graph homology and stability of coupled oscillator networks there are a number of models of coupled oscillator networks where the question of the stability of fixed points reduces to calculating the index of a graph laplacian some examples of such models include the kuramoto and kuramoto sakaguchi equations as well as the swing equations which govern the behavior of generators coupled in an electrical network we show that the index calculation can be related to a dual calculation which is done on the first homology group of the graph rather than the vertex space we also show that this representation is computationally attractive for relatively sparse graphs where the dimension of the first homology group is low as is true in many applications we also give explicit formulae for the dimension of the unstable manifold to a phase locked solution for graphs containing one or two loops as an application we present some novel results for the kuramoto model defined on a ring and compute the longest possible edge length for a stable solution

opinion dynamics in social networks with hostile camps consensus vs polarization most of the distributed protocols for multi agent consensus assume that the agents are mutually cooperative and trustful and so the couplings among the agents bring the values of their states closer opinion dynamics in social groups however require beyond these conventional models due to ubiquitous competition and distrust between some pairs of agents which are usually characterized by repulsive couplings and may lead to clustering of the opinions a simple yet insightful model of opinion dynamics with both attractive and repulsive couplings was proposed recently by c altafini who examined first order consensus algorithms over static signed graphs this protocol establishes modulus consensus where the opinions become the same in modulus but may differ in signs in this paper we extend the modulus consensus model to the case where the network topology is an arbitrary time varying signed graph and prove reaching modulus consensus under mild sufficient conditions of uniform connectivity of the graph for cut balanced graphs not only sufficient but also necessary conditions for modulus consensus are given

an inverse scattering series method for attenuating multiples in seismic reflection data we present a multidimensional multiple attenuation method that does not require any subsurface information for either surface or internal multiples to derive these algorithms we start with a scattering theory description of seismic data we then introduce and develop several new theoretical concepts concerning the fundamental nature of and the relationship between forward and inverse scattering these include 1 the idea that the inversion process can be viewed as a series of steps each with a specific task 2 the realization that the inverse scattering series provides an opportunity for separating out subseries with specific and useful tasks 3 the recognition that these task specific subseries can have different and more favorable data requirements convergence and stability conditions than does the original complete inverse series and most importantly 4 the development of the first method for physically interpreting the contribution that individual terms and pieces of terms in the inv

event driven multi consensus of multi agent networks with repulsive links due to diversification in environment a network of agents may have several emergent behaviors this paper introduces an event driven paradigm for realizing multi consensus which as a generic version of group cluster consensus depends both on the initial underlying topology and initial states for the network feature we resort to a distributed event driven paradigm since event driven control has advantages on communication reduction and control energy saving moreover to relax assumption on network topology repulsive links are exploited at event instants to facilitate multiple coordination to realize multi consensus we design a distributed event driven controller based on coupled intra subgroup and extra subgroup information in this context with different control strengths the finial value of man would be varying this phenomenon matches the principle of multi consensus in the current study based on lasalle s invariance principle we prove that under the proposed event driven configuration the joint cooperation and competition contributes to multi consensus provided that the sampling period is no larger than a positive threshold it is shown there is no further requirement on network topologies in pursuit of multiple coordination this paper studies multiple coordination of multi agent networks under an event driven paradigm for an undirected connected graph a node clustering scheme is first adopted to ensure a relatively strong degree of connectivity within each potential subgroup and some repulsive effect is used to deal with the extra subgroup links to reduce unnecessary communication a distributed event driven controller is designed via coupled intra subgroup and extra subgroup information based on the lasalle s invariance principle it is shown that under the proposed event driven control configuration multi agent networks can realize multi consensus without any balanced requirement on the underlying topologies simulation work is presented to validate the theoretical results

collision free consensus in multi agent networks this paper addresses the collision free consensus problem in a network of agents with single integrator dynamics distributed algorithms with local interactions are proposed to achieve consensus while guaranteeing collision free among agents during the evolution of the multi agent networks the novelty of the proposed algorithms lies in the definition of neighbors for each agent which is different from the usual sense that neighbors are selected by the distance between agents in the state space in the proposed strategies the neighbor set for each agent is determined by the distance or difference between agents in the index space after ordering and labeling all agents according to certain ordering rules including weighted order and lexicographic order the consensus analysis of the proposed algorithms is presented with some existing results on algebraic graph theory and matrix analysis meanwhile by realizing the relations between order preservation and collision free a systematic analysis framework on order preservation and hence collision free for agents in arbitrary dimension is provided based on tools from monotone systems theory illustrated numerical examples are presented to validate the effectiveness of the proposed strategies

stability criteria for matrices in this paper we study the stability of matrices using technologies of special matrices analysis several simple criteria for the stability for the matrix a aij cn n which is not diagonally dominant are obtained by aid of simple algebraic conditions of aij only

