a solution procedure for second order difference equations and its application to electromagnetic wave diffraction in a wedge shaped region this paper proposes an efficient solution procedure for second order functional difference equations and outlines this procedure through investigating electromagnetic wave diffraction by a canonical structure comprising an impedance wedge and an impedance sheet bisecting the exterior region of the wedge applying the sommerfeld malyuzhinets technique to the original boundary value problem yields a linear system of equations for the two coupled spectral functions eliminating one spectral function leads to a second order difference equation for the other the chief steps in this work consist of transforming the second order equation into a simpler one by making use of a generalized malyuzhinets function and in expressing the solution to the latter in an integral form with help of the so called s integrals from this integral expression one immediately obtains a fredholm equation of the second kind for points on the imaginary axis of the complex plane solving this integral equation by means of the well known quadrature method enables us to calculate the sought for spectral function inside the basic strip via an interpolation formula and outside it via an analytic extension the second spectral function is obtained through its dependence upon the first the uniform asymptotic solution which is of particular interest in the geometrical theory of diffraction follows by evaluating the sommerfeld integrals in the far field from the exact one several examples demonstrate the efficiency and accuracy of the proposed procedure as well as typical behaviour of the far field solutions for such a canonical problem of diffraction theory

faces of the cone of euclidean distance matrices characterizations structure and induced geometry in this paper we obtain new characterizations of the faces of the cone of euclidean distance matrices in one case the characterization is based on a special subspace associated with each distance matrix in other case on linear restrictions of coordinate matrices we also relate the faces to the supporting hyperplanes of the cone and we show how the supporting hyperplanes induce certain geometry on the configurations that belong to that face

h control of markov jump systems with time varying delay and incomplete transition probabilities this paper addresses the h control of continuous markov jump systems with interval time varying delay and incomplete transition probabilities a linearization method is used to handle unknown transition probabilities meanwhile the wirtinger based integral inequality and the reciprocally convex technique are adopted to deal with the time varying delay additionally a separating technique is employed to tackle the coupling among lyapunov variable system matrix and controller parameter based on these strategies new sufficient conditions for the closed loop system to be stochastically stable are formulated in the framework of linear matrix inequalities finally numerical examples are provided to demonstrate the effectiveness of the proposed method

passivity based sliding mode control of uncertain singular markovian jump systems with time varying delay and nonlinear perturbations in this paper a sliding mode control smc with passivity of uncertain singular markovian jump systems smjs with time varying delay and nonlinear perturbations is investigated firstly a new integral type switching surface is designed secondly by introducing free matrix method and lyapunov functionals a delay dependent sufficient condition in terms of strict linear matrix inequalities lmi is derived for the resulting sliding mode dynamics such that the closed loop system is stochastically admissible and robustly passive for all admissible uncertainties thirdly a smc law is synthesized to drive the system trajectories onto the predefined switching surface in a finite time finally numerical examples are provided to demonstrate the effectiveness of the proposed method

moore penrose inverse of a euclidean distance matrix abstract we obtain expressions for the moore penrose inverse of a euclidean distance matrix edm that are determined only by the positive semidefinite matrix associated with the edm the results complement formulas for the moore penrose inverse of an edm given in balaji and bapat 2007 2 a formula for the inverse of a principal submatrix of an edm is also derived whose expression uses the schur complement of the laplacian of the edm as an application we obtain an expression for the terminal wiener index of a tree

on cartesian product of euclidean distance matrices abstract if a r m m and b r n n we define the product a b as a b a j n j m b where denotes the kronecker product and j n is the n n matrix of all ones we refer to this product as the cartesian product of a and b since if d 1 and d 2 are the distance matrices of graphs g 1 and g 2 respectively then d 1 d 2 is the distance matrix of the cartesian product g 1 g 2 we study cartesian products of euclidean distance matrices edms we prove that if a and b are edms then so is the product a b we show that if a is an edm and u is symmetric then a u is an edm if and only if u c j n for some c it is shown that for edms a and b a b is spherical if and only if both a and b are spherical if a and b are edms then we derive expressions for the rank and the moore penrose inverse of a b in the final section we consider the product a b for arbitrary matrices for a r m m b r n n we show that all nonzero minors of a b of order m n 1 are equal an explicit formula for a nonzero minor of order m n 1 is proved the result is shown to generalize the familiar fact that the determinant of the distance matrix of a tree on n vertices does not depend on the tree and is a function only of n

