bulk universality for generalized wigner matrices consider n n hermitian or symmetric random matrices h where the distribution of the i j matrix element is given by a probability measure ij with a subexponential decay let sigma ij 2 be the variance for the probability measure ij with the normalization property that sum i sigma 2 ij 1 for all j under essentially the only condition that c le n sigma ij 2 le c 1 for some constant c 0 we prove that in the limit n the eigenvalue spacing statistics of h in the bulk of the spectrum coincide with those of the gaussian unitary or orthogonal ensemble gue or goe we also show that for band matrices with bandwidth m the local semicircle law holds to the energy scale m 1

best constants in martingale version of rosenthal s inequality the following generalization of rosenthal s inequality was proved by burkholder a 1 p s f p d ast p leq f ast p leq b p s f p d ast p for all martingales f n it is known that a p grows like sqrt p as p rightarrow infty in this paper we prove that the growth rate of b p as p rightarrow infty is p ln p

consensus of multi agent networks with aperiodic sampled communication via impulsive algorithms using position only measurements in this technical note an impulsive consensus algorithm is proposed for second order continuous time multi agent networks with switching topology the communication among agents occurs at sampling instants based on position only measurements by using the property of stochastic matrices and algebraic graph theory some sufficient conditions are obtained to ensure the consensus of the controlled multi agent network if the communication graph has a spanning tree jointly a numerical example is given to illustrate the effectiveness of the proposed algorithm

synchronization of continuous dynamical networks with discrete time communications in this paper synchronization of continuous dynamical networks with discrete time communications is studied though the dynamical behavior of each node is continuous time the communications between every two different nodes are discrete time i e they are active only at some discrete time instants moreover the communication intervals between every two communication instants can be uncertain and variable by choosing a piecewise lyapunov krasovskii functional to govern the characteristics of the discrete communication instants and by utilizing a convex combination technique a synchronization criterion is derived in terms of linear matrix inequalities with an upper bound for the communication intervals obtained the results extend and improve upon earlier work simulation results show the effectiveness of the proposed communication scheme some relationships between the allowable upper bound of communication intervals and the coupling strength of the network are illustrated through simulations on a fully connected network a star like network and a nearest neighbor network

zeroth order method for distributed optimization with approximate projections this paper studies the problem of minimizing a sum of possible nonsmooth convex functions that are corresponding to multiple interacting nodes subject to a convex state constraint set time varying directed network is considered here two types of computational constraints are investigated in this paper one where the information of gradients is not available and the other where the projection steps can only be calculated approximately we devise a distributed zeroth order method the implementation of which needs only functional evaluations and approximate projection in particular we show that the proposed method generates expected function value sequences that converge to the optimal value provided that the projection errors decrease at appropriate rates

on impulsive control of a periodically forced chaotic pendulum system we consider impulsive control of a periodically forced pendulum system which has rich chaos and bifurcation phenomena a new impulsive control method for chaos suppression of this pendulum system is developed some simple sufficient conditions for driving the chaotic state to its zero equilibrium are presented and some criteria for eventually exponentially asymptotical stability are established this work provides a rigorous theoretical analysis to support some early experimental observations on controlling chaos in the periodically forced pendulum system

a finitization of the bead process the bead process is the particle system defined on parallel lines with underlying measure giving constant weight to all configurations in which particles on neighbouring lines interlace and zero weight otherwise motivated by the statistical mechanical model of the tiling of an abc hexagon by three species of rhombi a finitized version of the bead process is defined the corresponding joint distribution can be realized as an eigenvalue probability density function for a sequence of random matrices the finitized bead process is determinantal and we give the correlation kernel in terms of jacobi polynomials two scaling limits are considered a global limit in which the spacing between lines goes to zero and a certain bulk scaling limit in the global limit the shape of the support of the particles is determined while in the bulk scaling limit the bead process kernel of boutillier is reclaimed after appropriate identification of the anisotropy parameter therein

asynchronous l 2 l filtering for discrete time stochastic markov jump systems with randomly occurred sensor nonlinearities this paper is concerned with the problem of asynchronous l 2 l filtering for discrete time stochastic markov jump systems with sensor nonlinearity the sensor nonlinearity is assumed to occur randomly according to a stochastic variable satisfying the bernoulli distribution a sufficient condition is first given such that the resultant filtering error system which is a kind of nonhomogeneous markov jump system is stochastically stable with a guaranteed l 2 l performance index then the existence criterion of the desired asynchronous filter with piecewise homogeneous markov chain is proposed in terms of a set of linear matrix inequalities a numerical example is given to show the effectiveness and potential of the developed theoretical results

