new criteria of passivity analysis for fuzzy time delay systems with parameter uncertainties this paper investigates the passivity problem for a class of uncertain stochastic fuzzy nonlinear systems with mixed delays and nonlinear noise disturbances by employing an improved free weighting matrix approach the fuzzy system is based on the takagi sugeno model that is often used to represent the complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning to reflect more realistic dynamical behaviors of the system the parameter uncertainties the stochastic disturbances and nonlinearities are considered where the parameter uncertainties enter into all the system matrices the stochastic disturbances are given in the form of a brownian motion the mixed delays comprise both discrete and distributed time varying delays by taking the relationship among the time delays their lower and upper bounds into account some less conservative linear matrix inequality based delay dependent passivity criteria are obtained without ignoring any useful terms in the derivative of lyapunov functional finally numerical examples are given to demonstrate the effectiveness and merits of the proposed methods

cored hypergraphs power hypergraphs and their laplacian h eigenvalues abstract in this paper we introduce the class of cored hypergraphs and power hypergraphs and investigate the properties of their laplacian h eigenvalues from an ordinary graph one may generate a k uniform hypergraph called the kth power hypergraph of that graph power hypergraphs are cored hypergraphs but not vice versa sunflowers loose paths and loose cycles are power hypergraphs while squids generalized loose s paths and loose s cycles for 2 s k 2 are cored hypergraphs but not power graphs in general we show that the largest laplacian h eigenvalue of an even uniform cored hypergraph is equal to its largest signless laplacian h eigenvalue especially we find out these largest h eigenvalues for even uniform squids moreover we show that the largest laplacian h eigenvalue of an odd uniform squid loose path and loose cycle is equal to the maximum degree i e 2 we also compute the laplacian h spectra of the class of sunflowers when k is odd the laplacian h spectra of the loose cycle of size 3 and the loose path of length 3 are characterized as well

the first few unicyclic and bicyclic hypergraphs with largest spectral radii abstract a connected k uniform hypergraph with n vertices and m edges is called r cyclic if n m k 1 r 1 for r 1 or 2 the hypergraph is simply called unicyclic or bicyclic in this paper we investigate hypergraphs that attain largest spectral radii among all simple connected k uniform unicyclic and bicyclic hypergraphs specifically by using some edge operations the formula on power hypergraph eigenvalues the weighted incidence matrix and a result on linear unicyclic hypergraphs we determined the first five hypergraphs with largest spectral radius among all unicyclic hypergraphs and the first three over all bicyclic hypergraphs

a meshless symplectic method for two dimensional schrdinger equation with radial basis functions in this study we propose a meshless symplectic algorithm for two dimensional time dependent schrdinger equation with radial basis functions rbfs approximation theory the truncation error and global error are also investigated the numerical experiments show that the scheme is higher order accuracy easy to implement with the scattered knots furthermore the algorithm possesses a long time tracking capability

on the spectral radius of uniform hypertrees abstract we determine the unique hypertrees with maximum spectral radius among k uniform non hyper caterpillars with m edges and diameter d for 4 d m 2 among k uniform non hyper caterpillars with m edges for m 6 among k uniform hypertrees with m edges and independence number for m k 1 1 k m among k uniform hypertrees with m edges and matching number for 1 m k 1 1 k and among k uniform hypertrees with m edges and s branch vertices for 0 s m 1 2 respectively

ordering of some uniform supertrees with larger spectral radii abstract a supertree is a connected and acyclic hypergraph we study some uniform supertrees with larger spectral radii we first define a new type of edge moving operation on hypergraphs and study its applications on the comparison of the spectral radii of hypergraphs by using this new operation on some supertrees together with the general edge moving operation introduced by li shao and qi in 2015 and using a result by zhou et al in 2014 about the relation between the spectral radii of an ordinary graph and its power hypergraph we are able to determine the first eight k uniform supertrees on n vertices with the largest spectral radii

the maximum spectral radii of uniform supertrees with given degree sequences abstract this paper generalizes the breadth first search ordering on trees to k uniform supertrees by using 2 switch operation and edge moving operation on supertrees we determine the unique k uniform supertree with the maximum spectral radius among all k uniform supertrees with a given degree sequence moreover we generalize the majorization theorem on trees to k uniform supertrees