on certain linear mappings between inner product and squared distance matrices abstract we obtain the spectral decomposition of four linear mappings the first is a mapping of the linear hull of all centered inner product matrices onto the linear hull of all the induced squared distance matrices it is based on the natural generalization of the cosine law of elementary euclidean geometry the other three mappings studied are 1 the adjoint and 1 extensions and applications particularly to multidimensional scaling are discussed in some detail

further results on exponential estimates of markovian jump systems with mode dependent time varying delays this technical note studies the problem of exponential estimates for markovian jump systems with mode dependent interval time varying delays a novel lyapunov krasovskii functional lkf is constructed with the idea of delay partitioning and a less conservative exponential estimate criterion is obtained based on the new lkf illustrative examples are provided to show the effectiveness of the proposed results

stabilization of discrete time markovian jump linear systems via time delayed controllers this paper is concerned with the stabilization problem for a class of discrete time markovian jump linear systems with time delays both in the system state and in the mode signal the delay in the system state may be time varying the delay in the mode signal is manifested as a constant mismatch of the modes between the controller and the system we first show that the resulting closed loop system is a time varying delayed markovian jump linear system with extended state space then a sufficient condition is proposed for the design of a controller such that the closed loop system is stochastically stable finally numerical simulation is used to illustrate the developed theory

output feedback control of markovian jump repeated scalar nonlinear systems this paper is concerned with the induced l2 dynamic output feedback controller dofc design problem for discrete time markovian jump repeated scalar nonlinear systems by employing both the switching sequence dependent lyapunov function approach and the positive definite diagonally dominant lyapunov function technique a sufficient condition is first established which guarantees the underlying system to be stochastically stable with an induced l2 disturbance attenuation performance then the desired full or reduced order dofcs are designed by using projection approach cone complementarity linearization procedure is employed to cast the nonconvex feasibility problem into a sequential minimization problem finally a numerical example is presented to show the effectiveness of the proposed methods

positive definite completions of partial hermitian matrices abstract the question of which partial hermitian matrices some entries specified some free may be completed to positive definite matrices is addressed it is shown that if the diagonal entries are specified and principal minors composed of specified entries are positive then if the undirected graph of the specified entries is chordal a positive definite completion necessarily exists furthermore if this graph is not chordal then examples exist without positive definite completions in case a positive definite completion exists there is a unique matrix in the class of all positive definite completions whose determinant is maximal and this matrix is the unique one whose inverse has zeros in those positions corresponding to unspecified entries in the original partial hermitian matrix additional observations regarding positive definite completions are made

majorization for the eigenvalues of euclidean distance matrices abstract this paper investigates the relation between the eigenvalues of a euclidean distance matrix edm and those of the corresponding positive semidefinite matrix more precisely let d 1 and d 2 be two edms and let b 1 and b 2 be the corresponding positive semidefinite matrices such that d i b i i 1 2 in this paper when the eigenvalues of b 1 majorizes those of b 2 a condition under which the eigenvalues of d 1 majorizes those of d 2 is derived

the real positive definite completion problem for a simple cycle abstract we consider the question of whether a real partial positive definite matrix in which the specified off diagonal entries consist of a full n cycle has a positive definite completion this lies in contrast to the previously studied chordal case we give two solutions in one we describe about n 2 independent conditions on angles associated with a normalization of the data that are necessary and sufficient the second is more computational and allows presentation of all positive definite completions as well as answering the existence question

connections between the real positive semidefinite and distance matrix completion problems abstract though the real symmetric positive semidefinite psd matrices and the euclidean distance matrices are closely related exact relationships between the corresponding completion problems are not apparent we establish strong partial relationships of two types this permits the transfer of some insights from one problem to the other and allows computational tools for the psd problem to be used for the distance problem