brief paper h filtering for uncertain stochastic time delay systems with sector bounded nonlinearities in this paper we deal with the robust h filtering problem for a class of uncertain nonlinear time delay stochastic systems the system under consideration contains parameter uncertainties ito type stochastic disturbances time varying delays as well as sector bounded nonlinearities we aim at designing a full order filter such that for all admissible uncertainties nonlinearities and time delays the dynamics of the filtering error is guaranteed to be robustly asymptotically stable in the mean square while achieving the prescribed h disturbance rejection attenuation level by using the lyapunov stability theory and ito s differential rule sufficient conditions are first established to ensure the existence of the desired filters which are expressed in the form of a linear matrix inequality lmi then the explicit expression of the desired filter gains is also characterized finally a numerical example is exploited to show the usefulness of the results derived

universality properties of gelfand tsetlin patterns a standard gelfand tsetlin pattern of depth n is a configuration of particles in 1 ldots n times mathbb r for each r in 1 ldots n r times mathbb r is referred to as the rth level of the pattern a standard gelfand tsetlin pattern has exactly r particles on each level r and particles on adjacent levels satisfy an interlacing constraint probability distributions on the set of gelfand tsetlin patterns of depth n arise naturally as distributions of eigenvalue minor processes of random hermitian matrices of size n we consider such probability spaces when the distribution of the matrix is unitarily invariant prove a determinantal structure for a broad subclass and calculate the correlation kernel in particular we consider the case where the eigenvalues of the random matrix are fixed this corresponds to choosing uniformly from the set of gelfand tsetlin patterns whose nth level is fixed at the eigenvalues of the matrix fixing q n in 1 ldots n and letting n under the assumption that frac q n n to alpha in 0 1 and the empirical distribution of the particles on the nth level converges weakly the asymptotic behaviour of particles on level q n is relevant to free probability theory saddle point analysis is used to identify the set in which these particles behave asymptotically like a determinantal random point field with the sine kernel

stabilization of linear systems with distributed input delay and input saturation this paper is concerned with stabilization of a linear system with distributed input delay and input saturation both constant and time varying delays are considered in the case that the input delay is constant under the stabilizability assumption on an auxiliary system it is shown that the system can be stabilized by state feedback for an arbitrarily large delay as long as the open loop system is not exponentially unstable in the case that the input delay is time varying but bounded it is shown that the system can be stabilized by state feedback if the non asymptotically stable poles of the open loop system are all located at the origin in both cases stabilizing controllers are explicitly constructed by utilizing the parametric lyapunov equation based low gain design approach we recently developed it is also shown that in the presence of actuator saturation and under the same assumptions on the system these controllers achieve semi global stabilization some discussions on the assumptions we impose on the system are given a numerical example illustrates the effectiveness of the proposed stabilization approach

distributed impulsive group consensus in second order multi agent systems under directed topology this paper investigates the impulsive group consensus problems of second order multi agent systems under directed network topology with acyclic partition two distributed impulsive sampled data protocols are presented to realise group consensus for both cases with leaders and leaderless and then some simple yet generic criteria on convergence for such algorithms are established it is shown that for the case with leaderless a feature of the present protocols is to give an explicit expression of group consensus states in terms of the initial values of the agents which allows us to develop a simple approach yielding the desired group or cluster consensus while for the case of virtual leaders a pinning like tracking technique is effectively designed to regulate all the agents access to the virtual leaders respectively for the purpose of practical control strategy finally simulation results are presented to illustrate the effectiveness of the theoretical analysis

product of random projections jacobi ensembles and universality problems arising from free probability we consider the product of two independent randomly rotated projectors the square of its radial part turns out to be distributed as a jacobi ensemble we study its global and local properties in the large dimension scaling relevant to free probability theory we establish asymptotics for one point and two point correlation functions as well as properties of largest and smallest eigenvalues