five dimensional interpolation recovering from acquisition constraints although 3d seismic data are being acquired in larger volumes than ever before the spatial sampling of these volumes is not always adequate for certain seismic processes this is especially true of marine and land wide azimuth acquisitions leading to the development of multidimensional data interpolation techniques simultaneous interpolation in all five seismic data dimensions inline crossline offset azimuth and frequency has great utility in predicting missing data with correct amplitude and phase variations although there are many techniques that can be implemented in five dimensions this study focused on sparse fourier reconstruction the success of fourier interpolation methods depends largely on two factors 1 having efficient fourier transform operators that permit the use of large multidimensional data windows and 2 constraining the spatial spectrum along dimensions where seismic amplitudes change slowly so that the sparseness and band limitation assumptions remain valid fourier reconstruction can be performed when enforcing a sparseness constraint on the 4d spatial spectrum obtained from frequency slices of five dimensional windows binning spatial positions into a fine 4d grid facilitates the use of the fft which helps on the convergence of the inversion algorithm this improves the results and computational efficiency the 5d interpolation can successfully interpolate sparse data improve avo analysis and reduce migration artifacts target geometries for optimal interpolation and regularization of land data can be classified in terms of whether they preserve the original data and whether they are designed to achieve surface or subsurface consistency

shaping regularization in geophysical estimation problems regularization is a required component of geophysical estimation problems that operate with insufficient data the goal of regularization is to impose additional constraints on the estimated model i introduce shaping regularization a general method for imposing constraints by explicit mapping of the estimated model to the space of admissible models shaping regularization is integrated in a conjugate gradient algorithm for iterative least squares estimation it provides the advantage of better control on the estimated model in comparison with traditional regularization methods and in some cases leads to a faster iterative convergence simple data interpolation and seismic velocity estimation examples illustrate the concept

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

stability analysis of diagonally equipotent matrices diagonally equipotent matrices are diagonally dominant matrices for which dominance is never strict in any coordinate they appear e g as laplacian matrices of signed graphs we show in this paper that for this class of matrices it is possible to provide a complete characterization of the stability properties based only on the signs of the entries of the matrices

nonsingularity singularity criteria for nonstrictly block diagonally dominant matrices abstract let a a ij n i j 1 c n n be a block irreducible matrix with nonsingular diagonal blocks v v i c n be a positive vector and let n j 1 2pt j i a 1 ii a ij v j v i i 1 n under these assumptions necessary and sufficient conditions for a to be singular are obtained based on a block generalization of wielandt s lemma the pointwise case n n of irreducible matrices with nonstrict generalized diagonal dominance is treated separately for an irreducible matrix a conditions necessary and sufficient for a boundary point of the union of the gerschgorin s circles and of the union of the ovals of cassini to be an eigenvalue of a are derived

the consensus problem in the behavioral approach abstract in this paper we investigate the multi agent consensus problem in a broad context by assuming both for the agents and for the distributed controllers higher order input output dynamic models the behavioral approach developed by jan willems seems to be the most appropriate set up where to investigate this general problem by making use of the behavioral approach we will show that the consensus problem can be naturally rephrased as a special case of stabilization problem the stabilization pertains only a part of the system variables the outputs and it is achieved through regular full interconnection of the agent models and of the controllers it turns out that if the communication among agents is described by a weighted undirected and connected graph then a necessary and sufficient condition for the consensus problem to be solvable is that the output is stabilizable from the input in the agents model in this respect the theory here developed for higher order input output models naturally extends the results about consensus derived in the state space approach

finite time median related group consensus over directed networks in this paper we investigate a novel finite time median related group consensus problem where the finial consensus value can be identified as a desired function of the median of initial states in

coordination of multi agent systems on interacting physical and communication topologies abstract a new framework is given for coordination of multi agent systems that are interconnected by a physical coupling digraph the edges of this graph represent physical couplings between agents that are fixed due to dynamical interactions on top of the physical graph distributed control protocols are designed where the allowed communications between agents for control purposes are prescribed by a second fixed communication digraph the physical and communication digraphs are generally different and the combination of these two graphs forms a cyber physical system the interactions between physical and communication graphs are the focus of this paper we consider different interactions between two graphs including the case when their pinned laplacian commutes the case of the communication graph with diagonalizable pinned laplacian and the case of two general graphs moreover within each graph the relations between the agents can be either collaborative or antagonistic to capture this the theory of bipartite consensus is used coordination protocols for different cases are designed that are distributed with respect to the communication graph and overcome the detrimental effects of the signed physical graph the proposed control methods are illustrated by simulation examples

bipartite and cooperative output synchronizations of linear heterogeneous agents this paper investigates cooperative output synchronization and bipartite output synchronization of a group of linear heterogeneous agents in a unified framework for a structurally balanced signed graph we prove that the bipartite output synchronization is equivalent to the cooperative output synchronization over an unsigned graph whose adjacency matrix is obtained by taking the absolute value of each entry in the adjacency matrix of the signed graph we obtain a new h criterion which is sufficient for both cooperative output synchronization and bipartite output synchronization

on l1 gain control of 2 d positive roesser systems with directional delays necessary and sufficient conditions abstract in this paper the problem of l 1 gain control is addressed for two dimensional 2 d positive roesser systems with directional delays a complete solution to the design problem is presented for the first time specifically by exploiting a new approach based on 2 d z transform an exact value of l 1 induced norm of the input output operator is obtained this analytical result is utilized to derive necessary and sufficient conditions under which a 2 d positive system with delays is asymptotically stable with a prescribed l 1 gain performance then by utilizing a vertex optimization approach necessary and sufficient conditions are established for the existence of a state feedback controller sfc that makes the closed loop system positive and stable subject to l 1 induced performance the proposed synthesis conditions are formulated in terms of linear programming lp which can be effectively solved by various convex algorithms to minimize the l 1 performance index