diffraction of a normally incident plane wave by an impedance wedge with its exterior bisected by a semi infinite impedance sheet this paper reports an application of a previously proposed procedure to diffraction of a normally incident arbitrarily polarized plane electromagnetic wave by a canonical structure which consists of a wedge with different face impedances and a semi infinite impedance sheet bisecting the exterior of the wedge the use of the sommerfeld malyuzhinets technique converts the original boundary value problem into a system of linear equations for two coupled spectral functions eliminating one of them we get a second order difference equation for the other spectral function from this function and the boundary condition on the upper wedge face we construct an even and in the basic strip regular new spectral function then we transform the second order equation into a simpler one by means of a generalized malyuzhinets function spl chi sub spl phi spl alpha and express the solution to the latter in an integral form with help of the so called s integrals solving a fredholm equation of the second kind for points on the imaginary axis of the complex plane which follows from the integral representation enables one to compute the sought for function the second spectral function is obtained via its dependence upon the first one we present a first order uniform asymptotic solution as well as numerical results

l2 l filtering for neutral markovian switching system with mode dependent time varying delays and partially unknown transition probabilities this paper investigates the problem of l 2 l filtering for neutral markovian switching systems with partially unknown transition probabilities for different system mode and delay mode the system under consideration involves discrete and mode dependent time varying delays based on the lyapunov krasovskii functional an approach to design a filter such that the filtering error system is stochastically stable with a prescribed l 2 l performance by using free weighting matrices free connection weighting matrix method and convex combination approach sufficient conditions for the existence of l 2 l filters are expressed in terms of linear matrix inequalities lmis which can be solved by using matlab lmi control toolbox a numerical example is given to illustrate the effectiveness and potential of the proposed method

graph rigidity via euclidean distance matrices abstract let g v e be an incomplete graph with node set v edge set e and nonnegative weights ij s on the edges let each edge v i v j be viewed as a rigid bar of length ij which can rotate freely around its end nodes a realization of a graph g is an assignment of coordinates in some euclidean space to each node of g in this paper we consider the problem of determining whether or not a given realization of a graph g is rigid we show that each realization of g can be epresented as a point in a compact convex set r m and that a generic realization of g is rigid if and only if its corresponding point is a vertex of i e an extreme point with full dimensional normal cone

stability analysis for continuous systems with two additive time varying delay components this paper presents a new result of stability analysis for continuous systems with two additive time varying delay components which represent a general class of delay systems with strong application background in network based control systems this criterion is expressed as a set of linear matrix inequalities which can be readily tested by using standard numerical software a numerical example is provided to show the effectiveness and advantage of the proposed stability condition

mean square stochastic stability of linear time delay system with markovian jumping parameters this paper deals with the mean square stochastic stability of the class of linear time delay systems with markovian jumping parameters a delay independent sufficient condition for checking the stochastic stability of this class of systems is established a numerical example is given to show the usefulness of the proposed theoretical results

further results on h control for discrete time markovian jump time delay systems abstractthis paper studies the problem of h control for a class of discrete time markovian jump systems with time delay the purpose is to improve the existing results on h controller design for markovian jump systems a novel summation inequality is presented and an improved stability criterion for the system is derived by utilising the new inequality which is proved to be less conservative than most results in the literature then the state feedback controller is designed which guarantees the stochastic stability of the closed loop system with a given disturbance attenuation numerical examples are provided to illustrate the effectiveness and advantages of the proposed techniques

on euclidean distance matrices abstract if a is a real symmetric matrix and p is an orthogonal projection onto a hyperplane then we derive a formula for the moore penrose inverse of pap as an application we obtain a formula for the moore penrose inverse of an euclidean distance matrix edm which generalizes formulae for the inverse of a edm in the literature to an invertible spherical edm we associate a laplacian matrix which we define as a positive semidefinite n n matrix of rank n 1 and with zero row sums and prove some properties known results for distance matrices of trees are derived as special cases in particular we obtain a formula due to graham and lovasz for the inverse of the distance matrix of a tree it is shown that if d is a nonsingular edm and l is the associated laplacian then d 1 l is nonsingular and has a nonnegative inverse finally infinitely divisible matrices are constructed using edms

wiener hopf solution for impenetrable wedges at skew incidence a new wiener hopf approach for the solution of impenetrable wedges at skew incidence is presented mathematical aspects are described in a unified and consistent theory for angular region problems solutions are obtained using analytical and numerical analytical approaches several numerical tests from the scientific literature validate the new technique and new solutions for anisotropic surface impedance wedges are solved at skew incidence the solutions are presented considering the geometrical and uniform theory of diffraction coefficients total fields and possible surface wave contributions

