a new characterization of invariant subspaces of h 2 and applications to the optimal sensitivity problem this paper gives a new equivalent characterization for invariant subspaces of h 2 when the underlying structure is specified by the so called pseudorational transfer functions this plays a fundamental role in computing the optimal sensitivity for a certain important class of infinite dimensional systems including delay systems a closed formula easier to compute than the well known zhou khargonekar formula is given for optimal sensitivity for such systems an example is given to illustrate the result 2004 elsevier b v all rights reserved

formulas on preview and delayed h infty control a generalized hinfin control problem which covers preview and delayed control strategies is discussed based on a state space approach by introducing a hamiltonian matrix which is associated with a delay free generalized plant the analytic solution to the corresponding operator riccati equation is newly established based on the result obtained here the hinfin control problem is solved and for typical control problems e g hinfin and linear quadratic lq control for multiple input delay systems hinfin preview control some interpretations are provided on the resulting control system

a hamiltonian based solution to the two block h problem for general plants in h and rational weights a complete skew toeplitz type solution to the two block h 1 problem for innite dimensional stable plants with rational weights is derived with a basis free proof the solution consists of one riccati equation with a rank criterion for a transcendental function of a certain hamiltonian this gives a natural extension of the well known formula for the one block case an example is given to illustrate the result c 2000 elsevier science b v all rights reserved

compact toeplitz operators on the segal bargmann space abstract in this note we show that miao and zheng s characterization of compact operators on the bergman space of the unit disk that are finite sums of finite products of toeplitz operators with each one of the symbols belonging to bt also holds for the segal bargmann space of c n

weighted sensitivity minimization general plants in h and rational weights abstract for general plants in h and rational weighting functions the problem of computing the weighted h optimal sensitivity is considered a general formula is derived for a function whose singularities determine the optimal sensitivity 6 a determinantal expression for the optimal sensitivity is then deduced and related to a conjecture of zhou and khargonekar

singular values and vectors of a class of hankel operators abstract this paper considers the problem of determining the singular values and vectors of the class of hankel operators whose symbol can be written in the form w where is inner and w is rational we will obtain a new and simplified proof of the fact conjectured in 17 and first proved in 9 that the zeros of a certain determinantal expression coincide with the hankel singular values we will also show how this expression can be used to generate the singular vectors

some remarks on hamiltonians and the infinite dimensional one block h problem in this note a simple proof is given for the hamiltonian solution to the h optimal sensitivity for plants with arbitrary inner transfer function the approach combines skew toeplitz theory and state space representations and gives rise to a straightforward and basis free methodology

weighted sensitivity minimization for delay systems in this note we discuss the h infty sensitivity minimization problem for linear time invariant delay systems while the unweighted case reduces to simple nevanlinna pick interpolation the weighted case turns out to be much more complicated and demands certain functional analytic techniques for its solution

pseudo rational input output maps and their realizations a fractional representation approach to infinite dimensional systems this paper studies matrix fractional representation for impulse responses of a certain class of infinite dimensional linear systems which contains in particular delay differential systems such impulse responses are called pseudo rational in this paper this fractional representation is effectively used to derive concrete function space models from the abstract shift realizations given a fractional representation q 1 p a standard observable realization analogous to fuhrmann realizations for finite dimensional systems is associated to it a new notion of coprimeness called approximate left coprimeness is introduced and it is shown that the standard observable realization associated to the representation q 1 p is canonical if and only if q and p are approximately left coprime some examples are discussed to illustrate the relationships among various coprimeness concepts that have appeared in the literature

three dimensional acoustic scattering by layered media a novel surface formulation with operator expansions implementation the scattering of acoustic waves by irregular structures plays an important role in a wide range of problems of scientific and technological interest this talk focuses upon the rapid and highly accurate numerical approximation of solutions of helmholtz equations coupled across irregular periodic interfaces meant to model acoustic waves incident upon a multi layered medium a novel surface formulation for the problem is described in terms of boundary integral operators dirichlet neumann operators and a boundary perturbation methodology the method of operator expansions is proposed for its numerical simulation the method requires only the discretization of the layer interfaces so that the number of unknowns is an order of magnitude smaller than volumetric approaches while it avoids not only the need for specialized quadrature rules but also the dense linear systems characteristic of boundary integral element methods the approach is a generalization to multiple layers of malcolm nicholls operat

toeplitz operators with bmo symbols on the segal bargmann space we show that zorboska s criterion for compactness of toeplitz operators with bmo 1 symbols on the bergman space of the unit disc holds by a different proof for the segal bargmann space of gaussian square integrable entire functions on n we establish some basic properties of bmot p for p 1 and complete the characterization of bounded and compact toeplitz operators with bmo 1 symbols via the bargmann isometry and results of lo and englis we also give a compactness criterion for the gabor daubechies windowed fourier localization operators on l 2 n dv when the symbol is in a bmo 1 sobolev type space finally we discuss examples of the compactness criterion and counterexamples to the unrestricted application of this criterion for the compactness of toeplitz operators