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

a random matrix model from two dimensional yang mills theory we use fat graphs to give a unified treatment of various asymptotic freeness results in particular a random matrix model from two dimensional yang mills theory on the plane is presented

asymptotically liberating sequences of random unitary matrices a fundamental result of free probability theory due to voiculescu and subsequently refined by many authors states that conjugation by independent haar distributed random unitary matrices delivers asymptotic freeness in this paper we exhibit many other systems of random unitary matrices that when used for conjugation lead to freeness we do so by first proving a general result asserting asymptotic liberation under quite mild conditions and then we explain how to specialize these general results in a striking way by exploiting hadamard matrices in particular we recover and generalize results of the second named author and of tulino caire shamai and verdu

achieving the welch bound with difference sets consider a codebook containing n unit norm complex vectors in a k dimensional space in a number of applications the codebook that minimizes the maximal cross correlation amplitude i sub max is often desirable relying on tools from combinatorial number theory we construct analytically optimal codebooks meeting in certain cases the welch lower bound when analytical constructions are not available we develop an efficient numerical search method based on a generalized lloyd algorithm which leads to considerable improvement on the achieved i sub max over existing alternatives we also derive a composite lower bound on the minimum achievable i sub max that is effective for any codebook size n

multi consensus of multi agent systems with various intelligences using switched impulsive protocols in this paper multi consensus refers to that the states of multi agent systems asymptotically converge to several consistent values the concept of intelligence degree is introduced to characterize the level of agent intelligence based on that some distributed switched impulsive protocols are proposed using sampled position data and sampled velocity data alternately at sampling instants the continuous time multi agent system using the proposed protocols is equivalently transformed into a discrete time system some necessary and sufficient conditions on the communication network topology are obtained three types of multi consensus can be asymptotically achieved if and only if the directed network has a spanning tree and the feedback gains and sampling periods are chosen appropriately moreover the final states of multi consensus are analytically determined for second order multi agent systems which depend on the initial states of the agents the communication network topology and the feedback gains in the protocols numerical examples are finally presented to show the effectiveness of the proposed protocols and to verify the theoretical results

sampled data synchronization of chaotic lur e systems with time delays this paper studies the problem of sampled data control for master slave synchronization schemes that consist of identical chaotic lur e systems with time delays it is assumed that the sampling periods are arbitrarily varying but bounded in order to take full advantage of the available information about the actual sampling pattern a novel lyapunov functional is proposed which is positive definite at sampling times but not necessarily positive definite inside the sampling intervals based on the lyapunov functional an exponential synchronization criterion is derived by analyzing the corresponding synchronization error systems the desired sampled data controller is designed by a linear matrix inequality approach the effectiveness and reduced conservatism of the developed results are demonstrated by the numerical simulations of chua s circuit and neural network

impulsive multiconsensus of second order multiagent networks using sampled position data a multiconsensus problem of multiagent networks is solved in this paper where multiconsensus refers to that the states of multiple agents in each subnetwork asymptotically converge to an individual consistent value when there exist information exchanges among subnetworks a distributed impulsive protocol is proposed to achieve multiconsensus of second order multiagent networks in terms of three categories 1 stationary multiconsensus 2 the first dynamic multiconsensus and 3 the second dynamic multiconsensus this impulsive protocol utilizes only sampled position data and is implemented at sampling instants for those three categories of multiconsensus the control parameters in the impulsive protocol are designed respectively moreover necessary and sufficient conditions are derived under which each multiconsensus can be reached asymptotically several simulations are finally provided to demonstrate the effectiveness of the obtained theoretical results

optimal bounds for convergence of expected spectral distributions to the semi circular law let mathbf x x jk j k 1 n denote a hermitian random matrix with entries x jk which are independent for 1 le j le k le n we consider the rate of convergence of the empirical spectral distribution function of the matrix mathbf x to the semi circular law assuming that mathbf e x jk 0 mathbf e x jk 2 1 and that begin aligned sup n ge 1 sup 1 le j k le n mathbf e x jk 4 mu 4 infty end aligned and begin aligned sup 1 le j k le n x jk le d 0n frac 1 4 end aligned by means of a recursion argument it is shown that the kolmogorov distance between the expected spectral distribution of the wigner matrix mathbf w frac 1 sqrt n mathbf x and the semicircular law is of order o n 1

multi consensus of multi agent networks via a rectangular impulsive approach abstract a multi consensus problem is studied in multi agent networks the interaction mechanism of competition abstention cooperation among agents is introduced three rectangular impulsive protocols are proposed to solve multi consensus of second order multi agent networks with a directed topology these algorithms have the performance of dirac impulsive control and discrete time control necessary and sufficient conditions are obtained for the stationary multi consensus and the dynamic multi consensus numerical examples are provided to illustrate the effectiveness of the obtained criteria

