstractfinite time consensus tracking of high order integrator multi agent systems mas is investigated under an undirected topology when the leader s control input is known to all followers the homogeneous finite time control for a high order integrator is extended to a distributed protocol for the corresponding mas and a set of control gains are found by the parametric approach for robust control such that the multiple agents are simultaneously stabilised in finite time by keeping all characteristic polynomials hurwitz when it is only known to the leader s neighbouring followers a distributed observer is presented for each follower to estimate it in finite time and the combined observer based protocol achieves finite time consensus tracking in a fully distributed fashion simulation examples illustrate the effectiveness of the proposed scheme

analysis of consensus protocols with bounded measurement errors this paper analyzes two classes of consensus algorithms in the presence of bounded measurement errors the considered protocols adopt an updating rule based either on constant or vanishing weights under the assumption of bounded error the consensus problem is cast in a set membership framework and the agreement of the team is studied by analyzing the evolution of the feasible state set bounds on the asymptotic difference between the states of the agents are explicitly derived in terms of the bounds on the measurement noise and the values of the weight matrix

impulsive effects on quasi synchronization of neural networks with parameter mismatches and time varying delay this paper is concerned with the exponential synchronization issue of nonidentically coupled neural networks with time varying delay due to the parameter mismatch phenomena existed in neural networks the problem of quasi synchronization is thus discussed by applying some impulsive control strategies based on the definition of average impulsive interval and the extended comparison principle for impulsive systems some criteria for achieving the quasi synchronization of neural networks are derived more extensive ranges of impulsive effects are discussed so that impulse could either play an effective role or play an adverse role in the final network synchronization in addition according to the extended formula for the variation of parameters with time varying delay precisely exponential convergence rates and quasi synchronization errors are obtained respectively in view of different types impulsive effects finally some numerical simulations with different types of impulsive effects are presented to illustrate the effectiveness of theoretical analysis

cluster synchronization in directed networks of non identical systems with noises via random pinning control abstract this paper is concerned with the issue of mean square cluster synchronization in directed networks which consist of non identical nodes infected by communication noises the pinning control method is employed in designing controllers for guaranteeing cluster synchronization meanwhile all the controllers are supposed to occur with different probabilities by introducing the bernoulli stochastic variables based on the lyapunov stability theory and the stochastic theory the sufficient synchronization conditions are derived and proved theoretically which are mainly for the controllers to be designed and the noise intensities finally some numerical examples are presented to demonstrate the effectiveness of the results

synchronization analysis for nonlinearly coupled complex networks with an asymmetrical coupling matrix abstract in this paper the global synchronization for an array of nonlinearly coupled identical chaotic systems is investigated a distinctive feature of this work is to address synchronization issues for nonlinearly coupled complex networks with an asymmetrical coupling matrix by projecting the nonlinear coupling function onto a linear one and assuming the difference between them as a disturbing function we give some criteria for the global synchronization in virtual of the left eigenvector corresponding to the zero eigenvalue of the coupling matrix numerical examples are also provided to demonstrate the effectiveness of the theory

pinning synchronization of directed networks with switching topologies a multiple lyapunov functions approach this paper studies the global pinning synchronization problem for a class of complex networks with switching directed topologies the common assumption in the existing related literature that each possible network topology contains a directed spanning tree is removed in this paper using tools from m matrix theory and stability analysis of the switched nonlinear systems a new kind of network topology dependent multiple lyapunov functions is proposed for analyzing the synchronization behavior of the whole network it is theoretically shown that the global pinning synchronization in switched complex networks can be ensured if some nodes are appropriately pinned and the coupling is carefully selected interesting issues of how many and which nodes should be pinned for possibly realizing global synchronization are further addressed finally some numerical simulations on coupled neural networks are provided to verify the theoretical results

consensus of discrete time second order multiagent systems based on infinite products of general stochastic matrices traditionally the consensus of a discrete time multiagent system mas with a switching topology is transformed into the convergence problem of the infinite products of stochastic matrices which can be resolved by using the wolfowitz theorem however such a transformation is very difficult or even impossible for certain mass such as discrete time second order mass dtso mass whose consensus can only be transformed into the convergence problem of the infinite products of general stochastic matrices ipgsm these general stochastic matrices are matrices with row sum 1 but their elements are not necessarily nonnegative since there does not exist a general theory or an effective technique for dealing with the convergence of ipgsm establishing the consensus criteria for a dtso mas with a switching topology is rather difficult this paper concentrates on the consensus problem of a class of dtso mass and develops a method to cope with the corresponding ipgsm moreover it is pointed out that the method

