polynomial bound on the number of scattering poles on montre que dans la diffusion par un potentiel infiniment differentiable a support compact les poles de l operateur de diffusion sont a distribution polynomiale

problems on time varying port controlled hamiltonian systems geometric structure and dissipative realization to apply time varying port controlled hamiltonian pch systems to practical control designs two basic problems should be dealt with one is how to provide such time varying systems a geometric structure to guarantee the completeness of representations in mathematics and the other is how to express the practical system under consideration as a time varying pch system which is called the dissipative hamiltonian realization problem the paper investigates the two basic problems a suitable geometric structure for time varying pch systems is proposed first then the dissipative realization problem of time varying nonlinear systems is investigated and serval new methods and sufficient conditions are presented for the realization

feedback boundary control of linear hyperbolic systems with relaxation we consider boundary stabilization for one dimensional systems of linear hyperbolic partial differential equations with relaxation structure such equations appear in many applications by combining weighted lyapunov functions the structure is used to derive new stabilization results the result is illustrated with an application to boundary stabilization of water flows in open canals

interconnection and damping assignment passivity based control of port controlled hamiltonian systems passivity based control pbc is a well established technique that has shown to be very powerful to design robust controllers for physical systems described by euler lagrange el equations of motion for regulation problems of mechanical systems which can be stabilized shaping only the potential energy pbc preserves the el structure and furthermore assigns a closed loop energy function equal to the difference between the energy of the system and the energy supplied by the controller thus we say that stabilization is achieved via energy balancing unfortunately these nice properties of el pbc are lost when used in other applications which require shaping of the total energy for instance in electrical or electromechanical systems or even some underactuated mechanical devices our main objective in this paper is to develop a new pbc theory which extends to a broader class of systems the aforementioned energy balancing stabilization mechanism and the structure invariance towards this end we depart from the el description of the systems and consider instead port controlled hamiltonian models which result from the network modelling of energy conserving lumped parameter physical systems with independent storage elements and strictly contain the class of el models

displacement rank of the drazin inverse in this paper we study the displacement rank of the drazin inverse both sylvester displacement and the generalized displacement are discussed we present upper bounds for the ranks of the displacements of the drazin inverse the general results are applied to the group inverse of a structured matrix such as close to toeplitz generalized cauchy toeplitz plus hankel and bezoutians

generalized inversion of finite rank hankel and toeplitz operators with rational matrix symbols abstract the goal of the paper is a generalized inversion of finite rank hankel operators and hankel or toeplitz operators with block matrices having finitely many rows to attain it a left coprime fractional factorization of a strictly proper rational matrix function and the bezout equation are used generalized inverses of these operators and generating functions for the inverses are explicitly constructed in terms of the fractional factorization

the perturbation theory for the drazin inverse and its applications abstract let a and e be n n matrices and b a e denote the drazin inverse of a by ad we give an upper bound for the relative error b d a d a d under certain circumstances an error bound for the solution for the singular equations ax b b r a is also considered

index splitting for the drazin inverse and the singular linear system abstract an index splitting of a singular matrix a for the drazin inverse and its relative iterations for the minimal p norm solution of the singular linear system ax b b r a k k ind a are presented some convergence criteria are also given and a method is developed for constructing the index splitting of matrix a

feedback boundary control of linear hyperbolic equations with stiff source term abstractwe consider feedback boundary control of hyperbolic systems with stiff source terms by combining weighted lyapunov functions the structure is used to derive stabilisation results in our analysis we give stabilising feedback laws that allow a robust uniform exponential stabilisation for a whole range of values of an uncertain parameter with a decay rate that is independent of the parameter in particular we are interested in the limit case when the relaxation parameter approaches zero the result is illustrated with the numerical analysis on the decay rate of the lyapunov function in terms of the stiff parameter and an application to boundary stabilisation of gas dynamics in pipes

dirac structures and boundary control systems associated with skew symmetric differential operators associated with a skew symmetric linear operator on the spatial domain a b we define a dirac structure which includes the port variables on the boundary of this spatial domain this dirac structure is a subspace of a hilbert space naturally associated with this dirac structure is an infinite dimensional system we parameterize the boundary port variables for which the c 0 semigroup associated with this system is contractive or unitary furthermore this parameterization is used to split the boundary port variables into inputs and outputs similarly we define a linear port controlled hamiltonian system associated with the previously defined dirac structure and a symmetric positive operator defining the energy of the system we illustrate this theory on the example of the timoshenko beam