passivity analysis for discrete time stochastic markovian jump neural networks with mixed time delays in this paper passivity analysis is conducted for discrete time stochastic neural networks with both markovian jumping parameters and mixed time delays the mixed time delays consist of both discrete and distributed delays the markov chain in the underlying neural networks is finite piecewise homogeneous by introducing a lyapunov functional that accounts for the mixed time delays a delay dependent passivity condition is derived in terms of the linear matrix inequality approach the case of markov chain with partially unknown transition probabilities is also considered all the results presented depend upon not only discrete delay but also distributed delay a numerical example is included to demonstrate the effectiveness of the proposed methods

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

sampled data discrete time coordination algorithms for double integrator dynamics under dynamic directed interaction in this article we study two sampled data based discrete time coordination algorithms for multi vehicle systems with double integrator dynamics under dynamic directed interaction for both algorithms we derive sufficient conditions on the interaction graph the damping gain and the sampling period to guarantee coordination by using the property of infinity products of stochastic matrices when the conditions on the damping gain and the sampling period are satisfied the first algorithm guarantees coordination on positions with a zero final velocity if the interaction graph has a directed spanning tree jointly while the second algorithm guarantees coordination on positions with a constant final velocity if the interaction graph has a directed spanning tree at each time interval simulation results are presented to show the effectiveness of the theoretical results

bulk universality for generalized wigner matrices with few moments in this paper we consider n times n real generalized wigner matrices whose entries are only assumed to have finite 2 varepsilon th moment for some fixed but arbitrarily small varepsilon 0 we show that the stieltjes transforms m n z of these matrices satisfy a weak local semicircle law on the nearly smallest possible scale when eta mathfrak i z is almost of order n 1 as a consequence we establish bulk universality for local spectral statistics of these matrices at fixed energy levels both in terms of eigenvalue gap distributions and correlation functions meaning that these statistics converge to those of the gaussian orthogonal ensemble in the large n limit

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

coordination and consensus of networked agents with noisy measurements stochastic algorithms and asymptotic behavior this paper considers the coordination and consensus of networked agents where each agent has noisy measurements of its neighbors states for consensus seeking we propose stochastic approximation type algorithms with a decreasing step size and introduce the notions of mean square and strong consensus although the decreasing step size reduces the detrimental effect of the noise it also reduces the ability of the algorithm to drive the individual states towards each other the key technique is to ensure a trade off for the decreasing rate of the step size by following this strategy we first develop a stochastic double array analysis in a two agent model which leads to both mean square and strong consensus and extend the analysis to a class of well studied symmetric models subsequently we consider a general network topology and introduce stochastic lyapunov functions together with the so called direction of invariance to establish mean square consensus finally we apply the stochastic lyapunov analysis to a leader following scenario

synchronization of complex dynamical networks with hybrid coupling delays on time scales by handling multitude kronecker product terms the problem of synchronization is studied for complex dynamical networks with hybrid coupling delays on time scales the hybrid coupling delays consist of both discrete and distributed coupling delays some novel and useful synchronization criteria of complex dynamical networks are derived based on stability theory of error dynamical system by employing the standard lyapunov krasovskii functional matrix expansion method to handle multitude kronecker product terms and the modified jensen s inequalities on time scale new sufficient conditions guaranteeing the global exponential stability of the origin of complex dynamical networks are established interms of linear matrix inequality lmi numerical examples are included to demonstrate the effectiveness of the proposed method

global synchronization for discrete time stochastic complex networks with randomly occurred nonlinearities and mixed time delays in this paper the problem of stochastic synchronization analysis is investigated for a new array of coupled discrete time stochastic complex networks with randomly occurred nonlinearities rons and time delays the discrete time complex networks under consideration are subject to 1 stochastic nonlinearities that occur according to the bernoulli distributed white noise sequences 2 stochastic disturbances that enter the coupling term the delayed coupling term as well as the overall network and 3 time delays that include both the discrete and distributed ones note that the newly introduced rons and the multiple stochastic disturbances can better reflect the dynamical behaviors of coupled complex networks whose information transmission process is affected by a noisy environment e g internet based control systems by constructing a novel lyapunov like matrix functional the idea of delay fractioning is applied to deal with the addressed synchronization analysis problem by employing a combination of the linear matrix inequality lmi techniques the free weighting matrix method and stochastic analysis theories several delay dependent sufficient conditions are obtained which ensure the asymptotic synchronization in the mean square sense for the discrete time stochastic complex networks with time delays the criteria derived are characterized in terms of lmis whose solution can be solved by utilizing the standard numerical software a simulation example is presented to show the effectiveness and applicability of the proposed results