passivity and feedback passification of switched discrete time linear systems abstract this paper focuses on the passivity analysis and feedback passification for switched discrete time linear systems using multiple storage functions under a certain switching law controllers and switching laws are designed based on complete and partial state measurements respectively conditions for strict passivity of a switched discrete time system are obtained without the requirement of strict passivity of subsystems in the case of partial state measurements dynamic output feedback controllers for subsystems are designed and a switching law depending only on the state of the output feedback controllers is constructed to guarantee strict passivity of the closed loop switched system finally a numerical example is provided to demonstrate the feasibility of the theoretical results

spectra of uniform hypergraphs abstract we present a spectral theory of uniform hypergraphs that closely parallels spectral graph theory a number of recent developments building upon classical work has led to a rich understanding of symmetric hyperdeterminants of hypermatrices a k a multidimensional arrays symmetric hyperdeterminants share many properties with determinants but the context of multilinear algebra is substantially more complicated than the linear algebra required to address spectral graph theory i e ordinary matrices nonetheless it is possible to define eigenvalues of a hypermatrix via its characteristic polynomial as well as variationally we apply this notion to the adjacency hypermatrix of a uniform hypergraph and prove a number of natural analogs of basic results in spectral graph theory open problems abound and we present a number of directions for further study

on passivity of a class of discrete time switched nonlinear systems this paper analyzes the passivity and feedback passivity of discrete time switched nonlinear systems with passive and nonpassive modes that are affine in the control input when a nonpassive mode is active the increase in storage function is not necessarily bounded by the energy supplied to the switched system at every time step therefore a switched system with at least one nonpassive mode is defined to be nonpassive in the classical passivity theory in this paper we propose a framework to analyze the passivity of such switched systems in a more general sense we consider switched nonlinear systems which are affine in the control input and may consist of passive feedback passive modes and modes which cannot be rendered passive using feedback in the proposed framework we prove that a switched nonlinear system is locally feedback passive if and only if its zero dynamics are locally passive a lower bound on the ratio of total activation time between feedback passive and nonfeedback passive modes is obtained to guarantee passive zero dynamics finally we prove that two important properties of classical passivity still hold for the proposed passivity definition that is 1 output feedback control can be used to stabilize the switched system and 2 parallel and negative feedback interconnections of two such passive systems are also passive

a general product of tensors with applications abstract we study a general product of two n dimensional tensors a and b with orders m 2 and k 1 this product satisfies the associative law and is a generalization of the usual matrix product using this product many concepts and known results of tensors can be simply expressed and or proved and a number of applications of it will be given using the associative law of this tensor product and some properties on the resultant of a system of homogeneous equations on n variables we define the similarity and congruence of tensors which are also the generalizations of the corresponding relations for matrices and prove that similar tensors have the same characteristic polynomials thus the same spectra we study two special kinds of similarity permutational similarity and diagonal similarity and their applications in the study of the spectra of hypergraphs and nonnegative irreducible tensors we also define the direct product of tensors in matrix case it is also called the kronecker product and give its applications in the study of the spectra of two kinds of the products of hypergraphs we also give applications of this general product in the study of nonnegative tensors including a characterization of primitive tensors the upper bounds of primitive degrees and the cyclic indices of some nonnegative irreducible tensors

some properties of the spectral radius for general hypergraphs abstract in this paper the adjacency tensor of a general hypergraph is investigated we study the perron frobenius theorem for the general hypergraphs and obtain some relevant results based on it in particular the techniques of weighted incidence matrix and moving edge are extended to general hypergraphs for determining the structure with the maximum spectral radius a nearly m uniform supertree is both connected and acyclic in which each edge contains either m 1 or m vertices to begin with the structures obtaining the maximum spectral radius in two classes of nearly uniform supertrees are determined where one class is with given number of edges and the other is with given number of vertices