stability for the multifrequency inverse medium problem abstract the solution of a multi frequency 1d inverse medium problem consists of recovering the refractive index of a medium from measurements of the scattered waves for multiple frequencies in this paper rigorous stability estimates are derived when the frequency takes value in a bounded interval it is showed that the ill posedness of the inverse medium problem decreases as the width of the frequency interval becomes larger more precisely under certain regularity assumptions on the refractive index the estimates indicate that the power in holder stability is an increasing function of the largest value in the frequency band finally a lipschitz stability estimate is obtained for the observable part of the medium function defined through a truncated trace formula

pseudospectra of semiclassical pseudo differential operators the pseudo spectra or spectral instability of non selfadjoint operators is a topic of current interest in applied mathematics for example in computational fluid dynamics it affects the study of the stability of laminar flows in fact even for the most basic flows the computations entirely fails to predict what is observed in the experiments the explanation is that for non normal operators the resolvent could be very large far away from the spectrum which makes computation of the eigenvalues impossible the occurence of false eigenvalues is due to the existence of quasi modes i e approximate local solutions to the eigenvalue problem the quasi modes appear since the nirenberg treves condition psi is not satisfied for topological reasons less

scattering asymptotics for riemann surfaces in this article we prove the optimal polynomial lower bound for the number of resonances of a surface with hyperbolic ends we also give weyl asymptotics for the relative scattering phase of such a surface the proofs are based on trace formulae analogous to those of the euclidean odd dimensional scattering the main technical ingredient is a new proof of the poisson formula theorem 5 7 which is applicable in the euclidean case as well our lower bound seems to be the first example of an optimal polynomial lower bound for the number of resonances holding for a general class of higher dimensional elliptic operators with no symmetries the previous general lower bounds or asymptotics were either nonoptimal 25 58 9 one dimensional or radial 65 67 and 54 41 1 or they required some degeneracy of the

several complex variables and the distribution of resonances in potential scattering we study resonances associated to schrodinger operators with compactly supported potentials on d d 3 odd we consider potentials depending holomorphically on a parameter open image in new window for certain such families for all z except those in a pluripolar set the associated resonance counting function has order of growth d

sharp polynomial bounds on the number of scattering poles of radial potentials abstract it is shown that for scattering by a radially symmetric potential in r n n odd the number of poles in a disk of radius r satisfies an estimate n r c n r 1 n this bound is sharp as shown by the special case of potentials nonvanishing at the boundary where n r k n a n r n 1 o 1 a being the diameter of the support

generalized invertibility of hankel and toeplitz matrices abstract a result for the computation of the moore penrose inverse of hankel matrices over the field of the complex numbers is given by heinig and rost in this note some methods of characterizing and computing generalized inverses of hankel and toeplitz matrices over fields and over rings with the extended rao condition are presented the results were obtained by combining classical theory on the special structure of those classes of matrices with recent theory on generalized invertibility

approximate dissipative hamiltonian realization and construction of local lyapunov functions the key in applying energy based control approach is to be able to express the system under consideration as a dissipative hamiltonian system i e to obtain dissipative hamiltonian realization dhr for the system in general the precise dhr form is hard to obtain for nonlinear dynamic systems when a precise dhr does not exist for a dynamic system or such a precise realization is difficulty to obtain it is necessary to consider its approximate realization this paper investigates approximate dhr and construction of local lyapunov functions for time invariant nonlinear systems it is shown that every nonlinear affine system has an approximate dhr if linearization of the system is controllable based on the diagonal normal form of nonlinear dynamic systems a new algorithm is established for the approximate dhr finally we present the concept of kth degree approximate lyapunov function and provide a method to construct such a lyapunov function example studies show that the methodology presented in this paper is very effective

distribution of poles for scattering on the real line abstract the density of scattering poles is shown to be proportional to the length of the convex hull of the support of the potential in the case of a potential with finite singularities at the endpoints of the support asymptotic formulae for the poles are given while in the c 0 case an example of a potential with infinitely many scattering poles on i r is constructed the scattering amplitude of a compactly supported potential is also characterized