a new synchronization tracking technique for uncertain discrete network with spatiotemporal chaos behaviors abstract we propose a novel scheme to achieve synchronization tracking of uncertain discrete network with spatiotemporal chaos behaviors in this work the traditional method of sliding mode control is firstly modified for researching conveniently the synchronization tracking of uncertain discrete network further the network sliding mode surface and control input are designed and their effectiveness are analyzed at the same time we also design the adaptive law to identify availably the uncertain configuration coefficient of the network sliding mode surface finally an example about the small world network is considered to illustrate the application and effectiveness of the proposed scheme

on hybrid impulsive and switching systems and application to nonlinear control in this note a new class of hybrid impulsive and switching models is introduced and their asymptotic stability properties are investigated using switched lyapunov functions some new general criteria for exponential stability and asymptotic stability with arbitrary and conditioned impulsive switching are established in addition a new hybrid impulsive and switching control strategy for nonlinear systems is developed a typical example the unified chaotic system is given to illustrate the theoretical results

cumulants for random matrices as convolutions on the symmetric group in this paper we show that free cumulants can be naturally seen as the limiting value of cumulants of matrices we define these objects as functions on the symmetric group by some convolution relations involving the generalized moments we state that some characteristic properties of the free cumulants already hold for these cumulants

restricted isometry of fourier matrices and list decodability of random linear codes we prove that a random linear code over mathbb f q with probability arbitrarily close to 1 is list decodable at radius 1 1 q epsilon with list size l o 1 epsilon 2 and rate r omega q epsilon 2 log 3 1 epsilon up to the polylogarithmic factor in 1 epsilon and constant factors depending on q this matches the lower bound l omega q 1 epsilon 2 for the list size and upper bound r o q epsilon 2 for the rate previously only existence and not abundance of such codes was known for the special case q 2 guruswami et al 2002 in order to obtain our result we employ a relaxed version of the well known johnson bound on list decoding that translates the average hamming distance between codewords to list decoding guarantees we furthermore prove that the desired average distance guarantees hold for a code provided that a natural complex matrix encoding the codewords satisfies the restricted isometry property with respect to the euclidean norm for the case of random binary

robust extended dissipative control for sampled data markov jump systems this paper investigates the problem of the sampled data extended dissipative control for uncertain markov jump systems the systems considered are transformed into markov jump systems with polytopic uncertainties and sawtooth delays by using an input delay approach the focus is on the design of a mode independent sampled data controller such that the resulting closed loop system is mean square exponentially stable with a given decay rate and extended dissipative a novel exponential stability criterion and an extended dissipativty condition are established by proposing a new integral inequality the reduced conservatism of the criteria is demonstrated by two numerical examples furthermore a sufficient condition for the existence of a desired mode independent sampled data controller is obtained by solving a convex optimisation problem finally a resistance inductance and capacitance rlc series circuit is employed to illustrate the effectiveness of the proposed approach

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

delay dependent state estimation for delayed neural networks in this letter the delay dependent state estimation problem for neural networks with time varying delay is investigated a delay dependent criterion is established to estimate the neuron states through available output measurements such that the dynamics of the estimation error is globally exponentially stable the proposed method is based on the free weighting matrix approach and is applicable to the case that the derivative of a time varying delay takes any value an algorithm is presented to compute the state estimator finally a numerical example is given to demonstrate the effectiveness of this approach and the improvement over existing ones

universality at the edge of the spectrum in wigner random matrices we prove universality at the edge for rescaled correlation functions of wigner random matrices in the limit n as a corollary we show that after proper rescaling the 1th 2nd 3rd etc eigenvalues of wigner random hermitian resp real symmetric matrix weakly converge to the distributions established by tracy and widom in g u e g o e cases