on the cauchy problem of fourth order nonlinear schrodinger equations abstract in this paper we study the cauchy problem of the fourth order schrodinger equation i t u a u b 2 u u p for dimension 4 where p is an integer greater than 1 with initial data in besov spaces we prove that for any 4 p 2 1 4 n p 4 n q the cauchy problem of this equation is locally well posed in b 2 q s p r n and b 2 q s r n where s p n 2 4 p 1 and s s p and for any 1 q almost global well posedness holds in these spaces if initial data are small we also prove that if a 0 then global well posedness holds in these spaces for small initial data

self focusing with fourth order dispersion we analyze self focusing and singularity formation in the nonlinear schrodinger equation nls with high order dispersion i psi t pm delta q psi psi 2 sigma psi 0 in the isotropic mixed dispersion nls i psi t delta psi epsilon delta 2 psi psi 2 sigma psi 0 and in nonisotropic mixed dispersion nls equations which model propagation in fiber arrays

persistent flows in deterministic chains this paper studies the role of persistent flows in the convergence of infinite backward products of stochastic matrices of deterministic chains over networks with nonreciprocal interactions between agents an arc describing the interaction strength between two agents is said to be persistent if its weight function has an infinite l 1 norm convergence of the infinite backward products to a rank one matrix of a deterministic chain of stochastic matrices is equivalent to achieving consensus at the node states we discuss two balance conditions on the interactions between agents which generalize the arc balance and cut balance conditions in the literature respectively the proposed conditions require that such a balance should be satisfied over each time window of a fixed length instead of at each time instant we prove that in both cases global consensus is reached if and only if the persistent graph which consists of all the persistent arcs contains a directed spanning tree the convergence rates of the system to consensus are also provided in terms of the interactions between agents having taken place the results are obtained under a weak condition without assuming the existence of a positive lower bound of all the nonzero weights of arcs and are compared with the existing results illustrative examples are provided to validate the results and show the critical importance of the nontrivial lower boundedness of the self confidence of the agents

distributed averaging with random network graphs and noises we consider a discrete time distributed averaging algorithm over multi agent networks with measurement noises and time varying random graphs each agent updates its state by a weighted sum of pairwise state differences between its neighbors and itself with both additive and multiplicative measurement noises the network structure is modeled by a sequence of time varying random digraphs which may be spatially and temporally dependent by stochastic lyapunov method and the combination of algebraic graph theory and martingale convergence theory we obtain sufficient conditions for stochastic approximation type algorithms to achieve mean square and almost sure average consensus we prove that all states of the agents converge to a common random variable whose mathematical expectation is the average of initial values in mean square and almost surely if the sequence of digraphs is conditionally balanced and uniformly conditionally jointly connected an upper bound of the variance of the limit random variable that is the mean square steady state error for stochastic average consensus is given quantitatively related to the weights the algorithm gain and the energy level of the noises

technical communique sufficient conditions for the convergence of a class of nonlinear distributed consensus algorithms this paper is concerned with the convergence of a class of continuous time nonlinear consensus algorithms for single integrator agents in the consensus algorithms studied here the control input of each agent is assumed to be a state dependent combination of the relative positions of its neighbors in the information flow graph using a novel approach based on the smallest order of the nonzero derivative it is shown that under some mild conditions the convex hull of the agents has a contracting property a set valued lasalle like approach is subsequently employed to show the convergence of the agents to a common point the results are shown to be more general than the ones reported in the literature in some cases an illustrative example demonstrates how the proposed convergence conditions can be verified

signed bounded confidence models for opinion dynamics abstract the aim of this paper is to modify continuous time bounded confidence opinion dynamics models so that changes of opinion intended as changes of the sign of the initial states are never induced during the evolution such sign invariance can be achieved by letting opinions of different sign localized near the origin interact negatively or neglect each other or even repel each other in all cases it is possible to obtain sign preserving bounded confidence models with state dependent connectivity and with a clustering behavior similar to that of a standard bounded confidence model

a necessary and sufficient condition for consensus of continuous time agents over undirected time varying networks the average consensus problem of continuous time agents in undirected time varying networks is studied the network is allowed to be disconnected a notion called infinite integral connectivity is proposed based on the notion a necessary and sufficient condition for achieving consensus is given that is when the network topology is described by an undirected time varying graph g t the agents achieve consensus if and only if the infinite integral graph of g t over 0 is connected this criterion does not hold for directed networks

random noise attenuation using f x regularized nonstationary autoregression we have developed a novel method for random noise attenuation in seismic data by applying regularized nonstationary autoregression rna in the frequency space f x domain the method adaptively predicts the signal with spatial changes in dip or amplitude using f x rna the key idea is to overcome the assumption of linearity and stationarity of the signal in conventional f x domain prediction technique the conventional f x domain prediction technique uses short temporal and spatial analysis windows to cope with the nonstationary of the seismic data the new method does not require windowing strategies in spatial direction we implement the algorithm by an iterated scheme using the conjugate gradient method we constrain the coefficients of nonstationary autoregression na to be smooth along space and frequency in the f x domain the shaping regularization in least square inversion controls the smoothness of the coefficients of f x rna there are two key parameters in the proposed method filter length