quaternary convolutional codes from linear block codes over galois rings from a linear block code b over the galois ring gr 4 m with a k times n generator matrix and minimum hamming distance d a rate k n convolutional code over the ring z4 with squared euclidean free distance at least 2d and a nonrecursive encoder with memory at most m 1 is constructed when the generator matrix of b is systematic the convolutional encoder is systematic basic noncatastrophic and minimal long codes constructed in this manner are shown to satisfy a gilbert varshnmov bound

discontinuities and hysteresis in quantized average consensus we consider continuous time average consensus dynamics in which the agents states are communicated through uniform quantizers solutions to the resulting system are defined in the krasowskii sense and are proven to converge to conditions of practical consensus to cope with undesired chattering phenomena we introduce a hysteretic quantizer and we study the convergence properties of the resulting dynamics by a hybrid system approach

on the key equation we consider the set m a b a bh mod x2t of all solutions of the key equation for alternant codes where h is the syndrome polynomial in decoding these codes a particular solution m is sought subject to and being relatively prime and satisfying certain degree conditions we prove that these requirements specify uniquely as the minimal element of m analogous to the monic polynomial of minimal degree generating an ideal of f x with respect to a certain term order and that as such may be determined from an appropriate grobner basis of m motivated by this and other variations of the key equation such as that appropriate to errors and erasures decoding we derive a general algorithm for solving the congruence a bg mod xn for a range of term orders defined by the conditions on the particular solution required our techniques provide a unified approach to the solution of these key equations

finite time consensus for stochastic multi agent systems in this article we study the finite time consensus in probability for stochastic multi agent systems first we give the nonlinear consensus protocol for multi agent systems with gaussian white noise and define the concept of finite time consensus in probability second we prove that multi agent systems can achieve the finite time consensus in probability under five different kinds of communication topologies by using graph theory stochastic lyapunov theory and probability theory finally some simulation examples are provided to illustrate the effectiveness of the theoretical results

characterizations and criteria for synchronization of heterogeneous networks to linear subspaces in this paper we investigate synchronization issues in heterogeneous complex networks we start with a necessary condition for the existence of synchronous trajectories by analyzing the vector fie

on minimality of convolutional ring encoders convolutional codes are considered with code sequences modeled as semi infinite laurent series it is well known that a convolutional code c over a finite group g has a minimal trellis representation that can be derived from code sequences it is also well known that for the case that g is a finite field any polynomial encoder of c can be algebraically manipulated to yield a minimal polynomial encoder whose controller canonical realization is a minimal trellis in this paper we seek to extend this result to the finite ring case g bbzpr by introducing a so called ldquo p encoderrdquo we show how to manipulate a polynomial encoding scheme of a noncatastrophic convolutional code over bbzpr to produce a particular type of p encoder ldquominimal p encoderrdquo whose controller canonical realization is a minimal trellis with nonlinear features the minimum number of trellis states is then expressed as p gamma where gamma is the sum of the row degrees of the minimal p encoder in particular we show that any convolutional code over bbzpr admits a delay free p encoder which implies the novel result that delay freeness is not a property of the code but of the encoder just as in the field case we conjecture that a similar result holds with respect to catastrophicity i e any catastrophic convolutional code over bbzpr admits a noncatastrophic p encoder

pinning control of weighted general complex dynamical networks with time delay abstract time delays commonly exist in the real world in the present work we consider weighted general complex dynamical networks with time delay which are undirected and connected control of such networks by applying local feedback injections to a fraction of network nodes is investigated for both continuous time and discrete time cases both delay independent and delay dependent asymptotical stability criteria for network stabilization are derived it is also shown that the whole network can be stabilized by controlling only one node the efficiency of the derived results was illustrated by numerical examples

a constructive solution to interconnection and decomposition problems with multidimensional behaviors by a multidimensional behavior we mean the solution space of a linear constant coefficient system of partial difference or differential equations within the behavioral framework a natural concept of interconnection has been introduced by j c willems the regular interconnection problem can be formulated as follows given a behavior the plant find if possible another behavior a controller such that their interconnection is not redundant and is equal to a certain desired behavior we give a constructive solution to this problem which is in terms of polynomial matrix equations that can be solved using the theory of grobner bases we also study a dual problem concerning the existence of direct sum decompositions of multidimensional behaviors finally we present a unified framework for studying both problems as special cases of constructing relative complements in the lattice of behaviors