on an intrinsic formulation of time variant port hamiltonian systems in this contribution we present an intrinsic description of time variant port hamiltonian systems as they appear in modeling and control theory this formulation is based on the splitting of the state bundle and the use of appropriate covariant derivatives which guarantees that the structure of the equations is invariant with respect to time variant coordinate transformations in particular we will interpret our covariant system representation in the context of control theoretic problems typical examples are time variant error systems related to trajectory tracking problems which allow for a hamiltonian formulation furthermore we will analyze the concept of collocation and the balancing interaction of power flows in an intrinsic fashion

energy based lyapunov functions for forced hamiltonian systems with dissipation in this paper we propose a constructive procedure to modify the hamiltonian function of forced hamiltonian systems with dissipation in order to generate lyapunov functions for nonzero equilibria a key step in the procedure which is motivated from energy balance considerations standard in network modeling of physical systems is to embed the system into a larger hamiltonian system for which a series of casimir functions can be easily constructed interestingly enough for linear systems the resulting lyapunov function is the incremental energy thus our derivations provide a physical explanation to it an easily verifiable necessary and sufficient condition for the applicability of the technique in the general nonlinear case is given some examples that illustrate the method are given

simultaneous stabilization of a set of nonlinear port controlled hamiltonian systems this paper investigates simultaneous stabilization of a set of nonlinear port controlled hamiltonian pch systems and proposes a number of results on the design of simultaneous stabilization controllers for the pch systems firstly the case of two pch systems is studied using the dissipative hamiltonian structural properties the two systems are combined to generate an augmented pch system with which some results on the control design are then obtained for the case that there exist parametric uncertainties in the two systems hamiltonian structures an adaptive simultaneous stabilization controller is proposed when there are external disturbances and parametric uncertainties in the two systems two simultaneous stabilization controllers are designed for the systems one is a robust controller and the other is a robust adaptive one secondly the case of more than two pch systems is investigated and a new result is proposed for the simultaneous stabilization of the systems finally two illustrative examples are studied by using the results proposed in this paper simulations show that the simultaneous stabilization controllers obtained in this paper work very well

additive results for the wg drazin inverse abstract in this paper we prove the formula for the expression a b d w in terms of a b w a d w b d w assuming some conditions for a b and w here s d w denotes the generalized w weighted drazin inverse of a linear bounded operator s on a banach space

the drazin invertibility of the difference and the sum of two idempotent operators in this note some equivalents are established of the drazin invertibility of differences and sums of idempotent operators on a hilbert space

pseudo spectral methods for the spatial symplectic reduction of open systems of conservation laws a reduction method is presented for systems of conservation laws with boundary energy flow it is stated as a generalized pseudo spectral method which performs exact differentiation by using simultaneously several approximation spaces generated by polynomials bases and suitable choices of port variables the symplecticity of this spatial reduction method is proved when used for the reduction of both closed and open systems of conservation laws for any choice of collocation points i e for any polynomial bases the symplecticity of some more usual collocation schemes is discussed and finally their accuracy on approximation of the spectrum on the example of the ideal transmission line is discussed in comparison with the suggested reduction scheme

generalized inverses of hankel and toeplitz mosaic matrices abstract hankel and toeplitz mosaic matrices are block matrices with hankel or toeplitz blocks respectively it is shown that hankel and toeplitz mosaic matrices possess reflexive generalized inverses which are bezoutians furthermore the bezoutian structure of the moore penrose and group inverses is investigated

on drazin inverse of singular toeplitz matrix in this paper we show that the drazin inverse of singular toeplitz matrix can be represented as a sum of products of lower and upper triangular toeplitz matrices and give the explicit expression which generalizes the well known result by gohberg and semencul regarding the inverse of toeplitz matrix

grobner basis computation of drazin inverses with multivariate rational function entries in this paper we show how to apply grobner bases to compute the drazin inverse of a matrix with multivariate rational functions as entries when the coefficients of the rational functions depend on parameters we give sufficient conditions for the drazin inverse to specialize properly in addition we extend the method to weighted drazin inverses we present an empirical analysis that shows a good timing performance of the method

on the solution of singular linear systems of algebraic equations by semiiterative methods for a square matrixt n n where i t is possibly singular we investigate the solution of the linear fixed point problemx tx c by applying semiiterative methods sim s to the basic iterationx0 n xk tck 1 c k 1 such problems arise if one splits the coefficient matrix of a linear systemax b of algebraic equations according toa m n m nonsingular which leads tox m 1nx m 1b tx c even ifx tx c is consistent there are cases where the basic iteration fails to converge namely ift possesses eigenvalues 1 with 1 or if 1 is an eigenvalue oft with nonlinear elementary divisors in these cases and also ifx tx c is incompatible we derive necessary and sufficient conditions implying that a sim tends to a vector hat x which can be described in terms of the drazin inverse of i t we further give conditions under which hat x is a solution or a least squares solution of i t x c