scaled consensus problems on switching networks this note aims to solve a class of consensus problems on switching networks of agents in the sense that all agents reach agreement upon a consensus value but with different time varying scales that is multi agent networks achieve the so called scaled consensus necessary and sufficient conditions are established to guarantee the exponential convergence of agents under the action of distributed protocols which are conducted by nearest neighbor interaction rules simulation tests are performed to illustrate the scaled consensus performances for agents in the presence of time varying scales and switching topologies

delay independent incremental stability in time varying monotone systems satisfying a generalized condition of two sided scalability monotone systems generated by delay differential equations with explicit time variation are of importance in the modeling of a number of significant practical problems including the analysis of communications systems population dynamics and consensus protocols in such problems it is often of importance to be able to guarantee delay independent incremental asymptotic stability whereby all solutions converge toward each other asymptotically thus allowing the asymptotic properties of all trajectories of the system to be determined by simply studying those of some particular convenient solution it is known that the classical notion of quasimonotonicity renders time delayed systems monotone however this is not sufficient alone to obtain such guarantees in this work we show that by combining quasimonotonicity with a condition of scalability motivated by wireless networks it is possible to guarantee incremental asymptotic stability for a general class of systems that includes a variety of interesting examples furthermore we obtain as a corollary a result of guaranteed convergence of all solutions to a quantifiable invariant set enabling time invariant asymptotic bounds to be obtained for the trajectories even if the precise values of time varying parameters are unknown

the deformed consensus protocol this paper studies a generalization of the standard continuous time consensus protocol obtained by replacing the laplacian matrix of the communication graph with the so called deformed laplacian the deformed laplacian is a second degree matrix polynomial in the real variable s which reduces to the standard laplacian for s equal to unity the stability properties of the ensuing deformed consensus protocol are studied in terms of parameter s for some special families of undirected and directed graphs and for arbitrary graph topologies by leveraging the spectral theory of quadratic eigenvalue problems examples and simulation results are provided to illustrate our theoretical findings

classes of general h matrices let m a denote the comparison matrix of a square h matrix a that is m a is an m matrix h matrices such that their comparison matrices are nonsingular are well studied in the literature in this paper we study characterizations of h matrices with either singular or nonsingular comparison matrices the spectral radius of the jacobi matrix of m a and the generalized diagonal dominance property are used in the characterizations finally a classification of the set of general h matrices is obtained

on stability of interval matrices new sufficient and sometimes necessary and sufficient conditions are obtained for schur and hurwitz stability of interval matrices by relying on the concept of connective stability and m matrices the necessity part is broadened to include interval matrices with mixed signs of the off diagonal elements provided the sign patterns follow that of the morishima matrix the obtained results are extended to cover convex combinations of interval matrices

systems of ordinary differential equations which generate an order preserving flow a survey of results this article consists of a survey of results concerning the qualitative behavior of solutions of systems of ordinary differential equations which generate an order preserving flow we restrict our consideration to partial orderings on r n induced by any one of its orthants a flow preserves ordering if any two solutions x t and y t are ordered x t leqq y t for all t 0 whenever x 0 leqq y 0 many of the important results for such systems have only recently been obtained principally by m w hirsch who pointed out the tendency of their solutions to converge to equilibrium less well known are some global geometric constraints on the stable manifold of an equilibrium and the existence of heteroclinic orbits connecting ordered equilibria a particularly striking result for this class of systems is the easily computable necessary and sufficient condition for stability of an equilibrium one of our main goals is to show that by allowing partial orderings on r n generated by orthants

structural balance and dynamics over signed ba scale free network abstract by exploring the influence between dynamics and structural balance we divide a binary group with two nodes and a directed edge into three categories as balanced intermediate and unbalanced structure on this basis a co evolution model considering the dynamic mechanics of both opinions and relationships is designed global structural balance in four basic structures are explained in the simulation experiments over signed ba scale free network the impact of negative relationships on polarizing opinion the effect of intermediate state structure and the influences of five strategies on relaxation time are analyzed by introducing an unbalanced cycle two kinds of interesting results are discussed

lateral prediction for noise attenuation by t x and f x techniques attenuating random noise with a prediction filter in the time space domain generally produces results similar to those of predictions done in the frequency space domain however in the presence of moderate to high amplitude noise time space or t x prediction passes less random noise than does frequency space or f x prediction the f x prediction may also produce false events in the presence of parallel events where t x prediction does not these advantages of t x prediction are the result of its ability to control the length of the prediction filter in time an f x prediction produces an effective t x domain filter that is as long in time as the input data gulunay s f x domain prediction tends to bias the predictions toward the traces nearest the output trace allowing somewhat more noise to be passed but this bias may be overcome by modifying the system of equations used to calculate the filter the 3 d extension to the 2 d t x and f x prediction techniques allows improved noise attenuation because more samples are used in the predictions and the requirement that events be strictly linear is relaxed