new results on stability of discrete time systems with time varying state delay this note is concerned with the stability analysis of discrete time systems with time varying state delay by defining new lyapunov functions and by making use of novel techniques to achieve delay dependence several new conditions are obtained for the asymptotic stability of these systems the merit of the proposed conditions lies in their less conservativeness which is achieved by circumventing the utilization of some bounding inequalities for cross products between two vectors and by paying careful attention to the subtle difference between the terms sigmam k dk k 1 middot and sigma m k dm k 1 middot which is largely ignored in the existing literature these conditions are shown via several examples to be much less conservative than some existing result

on stabilization of uncertain linear systems with jump parameters in this paper we study the problem of robust stabilizability of the class of uncertain linear systems with markovian jumping parameters under the assumption of complete access to the continuous state the stochastic stabilizability of the nominal system and the boundedness of the system s uncertainties sufficient conditions which guarantee the robust stability of the uncertain systems are presented which are in terms of a set of coupled algebraic riccati equations a numerical example is given to illustrate the potential of the proposed technique

control of markovian jump discrete time systems with norm bounded uncertainty and unknown delay this paper studies the problem of control for discrete time delay linear systems with markovian jump parameters the system under consideration is subjected to both time varying norm bounded parameter uncertainty and unknown time delay in the state and markovian jump parameters in all system matrices we address the problem of robust state feedback control in which both robust stochastic stability and a prescribed h sub spl infin performance are required to be achieved irrespective of the uncertainty and time delay it is shown that the above problem can be solved if a set of coupled linear matrix inequalities has a solution

the asymptotic stability and exponential stability of nonlinear stochastic differential systems with markovian switching and with polynomial growth abstract this paper discusses the asymptotic stability and exponential stability of nonlinear stochastic differential systems with markovian switching sdswmss the systems coefficients are assumed to satisfy local lipschitz condition and polynomial growth condition by applying some novel techniques we propose some conditions under which such sdswmss are asymptotically stable and exponentially stable nontrivial examples are provided to illustrate our results

multispherical euclidean distance matrices abstract in this paper we introduce new necessary and sufficient conditions for an euclidean distance matrix to be multispherical the class of multispherical distance matrices studied in this paper contains not only most of the matrices studied by hayden et al 1996 2 but also many other multispherical structures that do not satisfy the conditions in hayden et al 1996 2 we also study the information provided by the origin of coordinates when it is placed at the center of the spheres and the origin representation property is satisfied these vectors associated with the origin of coordinates generate a number of supporting hyperplanes for a family of multispherical matrices and also describe part of the null space of the corresponding distance matrices

circum euclidean distance matrices and faces abstract we study the structure of circum euclidean distance matrices those euclidean distance matrices generated by points lying on a hypersphere we show for example that such euclidean distance matrices are characterized as having constant row sums and they constitute the interior of the cone of all euclidean distance matrices also we provide a formula for computing the radius of a representing configuration in the smallest embedding dimension r and show that rk d r 1 finally we obtain a geometric characterization of the faces of this cone given a configuration of points and its euclidean distance matrix d any matrix in the minimal face containing d comes from a configuration that is a linear perturbation of the points that generate d

robust controller design for uncertain systems with time delays lmi approach we present a robust output feedback controller design method for linear systems with norm bounded time varying parameter uncertainties and time varying delays in both states and controls and sufficient conditions for the existence of the robust output feedback controller of any order are given in terms of three linear matrix inequalities lmis furthermore we provide a parameterization of all robust controllers from the positive definite solutions of the lmis

distance matrices and regular figures abstract a regular figure which includes all regular polygons is a set of points on a hypersphere whose center coincides with their centroid we characterize all regular figures as those whose points generate a euclidean distance matrix edm with eigenvector e the vector of all ones restricting the classical maps of schoenberg gower and critchley for all edms to the subcone of edms with eigenvector e yields new geometrical information about the generating points and a simple formula for the radius of the hypersphere