on representations and integrability of mathematical structures in energy conserving physical systems in the present paper we elaborate on the underlying hamiltonian structure of interconnected energy conserving physical systems it is shown that a power conserving interconnection of port controlled generalized hamiltonian systems leads to an implicit generalized hamiltonian system and a power conserving partial interconnection to an implicit port controlled hamiltonian system the crucial concept is the notion of a generalized dirac structure defined on the space of energy variables or on the product of the space of energy variables and the space of flow variables in the port controlled case three natural representations of generalized dirac structures are treated necessary and sufficient conditions for closedness or integrability of dirac structures in all three representations are obtained the theory is applied to implicit port controlled generalized hamiltonian systems and it is shown that the closedness condition for the dirac structure leads to strong conditions on the input vector fields

some results on the generalized drazin inverse of operator matrices the generalized drazin inverse m d of a 2 2 operator matrix is considered where a x and d y are generalized drazin invertible expressions for the generalized drazin inverse m d of operator matrix m in terms of the individual blocks a b c d a d and d d are derived under some conditions

lagrangian modeling of switching electrical networks in this paper a general and systematic method is presented to model topologically complete electrical networks with or without multiple or single switches within the euler lagrange framework apart from the physical insight that can be obtained in this way the framework has proven to be useful for the application of passivity based control techniques which on a case by case basis already has shown to be useful for the control of power converters within the class of switching electrical networks the switches are assumed to be ideal and pulse width modulation is taken into account magnetic coupling of inductive elements is also included in the framework

control by interconnection and standard passivity based control of port hamiltonian systems the dynamics of many physical processes can be suitably described by port hamiltonian ph models where the importance of the energy function the interconnection pattern and the dissipation of the system is underscored to regulate the behavior of ph systems it is natural to adopt a passivity based control pbc perspective where the control objectives are achieved shaping the energy function and adding dissipation in this paper we consider the pbc techniques of control by interconnection cbi and standard pbc in cbi the controller is another ph system connected to the plant through a power preserving interconnection to add up their energy functions while in standard pbc energy shaping is achieved via static state feedback in spite of the conceptual appeal of formulating the control problem as the interaction of dynamical systems the current version of cbi imposes a severe restriction on the plant dissipation structure that stymies its practical application on the other hand standard pbc which is usually derived from a uninspiring and non intuitive ldquopassive output generationrdquo viewpoint is one of the most successful controller design techniques the main objectives of this paper are 1 to extend the cbi method to make it more widely applicable in particular to overcome the aforementioned dissipation obstacle 2 to show that various popular variants of standard pbc can be derived proceeding from a unified perspective 3 to establish the connections between cbi and standard pbc proving that the latter is obtained restricting the former to a suitable subset providing a nice geometric interpretation to standard pbc and comparing the size of the set of ph plants for which they are applicable

achievable casimirs and its implications on control of port hamiltonian systems in this paper we extend results on interconnections of port hamiltonian systems to infinite dimensional port hamiltonian systems and to mixed finite and infinite dimensional port hamiltonian systems the problem of achievable dirac structures is now studied for systems with dissipation in the finite dimensional infinite dimensional and the mixed finite and infinite dimensional case we also characterize the set of achievable casimirs and study its application for the control of port hamiltonian systems

sum rules for jacobi matrices and their applications to spectral theory we discuss the proof of and systematic application of case s sum rules for jacobi matrices of special interest is a linear combination of two of his sum rules which has strictly positive terms among our results are a complete classification of the spectral measures of all jacobi matrices j for which j j 0 is hilbert schmidt and a proof of nevai s conjecture that the szego condition holds if j j 0 is trace class

boundary stabilization of hyperbolic balance laws with characteristic boundaries abstract this article is concerned with boundary stabilization of one dimensional linear hyperbolic systems with characteristic boundaries we assume that the systems satisfy a physically relevant structural stability condition for hyperbolic relaxation problems which describe various non equilibrium phenomena by introducing new and simple lyapunov functions the structural stability condition is used to derive stabilization results for problems with characteristic boundaries the result is illustrated with an application to the transport of neurofilaments in axons a phenomenon studied in neuroscience