on the spectral radius of a class of non odd bipartite even uniform hypergraphs abstract in order to investigate the non odd bipartiteness of even uniform hypergraphs starting from a simple graph g we construct a generalized power of g denoted by g k s which is obtained from g by blowing up each vertex into a s set and each edge into a k 2 s set where s k 2 when s k 2 g k s is always odd bipartite we show that g k k 2 is non odd bipartite if and only if g is non bipartite and find that g k k 2 has the same adjacency respectively signless laplacian spectral radius as g so the results involving the adjacency or signless laplacian spectral radius of a simple graph g hold for g k k 2 in particular we characterize the unique graph with minimum adjacency or signless laplacian spectral radius among all non odd bipartite hypergraphs g k k 2 of fixed order and prove that 2 5 is the smallest limit point of the non odd bipartite hypergraphs g k k 2 in addition we obtain some results for the spectral radii of the weakly irreducible nonnegative tensors

perron frobenius theorem for nonnegative multilinear forms and extensions we prove an analog of perron frobenius theorem for multilinear forms with nonnegative coefficients and more generally for polynomial maps with nonnegative coefficients we determine the geometric convergence rate of the power algorithm to the unique normalized eigenvector

the first two largest spectral radii of uniform supertrees with given diameter abstract a supertree is a connected and acyclic hypergraph let s m d k be the set of k uniform supertrees with m edges and diameter d in this paper we determine the supertrees with the first two largest spectral radii among all supertrees in s m d k for 3 d m 1

efficient conversion of mixed logical dynamical systems into an equivalent piecewise affine form for hybrid systems described by switched linear difference equations linear threshold conditions automata and propositional logic conditions described in mixed logical dynamical form this note describes two algorithms for transforming such systems into an equivalent piecewise affine form where equivalent means that for the same initial conditions and input sequences the trajectories of the system are identical the proposed techniques exploit ideas from mixed integer programming and multiparametric programming

passivity analysis and passification of discrete time hybrid systems for discrete time hybrid systems in piecewise affine or piece wise polynomial pwp form this note proposes sufficient passivity analysis and synthesis criteria based on the computation of piecewise quadratic or pwp storage functions by exploiting linear matrix inequality techniques and sum of squares decomposition methods passivity analysis and synthesis of passifying controllers can be carried out through standard semidefinite programming packages providing a tool particularly important for stability of interconnected heterogeneous dynamical systems

losslessness feedback equivalence and the global stabilization of discrete time nonlinear systems in this paper a necessary and sufficient condition for a nonlinear system of the form spl sigma given by x k 1 f x k g x k u k y k h x k j x k u k to be lossless is given and it is shown that a lossless system can be globally asymptotically stabilized by output feedback if and only if the system is zero state observable then we investigate conditions under which spl sigma can be rendered lossless via smooth state feedback in particular we show that this is possible if and only if the system in question has relative degree spl lcub 0 0 spl rcub and has lossless zero dynamics under suitable controllability like rank conditions we prove that nonlinear systems having relative degree spl lcub 0 0 spl rcub and lossless zero dynamics can be globally stabilized by smooth state feedback as a consequence we obtain sufficient conditions for a class of cascaded systems to be globally stabilizable the global stabilization problem of the nonlinear system spl sigma without output is also investigated in this paper by means of feedback equivalence some of the results are parallel to analogous ones in continuous time but in many respects the theory is substantially different and many new phenomena appear

on some properties of the α spectral radius of the k uniform hypergraph abstract in this paper we show how the spectral radius changes under the edge grafting operations on connected k uniform hypergraphs we characterize the extremal hypertree for spectral radius among k uniform non caterpillar hypergraphs with given order size and diameter we also characterize the supertree with the second largest spectral radius among all k uniform supertrees on n vertices

the p spectral radius of k partite and k chromatic uniform hypergraphs abstract the p spectral radius of an r uniform hypergraph g of order n is defined for every real number p 1 as p g max x 1 p x n p 1 r i 1 i r e g x i 1 x i r it generalizes several hypergraph parameters including the lagrangian the spectral radius and the number of edges this paper presents solutions to several extremal problems about the p spectral radius of k partite and k chromatic hypergraphs of order n two of the main results are i let k r 2 and let g be a k partite r graph of order n for every p 1 p g p t k r n unless g t k r n where t k r n is the complete k partite r graph of order n with parts of size n k or n k ii let k 2 and let g be a k chromatic 3 graph of order n for every p 1 p g p q k 3 n unless g q k 3 n where q k 3 n is a complete k chromatic 3 graph of order n with classes of size n k or n k the latter statement generalizes a result of mubayi and talbot