on designing of sliding mode control for stochastic jump systems in this note we consider the problems of stochastic stability and sliding mode control for a class of linear continuous time systems with stochastic jumps in which the jumping parameters are modeled as a continuous time discrete state homogeneous markov process with right continuous trajectories taking values in a finite set by using linear matrix inequalities lmis approach sufficient conditions are proposed to guarantee the stochastic stability of the underlying system then a reaching motion controller is designed such that the resulting closed loop system can be driven onto the desired sliding surface in a limited time it has been shown that the sliding mode control problem for the markovian jump systems is solvable if a set of coupled lmis have solutions a numerical example is given to show the potential of the proposed techniques

mixed h sub 2 h sub spl infin control of discrete time markovian jump linear systems in this paper we consider the mixed h sub 2 h sub spl infin control problem for the class of discrete time linear systems with parameters subject to markovian jump linear systems it is assumed that both the state variable and the jump variable are available to the controller the transition probability matrix may not be exactly known but belongs to an appropriate convex set for this controlled discrete time markovian jump linear system the problem of interest can be stated in the following way find a robust with respect to the uncertainty on the transition markov probability matrix mean square stabilizing state and jump feedback controller that minimizes an upper bound for the h sub spl infin norm under the restriction that the h sub spl infin norm is less than a prespecified value spl delta the problem of the determination of the smallest h sub spl infin norm is also addressed we present an approximate version of these problems via linear matrix inequality optimization

on cell matrices a class of euclidean distance matrices abstract in this paper we study the set of cell matrices and its relationship with the cone of positive semidefinite diagonal matrices the set forms a convex polyhedral cone in the linear space of symmetric matrices we describe the faces of the cone and its polar we also provide a new linear inequality associated with cell matrices

exact solution to diffraction problem by wedges with a class of anisotropic impedance faces oblique incidence of a plane electromagnetic wave this paper studies diffraction of an obliquely incident arbitrarily polarized plane electromagnetic wave by an anisotropic impedance wedge with an opening angle 2 spl phi between 0 and 2 spl pi and presents a closed form exact solution to a class of impedance wedge faces and the related uniform asymptotic solution uas on use of a unitary similarity transform the boundary conditions on the wedge faces is brought into a form which makes the exactly soluble class of impedance faces evident the exact solution is found with help of the sommerfeld malyuzhinets 1896 1958 technique a generalized malyuzhinets function spl chi sub spl phi and the so called s integrals a standard procedure yields therefrom the uas the exact solution agrees with known analytical results in special cases and the numerical results of uas are confirmed by that of parabolic equation method pem

delay dependent robust stabilization of uncertain state delayed systems this paper concerns a problem of robust stabilization of uncertain state delayed systems a new delay dependent stabilization condition using a memoryless controller is formulated in terms of matrix inequalities an algorithm involving convex optimization is proposed to design a controller guaranteeing a suboptimal maximal delay such that the system can be stabilized for all admissible uncertainties

stability analysis of a class of hybrid stochastic retarded systems under asynchronous switching the stability of a class of hybrid stochastic retarded systems hsrss with an asynchronous switching controller is investigated in this model the controller design relies on the observed jumping parameters which are however delayed and thus can not be measured in real time precisely this delayed time interval referred to as the asynchronous switching interval is markovian and dependent on the actual switching signal the sufficient conditions under which the system is either stochastically asymptotic stable or input to state stable are obtained by applying the extended razumikhin type theorem to the asynchronous switching interval these results are less conservative as it is only required that the designed lyapunov function is non decreasing it is shown that the stability of the considered system can be guaranteed by a sufficiently small mode transition rate of the underlying markov process which is a conclusion similar to that in asynchronous deterministic switched systems the effectiveness and correctness of the obtained results are finally verified by a numerical example

robust h fuzzy control for uncertain nonlinear markovian jump systems with time varying delay this paper investigates the problem of robust h fuzzy control for a class of uncertain nonlinear markovian jump systems with time varying delay the class of systems under consideration is described by the takagi sugeno fuzzy model the goal of the paper is to design a mode dependent fuzzy state feedback controller such that the closed loop system is stochastically stable with a prescribed h performance of disturbance attenuation for all admissible parameter uncertainties in order to obtain a less conservative control design a new stochastic lyapunov krasovskii functional is first constructed by decomposing the delay interval into multiple equidistant subintervals then by employing this functional a delay decomposition approach to the design of robust h fuzzy controllers is developed in terms of linear matrix inequalities finally two examples are given to illustrate the merit and usability of the proposed design method