convergence properties of krylov subspace methods for singular linear systems with arbitrary index abstract krylov subspace methods have been recently considered to solve singular linear systems ax b in this paper we derive the necessary and sufficient conditions guaranteeing that a krylov subspace method converges to a vector adb px0 where ad is the drazin inverse of a and p is the projection p i a d a let k be the index of a we further show that a d b px 0 x 0 r a k 1 n a is a generalized least squares solution of ax b in r a k n a finally we present the convergence bounds for the quasi minimal residual algorithm qmr and transpose free quasi minimal residual algorithm tfqmr the index k of a in this paper can be arbitrary which extends to the main results of freund and hochbruck numer linear algebra appl 1 1994 403 420 that only considers the case k 1

on the resonances and eigenvalues for a 1d half crystal with localised impurity we consider the schrdinger operator h on the half line with a periodic potential p plus a compactly supported potential q for generic p its essential spectrum has an infinite sequence of open gaps we determine the asymptotics of the resonance counting function and show that for sufficiently high energy each non degenerate gap contains exactly one eigenvalue or antibound state giving asymptotics for their positions conversely for any potential q and for any sequences n 0 1 and xn 0 there exists a potential p such that xn is the length of the n th gap n and h has exactly n eigenvalues and 1 n antibound state in each high energy gap moreover we show that between any two eigenvalues in a gap there is an odd number of antibound states and hence deduce an asymptotic lower bound on the number of antibound states in an adiabatic limit

energy shaping of distributed parameter port hamiltonian systems based on finite element approximation the main contribution of this paper is a procedure for the control by energy shaping via casimir generation of infinite dimensional port hamiltonian systems based on a particular finite element approximation the proposed approach is justified by the fact that the adopted spatial discretization technique is able to preserve casimir functions in the closed loop system when going from the distributed to the approximated lumped parameter system besides the intrinsic difficulties related to the large number of state variables the finite element model is generally given in terms of a dirac structure and is completely a causal which implies that the plant dynamics is not given in standard input state output form but as a set of daes consequently the classical energy casimir method has to be extended in order to deal with dynamical systems with constraints usually appearing in the form of lagrangian multipliers the general methodology is illustrated with the help of an example in which the distributed parameter system is a lossless transmission line

distribution of scattering resonances for generic schrodinger operators abstract let v be the schrodinger operator acting on l 2 r d c with d 3 odd here v is a bounded real or complex valued function vanishing outside the closed ball of center 0 and radius a if v belongs to the class m a of potentials introduced by christiansen we show that when r the resonances of v scaled down by the factor r are asymptotically distributed with respect to an explicit probability distribution on the lower unit half disc of the complex plane the rate of convergence is also considered for subclasses of potentials

port hamiltonian modeling of a nonlinear timoshenko beam with piezo actuation in this paper we develop a mathematical model for the dynamics of a nonlinear timoshenko beam with piezoelectric actuation this model can then be used to design controllers with the goal of achieving a desired shape of the beam the control scheme can be used for several applications e g vibration control in structures or shape control for high precision structures like inflatable space reflectors the starting point of the control design is modeling for control we do this in the framework of port hamiltonian ph modeling which has favorable properties such as passivity and a hamiltonian representing the energy and serving as a lyapunov function that can be exploited for controller design an important property of the ph modeling framework is that it facilitates modeling multiphysics systems or systems which consist of several subsystems where all parts are modeled separately and then can be interconnected easily this is possible because any interconnection of finite dimensional ph systems yiel

on moore penrose inverses of toeplitz matrices abstract the moore penrose inverses of toeplitz matrices can always be represented as a sum of products of lower and upper triangular toeplitz matrices which extends the well known theorem by gohberg and semencul regarding the inverses of toeplitz matrices

brief generalized hamiltonian realization of time invariant nonlinear systems a key step in applying the hamiltonian function method is to express the system under consideration into a generalized hamiltonian system with dissipation which yields the so called generalized hamiltonian realization ghr in this paper we investigate the problem of ghr several new methods and the corresponding sufficient conditions are presented a major result is that if the jacobian matrix of a time invariant nonlinear system is nonsingular the system has a ghr whose structure matrix and hamiltonian function are given in simple forms then the orthogonal decomposition method and a sufficient condition for the feedback dissipative realization are proposed