brief paper a unified synchronization criterion for impulsive dynamical networks this paper focuses on the problem of globally exponential synchronization of impulsive dynamical networks two types of impulses are considered synchronizing impulses and desynchronizing impulses in previous literature all of the results are devoted to investigating these two kinds of impulses separately thus a natural question arises is there any unified synchronization criterion which is simultaneously effective for synchronizing impulses and desynchronizing impulses in this paper a unified synchronization criterion is derived for directed impulsive dynamical networks by proposing a concept named average impulsive interval the derived criterion is theoretically and numerically proved to be less conservative than existing results numerical examples including scale free and small world structures are given to show that our results are applicable to large scale networks

multivariate analysis and jacobi ensembles largest eigenvalue tracy widom limits and rates of convergence abstract let a and b be independent central wishart matrices in p variables with common covariance and having m and n degrees of freedom respectively the distribution of the largest eigenvalue of a b 1 b has numerous applications in multivariate statistics but is difficult to calculate exactly suppose that m and n grow in proportion to p we show that after centering and scaling the distribution is approximated to second order o p 2 3 by the tracy widom law the results are obtained for both complex and then real valued data by using methods of random matrix theory to study the largest eigenvalue of the jacobi unitary and orthogonal ensembles asymptotic approximations of jacobi polynomials near the largest zero play a central role

spectral distribution of random matrices from binary linear block codes let c be a binary linear block code of length n dimension k and minimum hamming distance d over gf 2 n let d denote the minimum hamming distance of the dual code of c over gf 2 n let e gf 2 n 1 1 n be the component wise mapping e vi 1 vi for v v1 v2 vn gf 2 n finally for p n let mmb c be a p n random matrix whose rows are obtained by mapping a uniformly drawn set of size p of the codewords of c under e it is shown that for d large enough and y p n 0 1 fixed as n the empirical spectral distribution of the gram matrix of 1 n mmb c resembles that of a random i i d rademacher matrix i e the marchenko pastur distribution moreover an explicit asymptotic uniform bound on the distance of the empirical spectral distribution of the gram matrix of 1 n mmb c to the marchenko pastur distribution as a function of y and d is presented

advanced sampled data synchronization control for complex dynamical networks with coupling time varying delays abstract this study addresses sampled data control in the synchronization problem of complex dynamical networks systems with a coupling time varying delay by constructing the augmented lyapunov krasovskii functionals and using some mathematical techniques a sampled data synchronization criterion is derived as the first result with the framework of linear matrix inequalities based on the first result a sampled data synchronization control method is proposed as the second result finally the effectiveness and superiority of the proposed results will be shown by comparing the maximum sampling period with the established results in two numerical examples

synchronization of a complex dynamical network with coupling time varying delays via sampled data control abstract in this paper the synchronization problem of a complex dynamical network with coupling time varying delays via delayed sampled data controller is investigated in order to make full use of the sawtooth structure characteristic of the sampling input delay a discontinuous lyapunov functional is proposed based on the extended wirtinger inequality from a convex representation of the sector restricted nonlinearity in system dynamics the stability condition based on lyapunov stability theory is obtained by utilization of linear matrix inequality formulation to find the controller which achieves the synchronization of a complex dynamical network with coupling time varying delay finally two numerical examples are given to illustrate the effectiveness of the proposed methods

the ppt square conjecture holds generically for some classes of independent states let be a random pure state on where is a random unit vector uniformly distributed on the sphere in let be a random induced state whose distribution is and let be a random induced state following the same distribution independent of let be a random state induced by the entanglement swapping of and we show that the empirical spectrum of converges almost surely to the marcenko pastur law with parameter c 2 as and as an application we prove that the state is separable generically if are ppt entangled

the spectral edge of unitary brownian motion the brownian motion u n t t ge 0 on the unitary group converges as a process to the free unitary brownian motion u t t ge 0 as n rightarrow infty in this paper we prove that it converges strongly as a process not only in distribution but also in operator norm in particular for a fixed time t 0 we prove that the unitary brownian motion has a spectral edge there are no outlier eigenvalues in the limit we also prove an extension theorem any strongly convergent collection of random matrix ensembles independent from a unitary brownian motion also converge strongly jointly with the brownian motion we give an application of this strong convergence to the jacobi process

rate of convergence to the semi circular law a stochastic bound of order op n 1 2 for the kolmogorov distance between the spectral distribution function of an n n matrix from wigner ensemble and the distribution function of the semi circular law is obtained the result holds assuming that the twelfth moment of the entries of the matrix is uniformly bounded