robust stability and control for uncertain neutral time delay systems in this article the problem of robust stability and stabilisation for a class of uncertain neutral systems with discrete and distributed time delays is considered by utilising a new lyapunov functional based on the idea of delay partitioning approach we employ the linear matrix inequality technique to derive delay dependent criteria which ensures the robust stability of uncertain neutral systems the obtained stability conditions are formulated in terms of linear matrix inequalities that can easily be solved by using standard software packages further the result is extended to study the robust stabilisation for uncertain neutral systems with parameter uncertainties a state feedback controller is proposed to guarantee the robust asymptotic stabilisation for uncertain systems and the controller is constructed in terms of the solution to a set of matrix inequalities finally numerical examples are presented to illustrate the effectiveness and conservatism of the obtained results it is shown that the

robust cal h _ infty filtering for markovian jump systems with randomly occurring nonlinearities and sensor saturation the finite horizon case this paper addresses the robust h filtering problem for a class of discrete time varying markovian jump systems with randomly occurring nonlinearities and sensor saturation two kinds of transition probability matrices for the markovian process are considered namely the one with polytopic uncertainties and the one with partially unknown entries the nonlinear disturbances are assumed to occur randomly according to stochastic variables satisfying the bernoulli distributions the main purpose of this paper is to design a robust filter over a given finite horizon such that the h disturbance attenuation level is guaranteed for the time varying markovian jump systems in the presence of both the randomly occurring nonlinearities and the sensor saturation sufficient conditions are established for the existence of the desired filter satisfying the h performance constraint in terms of a set of recursive linear matrix inequalities simulation results demonstrate the effectiveness of the developed filter design scheme

on stability independent of delay for linear systems a new criterion for asymptotic stability of solutions of certain linear differential difference equations independent of the delay duration is given in terms of solutions of a complex lyapunov matrix equation

the cell matrix closest to a given euclidean distance matrix abstract cell matrix introduced by jaklic and modic 6 is a special euclidean distance matrix edm that has a quite attractive and simple structure it is of interest to approximate an edm by a cell matrix in this paper we consider the problem of finding the cell matrix that is closest to a given edm with respect to the frobenius norm the majorization ordering of the eigenvalues of a cell matrix is also discussed

controllability stabilizability and continuous time markovian jump linear quadratic control consideration is given to the control of continuous time linear systems that possess randomly jumping parameters which can be described by finite state markov processes the relationship between appropriately defined controllability stabilizability properties and the solution of the infinite time jump linear quadratic jlq optimal control problems is also examined although the solution of the continuous time markov jlq problem with finite or infinite time horizons is known only sufficient conditions for the existence of finite cost constant stabilizing controls for the infinite time problem appear in the literature in this paper necessary and sufficient conditions are established these conditions are based on new definitions of controllability observability stabilizability and detectability that are appropriate for continuous time markovian jump linear systems these definitions play the same role for the jlq problem as the deterministic properties do for the linear quadratic regulator lqr problem

robust decentralized stabilization of markovian jump large scale systems a neighboring mode dependent control approach abstract this paper is concerned with the decentralized stabilization problem for a class of uncertain large scale systems with markovian jump parameters the controllers use local subsystem states and neighboring mode information to generate local control inputs a sufficient condition involving rank constrained linear matrix inequalities is proposed for the design of such controllers a numerical example is given to illustrate the developed theory

brief paper new results on stabilization of markovian jump systems with time delay this paper studies the problem of stochastic stabilization for a class of markovian jump systems with time delay a new delay dependent stochastic stability criterion on the stochastic stability of the system is derived based on a novel lyapunov krasovskii functional lkf approach the equivalence and superiority to existing results are demonstrated then a state feedback controller which guarantees the stochastic stability of the closed loop system is designed illustrative examples are provided to show the reduced conservatism and effectiveness of the proposed techniques