painleve formulas of the limiting distributions for nonnull complex sample covariance matrices in a recent study of large non null sample covariance matrices a new sequence of functions gener alizing the gue tracy widom distribution of random matrix theory was obtained this paper derives painleve formulas of these functions and use them to prove that they are indeed distribution functions applications of these new distribution functions to last passage percolation queues in tandem and to tally asymmetric simple exclusion process are also discussed as a part of the proof a representation of orthogonal polynomials on the unit circle in terms of an operator on a discrete set is presented

pid passivity based control of port hamiltonian systems in this note we address the problem of stabilization of port hamiltonian systems via the ubiquitous proportional integral derivative pid controller the design is based on passivity theory hence the first step is to identify all passive outputs of the system which is the first contribution of the paper adding a pid around this signal ensures that the closed loop system is mathcal l 2 stable for all positive pid gains global stability and or global attractivity of a desired constant equilibrium is also guaranteed for a new class of systems for which a lyapunov function can be constructed a second contribution is to prove that this class that is identified via some easily verifiable integrability conditions is strictly larger than the ones previously reported in the literature comparisons of the proposed pid controller with control by interconnection passivity based control are also discussed

explicit group inverse of an innovative patterned matrix in this paper we present an innovative patterned matrix rfpl toeplitz matrix is neither the extension of toeplitz matrix nor its special case we show that the group inverse of this new patterned matrix can be represented as the sum of products of lower and upper triangular toeplitz matrices first the explicit expression of the group inverse of an rfpl toeplitz matrix is obtained second the decomposition of the group inverse is given finally an example demonstrates availability of the two methods for the group inverse

asymptotic number of scattering resonances for generic schrodinger operators let v be the schrodinger operator acting on l 2 mathbb r d mathbb c with d geq 3 odd here v is a bounded real or complex function vanishing outside the closed ball of center 0 and of radius a let n v r denote the number of resonances of v with modulus r we show that if the potential v is generic in a sense of pluripotential theory then n v r c d a dr d o r d 3 over 16 epsilon quad mbox as r to infty for any e 0 where c d is a dimensional constant

generalized drazin inverses of anti triangular block matrices abstract in this paper we give formulae for the generalized drazin inverse m d of an anti triangular matrix m a b c 0 in two different ways one is to express m d in terms of a d with arbitrary b and c the other is to express m d in terms of b d and c d with arbitrary a moreover the results are applied to obtain generalized drazin inverses of various structured matrices and some special cases are analyzed

stabilization analysis of time delay hamiltonian systems in the presence of saturation abstract the stabilization of a class of hamiltonian systems with state time delay and input saturation is addressed in this paper sufficient conditions are derived by using lyapunov krasovskii functional theorem to guarantee the systems as well as the resulted closed loop systems by output feedback to be asymptotically stable when input saturation effectively occurs a numerical example is presented to illustrate the effectiveness of the obtained results in this paper

resonances for dirac operators on the half line abstract we consider the 1d dirac operator on the half line with compactly supported potentials we study resonances as the poles of scattering matrix or equivalently as the zeros of modified fredholm determinant we obtain the following properties of the resonances 1 asymptotics of counting function 2 estimates on the resonances and the forbidden domain

some properties of conservative port contact systems the dynamics of open irreversible thermodynamic systems that is systems including both the balance equation of the energy and the entropy has been formulated as contact vector fields with generating functions depending on some external control variable and called conservative port contact systems in this paper we relate the dynamical properties of these systems equilibrium points asymptotic stability to properties of the generating functions the contact hamiltonian functions we show that the equilibrium points of the system satisfy certain conditions involving the contact hamiltonian function we also consider lyapunov s first theorem to emphasize a stability criterion for the equilibrium points in terms of this contact hamiltonian function and relate it to some thermodynamical properties these results are then related to the physical phenomena that are taking place in the system

displacement structure theory and applications in this survey paper we describe how strands of work that are important in two different fields matrix theory and complex function theory have come together in some work on fast computational algorithms for matrices with what we call displacement structure in particular a fast triangularization procedure can be developed for such matrices generalizing in a striking way an algorithm presented by schur 1917 j reine angew math 147 1917 pp 205 232 in a paper on checking when a power series is bounded in the unit disc this factorization algorithm has a surprisingly wide range of significant applications going far beyond numerical linear algebra we mention among others inverse scattering analytic and unconstrained rational interpolation theory digital filter design adaptive filtering and state space least squares estimation