on controllability of delayed boolean control networks this paper is devoted to studying the trajectory and state controllability of boolean control networks bcns with time delay in contrast to bcns without time delay the dynamics of delayed bcns are determined by a sequence of initial states named here trajectories trajectory controllability means that there exists a control signal steering a system from an initial trajectory to a desired trajectory while state controllability means that there exists a control signal steering an initial state to a given state here both trajectory controllability and state controllability will be studied it should be noted that in this paper trajectory controllability does not mean tracking or following a given trajectory in fact it means to control bcns to a destination trajectory of length mu at the k th step using the semi tensor product of matrices the delayed bcns are first converted into an equivalent algebraic description and then some necessary and sufficient conditions are derived for the trajecto

finite time distributed consensus via binary control protocols this paper investigates the finite time distributed consensus problem for multi agent systems using a binary consensus protocol and the pinning control scheme compared with other consensus algorithms which need the complete state or output information of neighbors the proposed algorithm only requires sign information of the relative state measurements that is the differences between a node s state and that of its neighbors this corresponds to only requiring a single bit quantization error relative to each neighbor this signum protocol is realistic in terms of observed behavior in animal groups where relative motion is determined not by full time signal measurements but by coarse estimates of relative heading differences between neighbors the signum protocol does not require explicit measurement of time signals from neighbors and hence has the potential to significantly reduce the requirements for both computation and sensing analysis of discontinuous dynamical systems is used including the filippov solutions and set valued lie derivative based on the second order information on the evolution of lyapunov functions the conditions that guarantee the finite time consensus for the systems are identified numerical examples are given to illustrate the theoretical results

on behaviors and convolutional codes it is well known that a convolutional code is essentially a linear system defined over a finite field in this paper we elaborate on this connection we define a convolutional code as the dual of a complete linear behavior in the sense of willems 1979 using ideas from systems theory we describe a set of generalized first order descriptions for convolutional codes as an application of these ideas we present a new algebraic construction for convolutional codes

controllability of complex networks via pinning we study the problem of controlling a general complex network toward an assigned synchronous evolution by means of a pinning control strategy we define the pinning controllability of the network in terms of the spectral properties of an extended network topology the roles of the control and coupling gains as well as of the number of pinned nodes are also discussed

feature selection and kernel learning for local learning based clustering the performance of the most clustering algorithms highly relies on the representation of data in the input space or the hilbert space of kernel methods this paper is to obtain an appropriate data representation through feature selection or kernel learning within the framework of the local learning based clustering llc wu and scholkopf 2006 method which can outperform the global learning based ones when dealing with the high dimensional data lying on manifold specifically we associate a weight to each feature or kernel and incorporate it into the built in regularization of the llc algorithm to take into account the relevance of each feature or kernel for the clustering accordingly the weights are estimated iteratively in the clustering process we show that the resulting weighted regularization with an additional constraint on the weights is equivalent to a known sparse promoting penalty hence the weights of those irrelevant features or kernels can be shrunk toward zero extensive experiments show the efficacy of the proposed methods on the benchmark data sets

observer based distributed consensus for general nonlinear multi agent systems with interval control inputs in this paper observer based distributed consensus for general nonlinear multi agent systems with interval control inputs under strongly connected balanced topology is encountered when the relative states of agents are unavailable or undesirable theoretical analysis method is further extended to the case of general nonlinear multi agent systems under switching setting moreover tracking problem on the leader follower scenario is also explicitly investigated under a mutual assumption that the communication graph which represents the interaction among agents contains a directed spanning tree with the leader as its root it is shown that the consensus for underlying considered multi agent systems can be desirable as long as the data missing rate does not exceed a certain threshold finally simulation examples are presented to effectively corroborate the analytical findings

finite time convergent gradient flows with applications to network consensus this paper introduces the normalized and signed gradient dynamical systems associated with a differentiable function extending recent results on nonsmooth stability analysis we characterize their asymptotic convergence properties and identify conditions that guarantee finite time convergence we discuss the application of the results to consensus problems in multi agent systems and show how the proposed nonsmooth gradient flows achieve consensus in finite time

a linear algebra approach to minimal convolutional encoders the authors review the work of g d forney jr on the algebraic structure of convolutional encoders upon which some new results regarding minimal convolutional encoders rest an example is given of a basic convolutional encoding matrix whose number of abstract states is minimal over all equivalent encoding matrices however this encoding matrix can be realized with a minimal number of memory elements neither in controller canonical form nor in observer canonical form thus this encoding matrix is not minimal according to forney s definition of a minimal encoder to resolve this difficulty the following three minimality criteria are introduced minimal basic encoding matrix minimal encoding matrix and minimal encoder it is shown that all minimal basic encoding matrices are minimal and that there exist minimal encoding matrices that are not minimal basic several equivalent conditions are given for an encoding matrix to be minimal it is proven that the constraint lengths of two equivalent minimal basic encoding matrices are equal one by one up to a rearrangement all results are proven using only elementary linear algebra