practical stability controllability and optimal control of stochastic markovian jump systems with time delays the notions of the practical stability in probability and in the pth mean and the practical controllability in probability and in the pth mean are introduced for some stochastic systems with markovian jump parameters and time varying delays sufficient conditions on such practical properties are obtained by using the comparison principle and the lyapunov function methods besides for a class of stochastic nonlinear systems with markovian jump parameters and time varying delays existence conditions of optimal control are discussed particularly for linear systems optimal control and the corresponding index value are presented for a class of quadratic performance indices with jumping weighted parameters

characterization of multispherical and block structures of euclidean distance matrices abstract this paper presents some new characterizations of euclidean distance matrices edms of special structures more specifically we discuss multispherical and block structured edms each of which can be viewed as a generalization of spherical edm we focus on a well known inequality that characterizes spherical edms and extend it to the sets of multispherical and block structured edms some related results are also presented

the best euclidian fit to a given distance matrix in prescribed dimensions abstract in this paper we determine the euclidean distance matrix which is closest to a given not necessarily euclidian one we admit a wide class of appropriate matrix norms as measures of closeness majorization results on sums of eigenvalues of symmetric matrices serve as basic tools

properties of euclidean and non euclidean distance matrices abstract a distance matrix d of order n is symmetric with elements 1 2 d ij 2 where dii 0 d is euclidean when the 1 2 n n 1 quantities dij can be generated as the distances between a set of n points x n p in a euclidean space of dimension p the dimensionality of d is defined as the least value of p rank x of any generating x in general p 1 and p 2 are also acceptable but may include imaginary coordinates even when d is euclidean basic properties of euclidean distance matrices are established in particular when rank d it is shown that depending on whether etd e is not or is zero the generating points lie in either p 1 dimensions in which case they lie on a hypersphere or in p 2 dimensions in which case they do not the notation e is used for a vector all of whose values are one when d is non euclidean its dimensionality p r s will comprise r real and s imaginary columns of x and r s are invariant for all generating x of minimal rank higher ranking representations can arise only from p 1 r 1 s or p 1 r s 1 or p 2 r 1 s 1 so that not only are r s invariant but they are both minimal for all admissible representations x

a novel technique for the solution of second order difference equations the class of second order difference equations that arise in the diffraction of a plane wave at skew incidence on an impedance wedge is investigated for a typical equation which was solved by the introduction of elliptic integrals it is shown that the solution can be obtained in a very trivial manner from a convolution type integral equation and the results are in complete agreement with those previously found

memoryless h sup spl infin controllers for state delayed systems in this note a memoryless h sup spl infin controller for the state delayed system is presented the controller is a delay independent stabilizer for the state delayed system which also reduces the h sup spl infin norm of the closed loop transfer function from the disturbance to the controlled output to a prescribed level the controller can be obtained by solving a modified riccati equation

approximation by matrices positive semidefinite on a subspace abstract we obtain the best approximation to a matrix by matrices positive semidefinite on a subspace as a by product we present two new characterizations of euclidean distance matrices

approximate and exact completion problems for euclidean distance matrices using semidefinite programming abstract a partial pre distance matrix a is a matrix with zero diagonal and with certain elements fixed to given nonnegative values the other elements are considered free the euclidean distance matrix completion problem chooses nonnegative values for the free elements in order to obtain a euclidean distance matrix edm the nearest or approximate euclidean distance matrix problem is to find a euclidean distance matrix edm that is nearest in the frobenius norm to the matrix a when the free variables are discounted in this paper we introduce two algorithms one for the exact completion problem and one for the approximate completion problem both use a reformulation of edm into a semidefinite programming problem sdp the first algorithm is based on an implicit equation for the completion that for many instances provides an explicit solution the other algorithm is based on primal dual interior point methods that exploit the structure and sparsity included are results on maps that arise that keep the edm and sdp cones invariant we briefly discuss numerical tests