delay independent asymptotic stability in monotone systems monotone systems comprise an important class of dynamical systems that are of interest both for their wide applicability and because of their interesting mathematical properties it is known that under the property of quasimonotonicity time delayed systems become monotone and some remarkable properties have been reported for such systems these include for example the fact that for linear systems global asymptotic stability of the undelayed system implies global asymptotic stability for the delayed system under arbitrary bounded delays nevertheless extensions to nonlinear systems have thus far relied primarily on the conditions of homogeneity and subhomogeneity and it has been conjectured that these can be relaxed our aim in this paper is to show that this is feasible for a general class of nonlinear monotone systems by deriving convergence results in which simple properties of the undelayed system lead to delay independent stability in particular one of our results shows that if the undelayed system has a convergent trajectory that is unbounded in all components as t rightarrow infty then the system is globally asymptotically stable for arbitrary bounded time varying delays this follows from a more general result derived in the paper that allows to quantify delay independent regions of attraction which can be used to prove global asymptotic stability for various classes of systems these also recover various known delay independent stability results that are discussed within the paper

exponential stability of two dimensional homogeneous monotone systems with bounded directional delays one dimensional 1 d monotone systems have received considerable attention recently due to their wide applicability and interesting mathematical properties one of these special properties is that for lti monotone systems exponential stability is insensitive to time delays some extensions to 1 d nonlinear monotone systems based on conditions of homogeneity have also been reported in this paper we study the problem of exponential stability of discrete time 2 d nonlinear monotone systems described by the roesser model with time varying delays specifically based on the monotone property and homogeneity of the associated vector fields necessary and sufficient delay independent exponential stability conditions are derived the magnitudes of delays are also taken into deriving an explicit estimation of the exponential decay rate which correlates the impact of delays on the system performance two examples are given to demonstrate the effectiveness of the obtained results

seismic trace interpolation in the f x domain interpolation of seismic traces is an effective means of improving migration when the data set exhibits spatial aliasing a major difficulty of standard interpolation methods is that they depend on the degree of reliability with which the various geological events can be separated in this respect a multichannel interpolation method is described which requires neither a priori knowledge of the directions of lateral coherence of the events nor estimation of these directions the method is based on the fact that linear events present in a section made of equally spaced traces may be interpolated exactly regardless of the original spatial interval without any attempt to determine their true dips the predictability of linear events in the f x domain allows the missing traces to be expressed as the output of a linear system the input of which consists of the recorded traces the interpolation operator is obtained by solving a set of linear equations whose coefficients depend only on the spectrum of the spatial prediction filter defined by the recorded traces synthetic examples show that this method is insensitive to random noise and that it correctly handles curvatures and lateral amplitude variations assessment of the method with a real data set shows that the interpolation yields an improved migrated section

on the consensus and bipartite consensus in high order multi agent dynamical systems with antagonistic interactions abstract the aim of this paper is to address consensus and bipartite consensus for a group of homogeneous agents under the assumption that their mutual interactions can be described by a weighted signed connected and structurally balanced communication graph this amounts to assuming that the agents can be split into two antagonistic groups such that interactions between agents belonging to the same group are cooperative and hence represented by nonnegative weights while interactions between agents belonging to opposite groups are antagonistic and hence represented by nonpositive weights in this framework bipartite consensus can always be reached under the stabilizability assumption on the state space model describing the dynamics of each agent on the other hand nontrivial standard consensus may be achieved only under very demanding requirements both on the laplacian associated with the communication graph and on the agents description in particular consensus may be achieved only if there is a sort of equilibrium between the two groups both in terms of cardinality and in terms of the weights of the conflicting interactions amongst agents

nonlinear second order multi agent systems subject to antagonistic interactions without velocity constraints abstract this paper studies the nonlinear second order multi agent systems without velocity information while subject to antagonistic interactions among the reciprocal agents when being free of nonlinear disturbances a necessary and sufficient condition for the consensus resp stability problem is presented which essentially shows that the coupling weights and topology structure suffice to assure the consensus resp stability of the agents whereas nonzero eigenvalues of the laplacian matrix also act a crucial role provided that merely the absolute information of the auxiliary variable is demanded the derived results implicitly manifest that structurally balanced graph resp isolated structurally balanced graph or containing the in isolated structurally balanced subgraph is merely the necessary condition for the consensus resp stability of the agents within the second order dynamical setting in the presence of nonlinear dynamics we explicitly extend the derived results with the help of the lyapunov based technique under quite mild assumptions furthermore some comparisons are presented in contrast to some of the existing literature finally numerical examples are given to validate the efficiency of the obtained results

recent directions in matrix stability abstract matrix stability has been intensively investigated in the past two centuries we review work that has been done in this topic focusing on the great progress that has been achieved in the last decade or two we start with classical stability criteria of lyapunov routh and hurwitz and lienard and chipart we then study recently proven sufficient conditions for stability with particular emphasis on p matrices we investigate conditions for the existence of a stable scaling for a given matrix we review results on other types of matrix stability such as d stability additive d stability and lyapunov diagonal stability we discuss the weak principal submatrix rank property shared by lyapunov diagonally semistable matrices we also discuss the uniqueness of lyapunov scaling factors maximal lyapunov scaling factors cones of real positive semidefinite matrices and their applications to matrix stability and inertia preserving matrices