an energy preserving description of nonlinear beam vibrations in modal coordinates abstract conserved quantities are identified in the equations describing large amplitude free vibrations of beams projected onto their linear normal modes this is achieved by writing the geometrically exact equations of motion in their intrinsic or hamiltonian form before the modal transformation for nonlinear free vibrations about a zero force equilibrium it is shown that the finite dimensional equations of motion in modal coordinates are energy preserving even though they only approximate the total energy of the infinite dimensional system for beams with constant follower forces energy like conserved quantities are also obtained in the finite dimensional equations of motion via casimir functions the duality between space and time variables in the intrinsic description is finally carried over to the definition of a conserved quantity in space which is identified as the local cross sectional power numerical examples are used to illustrate the main results

schrodinger operators in the twentieth century this paper reviews the past fifty years of work on spectral theory and related issues in nonrelativistic quantum mechanics

conditions on shifted passivity of port hamiltonian systems abstract in this paper we examine the shifted passivity property of port hamiltonian systems shifted passivity accounts for the fact that in many applications the desired steady state values of the input and output variables are nonzero and thus one is interested in passivity with respect to the shifted signals we consider port hamiltonian systems with strictly convex hamiltonian and derive conditions under which shifted passivity is guaranteed in case the hamiltonian is quadratic and state dependency appears in an affine manner in the dissipation and interconnection matrices our conditions reduce to negative semidefiniteness of an appropriately constructed constant matrix moreover we elaborate on how these conditions can be extended to the case when the shifted passivity property can be enforced via output feedback thus paving the path for controller design stability of forced equilibria of the system is analyzed invoking the proposed passivity conditions the utility and relevance of the results are illustrated with their application to a 6th order synchronous generator model as well as a controlled rigid body system

asymptotic distribution of resonances in one dimension abstract we determine the leading asymptotics of the resonance counting function for a class of schrodinger operators in one dimension whose potentials may have non compact support

brief paper power shaping control of reaction systems the cstr case power shaping control is a recent approach for the control of nonlinear systems based on the physics of the dynamical system it rests on the formulation of the dynamics in the brayton moser form one of the main obstacles for using the power shaping approach is to write the dynamics in the required form since a partial differential equation system submitted to sign constraints has to be solved this work comes within the framework of control design approaches that could possibly generate a closer link between the notions of energy that are specific to reaction systems as derived from thermodynamics concepts and the dynamic system stability theory the objective of this paper is to address the design of power shaping control to reaction systems and more particularly the step of solving the partial differential equation system in order to illustrate the approach we have selected the classical yet complex continuous stirred tank reactor cstr as a case study we show how using the power shaping approach leads to a global lyapunov function for the unforced exothermic cstr this lyapunov function is then reshaped by means of a controller in order to stabilize the process at a desired temperature

stabilization lyapunov functions and dissipation for linear time invariant systems any stabilizing controller for a given plant can be associated with a supply rate with respect to which the plant in open loop is half line dissipative we also prove the equivalence between the stability of the interconnection of two systems and their half line dissipativity with respect to a supply rate and its negative

resonances in one dimension and fredholm determinants we discuss resonances for schrodinger operators in whole and half line problems one of our goals is to connect the fredholm determinant approach of froese to the fourier transform approach of zworski another is to prove a result on the number of antibound states namely in a half line problem there are an odd number of antibound states between any two bound states

the hurwitz theorem for bessel functions and antibound states in spectral theory an 1889 result of hurwitz is that the bessel function j v c v 0 c 0 has no zeros for 2 n v n 1 with integer n a new application of this result is given which describes the behaviour of jost functions and antibound states for one dimensional schrodinger equations with exponentially decaying potential a new hurwitz type theorem with similar applications is developed for hypergeometric functions extensions are obtained where the power series are terminated after 2 n 1 terms and larger zero free intervals 2 n v are found

power shaping control writing the system dynamics into the brayton moser form power shaping control is an extension of energy balancing passivity based control that is based on a particular form of the dynamics the brayton moser form one of the main difficulties in this control approach is to write the dynamics in the suitable form since this requires the solution of a partial differential equation pde system with an additional sign constraint here a general methodology is described for solving this partial differential equation system the set of all solutions to the pde system is given as the solution of a linear equation system furthermore a necessary condition is given so that a solution of the linear system which meets the sign condition exists this methodology is illustrated on the case of a chemical reactor where the physical knowledge of the system is used to find a suitable solution