solution of a second order difference equation using the bilinear relations of riemann a recently proposed technique to solve a class of second order functional difference equations arising in electromagnetic diffraction theory is further investigated by applying it to a case of intermediate complexity the proposed approach is conceptually simple and relies on first obtaining well defined branched solutions to a pair of associated first order difference equations the construction of these branched expressions leads to an equation system whose solution requires relationships akin to riemann s bilinear relations for differentials of the first and third kinds their derivation necessitates the application of cauchy s theorem on riemann surfaces of in this particular instance genera one and three branch free solutions of the second order difference equation are then obtained by taking appropriate linear combinations of the branched solutions of the first order equations analysis and computation demonstrate that the resulting expressions have the desired analytical properties and recover known solutions in the appropriate limit

brief paper h filtering for 2d markovian jump systems this paper is concerned with the problem of h filtering for 2d discrete markovian jump systems the mathematical model of 2d jump systems is established upon the well known roesser model our attention is focused on the design of a full order filter which guarantees the filtering error system to be mean square asymptotically stable and has a prescribed h disturbance attenuation performance sufficient conditions for the existence of a desired filter are established in terms of linear matrix inequalities lmis and the corresponding filter design is cast into a convex optimization problem which can be efficiently solved by using commercially available numerical software a numerical example is provided to illustrate the effectiveness of the proposed design method

computing the nearest euclidean distance matrix with low embedding dimensions euclidean distance embedding appears in many high profile applications including wireless sensor network localization where not all pairwise distances among sensors are known or accurate the classical multi dimensional scaling cmds generally works well when the partial or contaminated euclidean distance matrix edm is close to the true edm but otherwise performs poorly a natural step preceding cmds would be to calculate the nearest edm to the known matrix a crucial condition on the desired nearest edm is for it to have a low embedding dimension and this makes the problem nonconvex there exists a large body of publications that deal with this problem some try to solve the problem directly and some are the type of convex relaxations of it in this paper we propose a numerical method that aims to solve this problem directly our method is strongly motivated by the majorized penalty method of gao and sun for low rank positive semi definite matrix optimization problems the basic geometric object in our study is the set of edms having a low embedding dimension we establish a zero duality gap result between the problem and its lagrangian dual problem which also motivates the majorization approach adopted numerical results show that the method works well for the euclidean embedding of network coordinate systems and for a class of problems in large scale sensor network localization and molecular conformation

sliding mode control of markovian jump systems with incomplete information on time varying delays and transition rates this paper is concerned with robust sliding mode control smc for continuous time markovian jump delay systems with incomplete transition rates trs the time varying delays are unclear and just bounded sometimes two methods are employed to investigate this control issue one is movement decomposition method by which reduced order sliding mode dynamics is obtained the other is via sliding mode observer and full order sliding mode dynamics is obtained on the estimation space in both cases sufficient conditions are established in terms of a set of coupled linear matrix inequalities lmis to ensure the sliding mode dynamics to be mean square exponentially stable moreover novel sliding mode controllers which need not full knowledge on time varying delays are synthesized to guarantee the reachability of the prescribed sliding surface finally numerical examples are provided to illustrate the effectiveness of the proposed methods

the cone of distance matrices abstract the geometry of the cone of euclidean distance matrices edms is analyzed using a new characterization of an edm the facial structure and the angle that edms of embedding dimension one make with the center ray are found this result follows from a complete analysis of the critical points of the distance function in frobenius norm from the matrix e consisting of zero diagonal and ones elsewhere to the edms of embedding dimension one

h disturbance attenuation for state delayed systems in this note the differential game and dissipation inequality are applied to the disturbance attenuation or h control for linear systems with delayed state firstly a simple sufficient condition on the existence of a suboptimal h state feedback controller is given which is independent of delay and an observer based dynamic output feedback solution is presented in terms of riccati inequalities or riccati equations secondly a sufficient condition on the existence of a delay dependent state feedback is presented and the criterion is presented by a matrix inequality which can be solved by numerical methods

robust h sub spl infin control of uncertain markovian jump systems with time delay this paper is concerned with the robust stochastic stabilizability and robust h sub spl infin disturbance attenuation for a class of uncertain linear systems with time delay and randomly jumping parameters the transition of the jumping parameters is governed by a finite state markov process sufficient conditions on the existence of a robust stochastic stabilizing and spl gamma suboptimal h sub spl infin state feedback controller are presented using the lyapunov functional approach it is shown that a robust stochastically stabilizing h sub spl infin state feedback controller can be constructed through the numerical solution of a set of coupled linear matrix inequalities