a criterion for exponential consensus of time varying non monotone nonlinear networks in this technical note we present new results on exponential consensus for continuous time nonlinear time varying networks a key feature in the following is that the monotonicity property is not required unlike most of existing literature on the subject moreover we give an estimate of the exponential rate of convergence towards the agreement manifold finally representative example and counterexample are given

stability of solitons described by nonlinear schrodinger type equations with higher order dispersion abstract steady solitons described by the fourth order nonlinear schrodinger type equations in one two and three dimensions with power law nonlinearities are studied conditions of existence and stability of such solitons are found numerical results demonstrating soliton existence stability and instability are described they agree with the developed theory

finite dimensional global attractor for a dissipative anisotropic fourth order schrodinger equation abstract we study the long time behavior of the solutions to a nonlinear damped anisotropic fourth order schrodinger type equation in r 2 we prove that this behavior is described by the existence of regular finite dimensional global attractor in the energy space

minimum weighted norm interpolation of seismic records in seismic data processing we often need to interpolate and extrapolate data at missing spatial locations the reconstruction problem can be posed as an inverse problem where from inadequate and incomplete data we attempt to reconstruct the seismic wavefield at locations where measurements were not acquired we propose a wavefield reconstruction scheme for spatially band limited signals the method entails solving an inverse problem where a wavenumber domain regularization term is included the regularization term constrains the solution to be spatially band limited and imposes a prior spectral shape the numerical algorithm is quite efficient since the method of conjugate gradients in conjunction with fast matrix vector multiplications implemented via the fast fourier transform fft is adopted the algorithm can be used to perform multidimensional reconstruction in any spatial domain

antileakage fourier transform for seismic data regularization in higher dimensions wide azimuth seismic data sets are generally acquired more sparsely than narrow azimuth seismic data sets this brings new challenges to seismic data regularization algorithms which aim to reconstruct seismic data for regularly sampled acquisition geometries from seismic data recorded from irregularly sampled acquisition geometries the fourier basedseismicdataregularizationalgorithmfirstestimates the spatial frequency content on an irregularly sampled input grid then it reconstructs the seismic data on any desired grid three main difficulties arise in this process the spectral leakage problem the accurate estimation of fourier components and the effective antialiasing scheme used inside the algorithm the antileakage fourier transform algorithm can overcome the spectral leakage problem and handles aliased data to generalize it to higher dimensions we propose an area weighting scheme to accurately estimate the fourier components however the computational cost dramatically increases with the sampling dimensions a windowed fourier transform reduces the computational cost in high dimension applications but causes undersampling in wavenumber domain and introduces some artifacts known as gibbs phenomena as a solution we propose a wavenumber domain oversampling inversion scheme the robustness and effectiveness of the proposed algorithm are demonstrated with some applications to both synthetic and real data examples

pinning bipartite synchronization for coupled nonlinear systems with antagonistic interactions and switching topologies abstract this paper studies the bipartite synchronization in a network of nonlinear systems with antagonistic interactions and switching topologies in order to obtain some conditions such that the network achieves bipartite synchronization for any initial conditions we design a pinning scheme to pin a part of agents under the assumptions that all signed graphs are structurally balanced and the nonlinear system satisfies a one sided lipschitz condition we derive conditions under which the network reaches bipartite synchronization for any initial conditions and arbitrary switching signals for a general switching signal especially the periodic switching signal some conditions related to switching signal are obtained finally we present two numerical examples to illustrate the effectiveness of the obtained results

intrinsic reduced attitude formation with ring inter agent graph this paper investigates the reduced attitude formation control problem for a group of rigid body agents using feedback based on relative attitude information under both undirected and directed cyc

on limits of powers of certain absolutely row stochastic matrices abstract we consider limits of powers of matrices that are absolutely row stochastic matrices a such that a is row stochastic we give graph theoretic criteria when such limits exist and if so determine their value in particular we show that for aperiodic connected matrices that satisfy opposition bipartiteness obipness a perron frobenius property holds here we call a obip also called structural balance in the literature when nodes in the graph corresponding to a can be partitioned into two groups such that within group links are non negative and across group links are non positive

seismic trace interpolation in the fourier transform domain a data adaptive interpolation method is designed and applied in the fourier transform domain f k or f kx ky for spatially aliased data the method makes use of fast fourier transforms and their cyclic properties thereby offering a significant cost advantage over other techniques that interpolate aliased data the algorithm designs and applies interpolation operators in the f k or f kx ky domain to fill zero traces inserted in the data in the t x or t x y domain at locations where interpolated traces are needed the interpolation operator is designed by manipulating the lower frequency components of the stretched transforms of the original data this operator is derived assuming that it is the same operator that fills periodically zeroed traces of the original data but at the lower frequencies and corresponds to the f k or f kx ky domain version of the well known f x or f x y domain trace interpolators the method is applicable to 2d and 3d data recorded sparsely in a horizontal plane the most comm