ordering trees by their largest eigenvalues abstract the set of trees with n vertices is denoted by t n hofmeister has determined the first five values of the largest eigenvalue of trees in t n and the corresponding trees for these values linear algebra appl 260 1997 43 in other words an order of the first five trees in t n by their largest eigenvalues has been given focus on the same purpose we shall give a partition for trees in t n first in the this paper and then extend this order to the eighth tree

uniform hypergraphs with the first two smallest spectral radii abstract the spectral radius of a uniform hypergraph g is the maximum modulus of the eigenvalues of the adjacency tensor of g for k 2 among connected k uniform hypergraphs with m 1 edges we show that the k uniform loose path with m edges is the unique one with smallest spectral radius and we also determine the unique ones with second smallest spectral radius when m 2

on the two largest eigenvalues of trees abstract very little is known about upper bounds for the largest eigenvalues of a tree that depend only on the vertex number starting from a classical upper bound for the largest eigenvalue some refinements can be obtained by successively removing trees from consideration the results can be used to characterize those trees that maximize the second largest eigenvalue this corrects a result from the literature and it includes a proof of a conjecture of neumaier the main tool for this endeavor is the theory of partial engenvectors

convex relaxations for l 2 gain analysis of piecewise affine polynomial systems this paper proposes some sufficient conditions based on the computation of polynomial and piecewise polynomial storage functions for gain analysis of discrete time piecewise affine or piecewise polynomial systems the computation of such storage functions is performed by means of convex optimisation techniques via the sum of squares decomposition of multivariate polynomials

stability and stabilizability of switched linear systems a survey of recent results during the past several years there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems this paper aims to briefly survey recent results in this field first the stability analysis for switched systems is reviewed we focus on the stability analysis for switched linear systems under arbitrary switching and we highlight necessary and sufficient conditions for asymptotic stability after a brief review of the stability analysis under restricted switching and the multiple lyapunov function theory the switching stabilization problem is studied and a variety of switching stabilization methods found in the literature are outlined then the switching stabilizability problem is investigated that is under what condition it is possible to stabilize a switched system by properly designing switching control laws note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature a necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here

on relationships among passivity positive realness and dissipativity in linear systems the notions of passivity and positive realness are fundamental concepts in classical control theory but the use of the terms has varied for lti systems these two concepts capture the same essential property of dynamical systems that is a system with this property does not generate its own energy but only stores and dissipates energy supplied by the environment this paper summarizes the connection between these two concepts for continuous and discrete time lti systems beyond that relationships are provided between classes of strictly passive systems and classes of positive real systems the more general framework of dissipativity is introduced to connect passivity and positive realness and also to survey other energy based results the frameworks of passivity indices and conic systems are discussed to connect to passivity and dissipativity after surveying relevant existing results some clarifying results are presented these involve connections between classes of passive systems and finite gain l2l2 stability as well as asymptotic stability additional results are given to clarify some of the more subtle conditions between classes of these systems and stability results this paper surveys existing connections between classes of passive and positive real systems and provides results that clarify more subtle connections between these concepts

the effect on the spectral radius of r graphs by grafting or contracting edges abstract let h n r be the set of all connected r graphs with given size n in this paper we investigate the effect on the spectral radius of r uniform hypergraphs by grafting or contracting an edge and then give the ordering of the r graphs with small spectral radius over h n r when n 20

symmetric nonnegative tensors and copositive tensors abstract we first prove two new spectral properties for symmetric nonnegative tensors we prove a maximum property for the largest h eigenvalue of a symmetric nonnegative tensor and establish some bounds for this eigenvalue via row sums of that tensor we show that if an eigenvalue of a symmetric nonnegative tensor has a positive h eigenvector then this eigenvalue is the largest h eigenvalue of that tensor we also give a necessary and sufficient condition for this we then introduce copositive tensors this concept extends the concept of copositive matrices symmetric nonnegative tensors and positive semi definite tensors are examples of copositive tensors the diagonal elements of a copositive tensor must be nonnegative we show that if each sum of a diagonal element and all the negative off diagonal elements in the same row of a real symmetric tensor is nonnegative then that tensor is a copositive tensor some further properties of copositive tensors are discussed