brief paper second order consensus in multi agent dynamical systems with sampled position data this paper studies second order consensus in multi agent dynamical systems with sampled position data a distributed linear consensus protocol with second order dynamics is designed where both the current and some sampled past position data are utilized it is found that second order consensus in such a multi agent system cannot be reached without any sampled position data under the given protocol while it can be achieved by appropriately choosing the sampling period a necessary and sufficient condition for reaching consensus of the system in this setting is established based on which consensus regions are then characterized it is shown that if all the eigenvalues of the laplacian matrix are real then second order consensus in the multi agent system can be reached for any sampling period except at some critical points depending on the spectrum of the laplacian matrix however if there exists at least one eigenvalue of the laplacian matrix with a nonzero imaginary part second order consensus cannot be reached for sufficiently small or sufficiently large sampling periods in such cases one nevertheless may be able to find some disconnected stable consensus regions determined by choosing appropriate sampling periods finally simulation examples are given to verify and illustrate the theoretical analysis

exponential estimates and stabilization of uncertain singular systems with discrete and distributed delays this paper is concerned with exponential estimates and stabilization for a class of uncertain singular systems with discrete and distributed delays a sufficient condition which does not only guarantee the exponential stability and admissibility but also gives the estimates of decay rate and decay coefficient is established in terms of the linear matrix inequality lmi technique and a new lyapunov krasovskii functional the estimating procedure is implemented by solving a set of lmis which can be checked easily by effective algorithms under the proposed condition the algebraic subsystems possess the same decay rate as the differential ones moreover a state feedback stabilizing controller which makes the closed loop system exponentially stable and admissible with a prescribed lower bound of the decay rate is designed numerical examples are provided to illustrate the effectiveness of the theoretical results

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

consensus seeking in multiagent systems under dynamically changing interaction topologies this note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies both discrete and continuous update schemes are proposed for information consensus this note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves

approximation of haar distributed matrices and limiting distributions of eigenvalues of jacobi ensembles we develop a tool to approximate the entries of a large dimensional complex jacobi ensemble with independent complex gaussian random variables based on this and the author s earlier work in this direction we obtain the tracy widom law of the largest singular values of the jacobi emsemble moreover the circular law the marchenko pastur law the central limit theorem and the laws of large numbers for the spectral norms are also obtained

random subsets of structured deterministic frames have manova spectra abstract we draw a random subset of k k rows from a frame with n n rows vectors and m m columns dimensions where k k and m m are proportional to n n for a variety of important deterministic equiangular tight frames etfs and tight non etfs we consider the distribution of singular values of the k k subset matrix we observe that for large n n they can be precisely described by a known probability distribution wachter s manova multivariate anova spectral distribution a phenomenon that was previously known only for two types of random frames in terms of convergence to this limit the k k subset matrix from all of these frames is shown to be empirically indistinguishable from the classical manova jacobi random matrix ensemble thus empirically the manova ensemble offers a universal description of the spectra of randomly selected k k subframes even those taken from deterministic frames the same universality phenomena is shown to hold for notable random frames as well this description enables exact calculations of properties of solutions for systems of linear equations based on a random choice of k k frame vectors of n n possible vectors and has a variety of implications for erasure coding compressed sensing and sparse recovery when the aspect ratio m n m n is small the manova spectrum tends to the well known marcenko pastur distribution of the singular values of a gaussian matrix in agreement with previous work on highly redundant frames our results are empirical but they are exhaustive precise and fully reproducible

synchronization for complex dynamical networks with time delay and discrete time information the synchronization problem is studied for complex dynamical networks cdns with time delay based on discrete time communication pattern a new lyapunov functional is proposed which is positive definite at communication instants but not necessarily positive definite inside the communication intervals and can make full use of the available information about the discrete time communication pattern based on the lyapunov functional an exponential synchronization criterion is proposed to ensure the synchronization of the considered cdns the effectiveness of the developed results are shown by the numerical simulation

on eigenvalues of the sum of two random projections we study the behavior of eigenvalues of matrix p n q n where p n and q n are two n by n random orthogonal projections we relate the joint eigenvalue distribution of this matrix to the jacobi matrix ensemble and establish the universal behavior of eigenvalues for large n the limiting local behavior of eigenvalues is governed by the sine kernel in the bulk and by either the bessel or the airy kernel at the edge depending on parameters we also study an exceptional case when the local behavior of eigenvalues of p n q n is not universal in the usual sense