distributed algorithms for reaching consensus on general functions this paper presents analysis and design results for distributed consensus algorithms in multi agent networks we consider continuous consensus functions of the initial state of the network agents under mild smoothness assumptions we obtain necessary and sufficient conditions characterizing any algorithm that asymptotically achieves consensus this characterization is the building block to obtain various design results for networks with weighted directed interconnection topologies we first identify a class of smooth functions for which one can synthesize in a systematic way distributed algorithms that achieve consensus we apply this result to the family of weighted power mean functions and characterize the exponential convergence properties of the resulting algorithms we establish the validity of these results for scenarios with switching interconnection topologies finally we conclude with two discontinuous distributed algorithms that achieve respectively max and min consensus in finite time

seismic trace interpolation in the f x y domain seismic trace interpolation is implemented as a 2 d x y spatial prediction performed separately on each frequency f slice this so called f x y domain trace interpolation method is based on the relation that the linear prediction lp operator estimated at a given frequency may be used to predict data at a higher frequency but a smaller trace spacing the relationship originally given for thef x domain trace interpolation is successfully extended to the f x y domain the extension is achieved by masking the data samples selectively from the input frequency slice to design the lp operators two interpolation algorithms using the full step and the fractional step predictions respectively are developed both methods use an all azimuth prediction in the x y domain but the fractional step prediction method is computationally more efficient while the interpolation method can be applied to a common offset cube of 3 d seismic it can also be applied to 2 d seismic traces for prestack data processing sy

antileakage least squares spectral analysis for seismic data regularization and random noise attenuation spatial transformation of irregularly sampled data series to regularly sampled data series is a challenging problem in many areas such as seismology the classical fourier analysis is limited to regularly sampled data series on the other hand the least squares spectral analysis lssa can analyze irregularly sampled data series although the lssa method takes into account the correlation among the sinusoidal basis functions of irregularly spaced series it still suffers from the problem of spectral leakage energy leaks from one spectral peak into another we propose an iterative method called antileakage lssa to attenuate the spectral leakage and consequently regularize irregular data series in this method we first search for a spectral peak with the highest energy and then we remove suppress it from the original data series in the next step we search for a new peak with the highest energy in the residual data series and remove the new and the old components simultaneously from the original data

state agreement for continuous time coupled nonlinear systems two related problems are treated in continuous time first the state agreement problem is studied for coupled nonlinear differential equations the vector fields can switch within a finite family associated to each vector field is a directed graph based in a natural way on the interaction structure of the subsystems generalizing the work of moreau under the assumption that the vector fields satisfy a certain subtangentiality condition it is proved that asymptotic state agreement is achieved if and only if the dynamic interaction digraph has the property of being sufficiently connected over time the proof uses nonsmooth analysis second the rendezvous problem for kinematic point mass mobile robots is studied when the robots fields of view have a fixed radius the circumcenter control law of ando e ieee trans robotics automation 15 1999 pp 818 828 is shown to solve the problem the rendezvous problem is a kind of state agreement problem but the interaction structure is state dependent

well posedness of higher order nonlinear schrodinger equations in sobolev spaces hs rn and applications in this paper we establish local well posedness in the sobolev space hs rn with s s0 for a general class of nonlinear dispersive equations of the type tu ip dx u f u where p dx is an elliptic differential operator on rn with a real symbol f u is a nonlinear function which behaves like u u for some constant 0 and s0 is a critical index suggested by a standard scaling argument by using such local result and conservation laws we improve the known and obtain some new global well posedness results for the fourth order nonlinear schrodinger equation i tu a u b 2u c u u

convergence analysis of directed signed networks via an m matrix approach abstractthis paper aims at solving convergence problems on directed signed networks with multiple nodes where interactions among nodes are described by signed digraphs the convergence analysis is

convergence rate for discrete time multiagent systems with time varying delays and general coupling coefficients multiagent systems mass are ubiquitous in our real world there is an increasing attention focusing on the consensus or synchronization problem of mass over the past decade although there are numerous results reported on the convergence of a discrete time mas based on the infinite products of matrices few results are on the convergence rate because of the switching topology the traditional eigenvalue analysis and the lyapunov function methods are both invalid for the convergence rate analysis of an mas with a switching topology therefore the estimation of the convergence rate for a discrete time mas with time varying delays remains a difficult problem to overcome the essential difficulty of switching topology this paper aims at developing a contractive set approach to analyze the convergence rate of a discrete time mas in the presence of time varying delays and generalized coupling coefficients using the proposed approach we obtain an upper bound of the convergence rate under the condition of joint connectivity in particular the proposed method neither requires the nonnegative property of the coupling coefficients nor the basic assumption of a uniform lower bound for all positive coupling coefficients which have been widely applied in the existing works on this topic as an application of the main results we will show that the classical vicsek model with time delays can realize synchronization if the initial topology is connected

controllability of multi agent systems with directed and weighted signed networks abstract this paper studies the controllability of multi agent systems with signed networks which are represented by directed weighted signed graphs the adjacency weights of network depict the property of interactions positive weight means cooperative interaction while negative weight antagonistic interaction first by using switching equivalent transformation the controllability of three kinds of signed networks is studied structurally balanced anti balanced and strictly unbalanced it is shown that the controllability of the structurally balanced network is equivalent to that of the associated underlying network then a graph theoretic necessary condition for controllability is given by virtue of almost equitable partition of directed weighted signed networks furthermore some necessary and sufficient conditions are given for the controllability of generic linear multi agent systems in addition several examples are presented to illustrate the theoretical results