minimal grobner bases and the predictable leading monomial property abstract we focus on grobner bases for modules of univariate polynomial vectors over a ring we identify a useful property the predictable leading monomial plm property that is shared by minimal grobner bases of modules in f x q no matter what positional term order is used the plm property is useful in a range of applications and can be seen as a strengthening of the wellknown predictable degree property row reducedness a terminology introduced by forney in the 70 s because of the presence of zero divisors minimal grobner bases over a finite ring of the type z p r where p is a prime integer and r is an integer 1 do not necessarily have the plm property in this paper we show how to derive from an ordered minimal grobner basis a so called minimal grobner p basis that does have a plm property we demonstrate that minimal grobner p bases lend themselves particularly well to derive minimal realization parametrizations over z p r applications are in coding and sequences over z p r

on constructing a shortest linear recurrence relation it has been shown in the literature that a formulation of the minimal partial realization problem in terms of exact modeling of a behavior lends itself to an iterative polynomial solution for the scalar case we explicitly present such a solution in full detail unlike classical solution methods based on hankel matrices the algorithm is constructive it iteratively constructs a partial realization of minimal mcmillian degree the algorithm is known in information theory as the berlekamp massey algorithm and is used for constructing a shortest linear recurrence relation for a finite sequence of numbers

an efficient algorithm for constructing minimal trellises for codes over finite abelian groups we present an efficient algorithm for computing the minimal trellis for a group code over a finite abelian group given a generator matrix for the code we also show how to compute a succinct representation of the minimal trellis for such a code and present algorithms that use this information to compute efficiently local descriptions of the minimal trellis this extends the work of kschischang and sorokine see ibid vol 41 no 6 p 1926 37 1995 who treated the case of linear codes over fields an important application of our algorithms is to the construction of minimal trellises for lattices a key step in our work is handling codes over cyclic groups c sub p spl alpha where p is a prime such a code can be viewed as a module over the ring z sub p spl alpha because of the presence of zero divisors in the ring modules do not share the useful properties of vector spaces we get around this difficulty by restricting the notion of linear combination to a p linear combination and by introducing the notion of a p generator sequence which enjoys properties similar to those of a generator matrix for a vector space

on exponential synchronization of kuramoto oscillators in this technical note we study the problem of exponential synchronization for one of the most popular models of coupled phase oscillators the kuramoto model we consider the special case of finite oscillators with distinct bounded natural frequencies our first result derives a lower bound on the coupling gain which is necessary for the onset of synchronization this bound improves the one derived by jadbabaie we then calculate a lower bound on the coupling gain that is sufficient to guarantee oscillator synchronization and derive further sufficient conditions to ensure exponential synchronization of the angular frequencies of all oscillators to the mean natural frequency of the group we also characterize the coupling gain that is sufficient for the oscillator phase differences to approach any desired compact set in finite time

synchronization of discrete dynamical networks with non delayed and delayed coupling in this paper synchronization of discrete dynamical networks with both non delayed and delayed couplings are studied firstly a class of complex networks with invariable topology structure are considered secondly a class of complex networks with variable topology structure are discussed based on lyapunov function method and linear matrix inequalities the sufficient conditions for asymptotically local synchronization of the above two classes of networks are presented respectively finally numerical examples are provided to verify our results

mean field theory for scale free random networks random networks with complex topology are common in nature describing systems as diverse as the world wide web or social and business networks recently it has been demonstrated that most large networks for which topological information is available display scale free features here we study the scaling properties of the recently introduced scale free model that can account for the observed power law distribution of the connectivities we develop a mean eld method to predict the growth dynamics of the individual vertices and use this to calculate analytically the connectivity distribution and the scaling exponents the mean eld method can be used to address the properties of two variants of the scale free model that do not display power law scaling c 1999 elsevier science b v all rights reserved

graph theory based pinning synchronization of stochastic complex dynamical networks this paper is concerned with the adaptive pinning synchronization problem of stochastic complex dynamical networks cdns based on algebraic graph theory and lyapunov theory pinning controller design conditions are derived and the rigorous convergence analysis of synchronization errors in the probability sense is also conducted compared with the existing results the topology structures of stochastic cdn are allowed to be unknown due to the use of graph theory in particular it is shown that the selection of nodes for pinning depends on the unknown lower bounds of coupling strengths finally an example on a chua s circuit network is given to validate the effectiveness of the theoretical results