local spectral statistics of the addition of random matrices we consider the local statistics of h v x v u y u where v and u are independent haar distributed unitary matrices and x and y are deterministic real diagonal matrices in the bulk we prove that the gap statistics and correlation functions coincide with the gue in the limit when the matrix size n rightarrow infty under mild assumptions on x and certain rigidity assumptions on y the latter being an assumption on the convergence of the eigenvalues of y to the quantiles of its limiting spectral measure which we assume to have a density our method relies on running a carefully chosen diffusion on the unitary group and comparing the resulting eigenvalue process to dyson brownian motion our method also applies to the case when v and u are drawn from the orthogonal group our proof relies on the local law for h proved in bao et al commun math phys 349 3 947 990 2017 j funct anal 271 3 672 719 2016 adv math 319 251 291 2017 as well as the dbm convergence results of landon and yau commun math phys 355 3 949 1000 2017 and landon et al adv math 346 1137 1332 2019

observer based output feedback control of linear systems with input and output delays abstract this paper is concerned with observer based output feedback control of linear systems with both multiple input and output delays our recently developed truncated predictor feedback tpf approach for state feedback stabilization of time delay systems is generalized to the design of observers by imposing some restrictions on the open loop system two classes of observer based output feedback controllers one being finite dimensional and the other infinite dimensional are constructed it is further shown that the infinite dimensional observer based output feedback controllers can be generalized to linear systems with both time varying input and output delays it is also shown that the separation principle holds for the infinite dimensional observer based output feedback controllers but does not hold for the finite dimensional ones numerical examples are worked out to illustrate the effectiveness of the proposed approaches

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

extended dissipative synchronization of complex dynamical networks with additive time varying delay and discrete time information abstract the problem of extended dissipativity analysis of complex dynamical networks with additive time varying delays and discrete time information is considered in this article by utilizing the lyapunov functional method jensen s inequality and free weighting matrix analysis techniques we established sufficient criterion such that the complex dynamical networks is synchronized further the extended dissipativity analysis problem which contains h performance passivity performance and l 2 l performance in a unified framework is studied the derived criteria are expressed in terms of linear matrix inequalities that can be easily checked by using the standard numerical softwares illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed results

brief paper a novel stability analysis of linear systems under asynchronous samplings this article proposes a novel approach to assess the stability of continuous linear systems with sampled data inputs the method which is based on the discrete time lyapunov theorem provides easy tractable stability conditions for the continuous time model sufficient conditions for asymptotic and exponential stability are provided dealing with synchronous and asynchronous samplings and uncertain systems an additional stability analysis is provided for the cases of multiple sampling periods and packet losses several examples show the efficiency of the method

consensus of second order multi agent systems via impulsive control using sampled hetero information in this paper the consensus problem for second order multi agent systems using impulsive control with sampled hetero information is investigated necessary and sufficient conditions for sampling interval to achieve consensus for the second order multi agent systems are obtained analysis for the upper bound of sampling interval convergence performance and communication cost of the proposed control protocols are also discussed some numerical examples are given to demonstrate the effectiveness of the proposed control protocols

stability of multiagent systems with time dependent communication links we study a simple but compelling model of network of agents interacting via time dependent communication links the model finds application in a variety of fields including synchronization swarming and distributed decision making in the model each agent updates his current state based upon the current information received from neighboring agents necessary and or sufficient conditions for the convergence of the individual agents states to a common value are presented thereby extending recent results reported in the literature the stability analysis is based upon a blend of graph theoretic and system theoretic tools with the notion of convexity playing a central role the analysis is integrated within a formal framework of set valued lyapunov theory which may be of independent interest among others it is observed that more communication does not necessarily lead to faster convergence and may eventually even lead to a loss of convergence even for the simple models discussed in the present paper

universality of the local spacing distribution in certain ensembles of hermitian wigner matrices consider an n n hermitian random matrix with independent entries not necessarily gaussian a so called wigner matrix it has been conjectured that the local spacing distribution i e the distribution of the distance between nearest neighbour eigenvalues in some part of the spectrum is in the limit as n the same as that of hermitian random matrices from gue we prove this conjecture for a certain subclass of hermitian wigner matrices