lyapunov diagonal semistability of real h matrices we characterize lyapunov diagonally stable real h matrices and those real h matrices which are lyapunov diagonally semistable but not lyapunov diagonally stable called lyapunov diagonally near stable the latter characterization is given in terms of the principal submatrix rank property defined here we apply our results to the numerical abscissas of real matrices one of our main tools is a slight strengthening of classical results of ostrowski which we derive from a fundamental theorem of wielandt

non linear protocols for optimal distributed consensus in networks of dynamic agents we consider stationary consensus protocols for networks of dynamic agents with fixed topologies at each time instant each agent knows only its and its neighbors state but must reach consensus on a group decision value that is function of all the agents initial state we show that the agents can reach consensus if the value of such a function is time invariant when computed over the agents state trajectories we use this basic result to introduce a non linear protocol design rule allowing consensus on a quite general set of values such a set includes e g any generalized mean of order p of the agents initial states as a second contribution we show that our protocol design is the solution of individual optimizations performed by the agents this notion suggests a game theoretic interpretation of consensus problems as mechanism design problems under this perspective a supervisor entails the agents to reach a consensus by imposing individual objectives we prove that such objectives can be chosen so that rational agents have a unique optimal protocol and asymptotically reach consensus on a desired group decision value we use a lyapunov approach to prove that the asymptotical consensus can be reached when the communication links between nearby agents define a time invariant undirected network finally we perform a simulation study concerning the vertical alignment maneuver of a team of unmanned air vehicles

continuous time consensus under persistent connectivity and slow divergence of reciprocal interaction weights in this paper we present new results on consensus for continuous time multiagent systems we introduce the assumptions of persistent connectivity of the interaction graph and of slow divergence of reciprocal interaction weights persistent connectivity can be considered as the counterpart of the notion of ultimate connectivity used in discrete time consensus protocols slow divergence of reciprocal interaction weights generalizes the assumption of cut balanced interactions we show that under these two assumptions the continuous time consensus protocol succeeds the states of all the agents converge asymptotically to a common value moreover our proof allows us to give an estimate of the rate of convergence towards the consensus we also provide examples that make us think that both of our assumptions are tight

consensus problems on networks with antagonistic interactions in a consensus protocol an agreement among agents is achieved thanks to the collaborative efforts of all agents expresses by a communication graph with nonnegative weights the question we ask in this paper is the following is it possible to achieve a form of agreement also in presence of antagonistic interactions modeled as negative weights on the communication graph the answer to this question is affirmative on signed networks all agents can converge to a consensus value which is the same for all agents except for the sign necessary and sufficient conditions are obtained to describe cases in which this is possible these conditions have strong analogies with the theory of monotone systems linear and nonlinear laplacian feedback designs are proposed

3d interpolation of irregular data with a pocs algorithm seismic surveys generally have irregular areas where data cannot be acquired these data should often be interpolated a projection onto convex sets pocs algorithm using fourier transforms allows interpolation of irregularly populated grids of seismic data with a simple iterative method that produces high quality results the original 2d image restoration method the gerchberg saxton algorithm is extended easily to higher dimensions and the 3d version of the process used here produces much better interpolations than typical 2d methods the only parameter that makes a substantial difference in the results is the number of iterations used and this number can be overestimated without degrading the quality of the results this simplicity is a significant advantage because it relieves the user of extensive parameter testing although the cost of the algorithm is several times the cost of typical 2d methods the method is easily parallelized and still completely practical

the evolution of beliefs over signed social networks we study the evolution of opinions or beliefs over a social network modeled as a signed graph the sign attached to an edge in this graph characterizes whether the corresponding individuals or end nodes are friends positive links or enemies negative links pairs of nodes are randomly selected to interact over time and when two nodes interact each of them updates its opinion based on the opinion of the other node and the sign of the corresponding link this model generalizes the degroot model to account for negative links when two adversaries interact their opinions go in opposite directions we provide conditions for convergence and divergence in expectation in mean square and in almost sure sense and exhibit phase transition phenomena for these notions of convergence depending on the parameters of the opinion update model and on the structure of the underlying graph we establish a no survivor theorem stating that the difference in opinions of any two nodes diverges whenever opinions in the network diverge as a whole we also prove a live or die lemma indicating that almost surely the opinions either converge to an agreement or diverge finally we extend our analysis to cases where opinions have hard lower and upper limits in these cases we study when and how opinions may become asymptotically clustered to the belief boundaries and highlight the crucial influence of strong or weak structural balance of the underlying network on this clustering phenomenon

convergence and state reconstruction of time varying multi agent systems from complete observability theory we study continuous time consensus dynamics for multi agent systems with undirected switching interaction graphs we establish a necessary and sufficient condition for exponential asymptotic consensus based on the classical theory of complete observability the proof is remarkably simple compared to similar results in the literature and the conditions for consensus are mild this observability based method can also be applied to the case where negatively weighted edges are present additionally as a by product of the observability based arguments we show that the nodes initial value can be recovered from the signals on the edges up to a shift of the network average