relationships between internal and external stability for infinite dimensional systems with applications to a servo problem a study is made of the relationships among various stability motions for a class of infinite dimensional systems which contains a class of systems not covered by existing methods e g those having infinitely many unstable poles it is proved that internal l sup 2 stability and exponential stability are equivalent and internal stability implies h sup infinity stability several necessary and sufficient conditions for internal stability are derived in particular under certain conditions a canonical realization is internally stable if it is externally stable these results are applied to the servo problem involving this class of systems it is shown that i an internal model is necessary for tracking ii an internal model along with closed loop stability implies tracking a typical example called a repetitive control system is discussed to illustrate the results

a reproducing kernel thesis for operators on bergman type function spaces abstract in this paper we consider the reproducing kernel thesis for boundedness and compactness for various operators on bergman type spaces in particular the results in this paper apply to the weighted bergman space on the unit ball the unit polydisc and more generally to weighted fock spaces

reachability of a class of infinite dimensional linear systems an external approach with applications to general neutral systems this paper studies the question of quasi approximate reachability of the standard observable realizations of pseudorational impulse responses introduced by the author the framework places the current theory of retarded and neutral delay differential systems into a unified input output framework several necessary and sufficient conditions for quasi reachability are derived in particular new criteria for quasireachability and eigenfunction completeness are obtained for general delay differential systems with no restriction on the type of delays furthermore as a byproduct the theory leads to necessary and sufficient conditions for approximate left coprimeness of matrices with distribution entries examples are discussed to illustrate the theory

on the mixed sensitivity minimization for systems with infinitely many unstable modes in this note we consider a class of linear time invariant systems with infinitely many unstable modes by using the parameterization of all stabilizing controllers and a data transformation we show that h controllers for such systems can be computed using the techniques developed earlier for infinite dimensional plants with finitely many unstable modes

a hamiltonian based solution to the mixed sensitivity optimization problem for stable pseudorational plants this paper considers the mixed sensitivity optimization problem for a class of infinite dimensional stable plants this problem is reducible to a two or one block h control problem with structured weighting functions we first show that these weighting functions violate the genericity assumptions of existing hamiltonian based solutions such as the well known zhou khargonekar formula then we derive a new closed form formula for the computation of the optimal performance level when the underlying plant structure is specified by a pseudorational transfer function 2005 elsevier b v all rights reserved

brief paper a new expression for the h2 performance limit based on state space representation this paper aims to clarify the performance limit via state space representation in order to handle multiple input multiple output systems in a transparent way to this end by applying some results on infinite dimensional control theory a closed formula for the h 2 performance limit is derived for systems with a special structure described in terms of a rational transfer matrix and a scalar inner function this formulation is capable of dealing with various control problems including h 2 control of a class of infinite dimensional systems the resulting formula given as a functional of the inner function helps us to understand how achievable h 2 performance deteriorates due to non minimum phase properties or unstable modes of plants

localization and compactness of operators on fock spaces abstract for 0 p let f p be the fock space induced by a weight function satisfying d d c 0 in this paper given p 0 1 we introduce the concept of weakly localized operators on f p we characterize the compact operators in the algebra generated by weakly localized operators as an application for 0 p we prove that an operator t in the algebra generated by bounded toeplitz operators with bmo symbols is compact on f p if and only if its berezin transform satisfies certain vanishing property at in the classical fock space we extend the axler zheng condition on linear operators t which ensures t is compact on f p for all possible 0 p

localization and berezin transform on the fock space abstract we introduce the notion of sufficiently localized operators on the fock space we show that if a is in the c algebra generated by the class of sufficiently localized operators then a is compact if and only if its berezin transform vanishes at infinity moreover we show that this class contains many familiar operators including all the toeplitz operators with bounded symbols

on the weighted sensitivity minimization problem for delay systems we consider the h optimal sensitivity problem for delay systems in particular we consider computation of inf w q q h jr where w s is any function in rh jr and in h jr is any inner function we derive a new explicit solution in the pure delay case where e sh h 0

a general framework for linear periodic systems with applications to h sup infinity sampled data control the authors present a framework for dealing with continuous time periodic systems the main tool is a lifting technique which provides a strong correspondence between continuous time periodic systems and certain types of discrete time time invariant systems with infinite dimensional input and output spaces despite the infinite dimensionality of the input and output spaces a lifted system has a finite dimensional state space if the original system does this fact permits rather constructive methods for analyzing these systems as a demonstration of the utility of this framework the authors use it to describe the continuous time i e intersample behavior of sampled data systems and to obtain a complete solution to the problem of parameterizing all controllers that constrain the l sup 2 induced norm of a sampled data system to within a certain bound

on standard h control problems for systems with infinitely many unstable poles abstract in this paper h control for a class of linear time invariant systems with infinitely many unstable poles is studied an example of such a plant is a high gain system with delayed feedback we formulate the problem via a generalized plant which consists of a rational transfer matrix and the inverse of a scalar possibly irrational inner function it is shown that the problem can be decomposed into a finite dimensional h control problem and an additional rank condition

finite rank criteria for h infty control of infinite dimensional systems this paper studies the hinfin control of infinite dimensional systems whose transfer matrices are expressible as a series connection of a rational transfer matrix and a scalar possibly irrational inner function this class of systems is adequate for describing many control problems in practice when weighting functions are rational and plants have at most finitely many unstable modes we show that this problem can be reduced to solving two matrix valued riccati equations and an additional rank condition furthermore the obtained controller structure is characterized by the inner function and controllers for the finite dimensional part this result provides us with a solution that is easily implementable without much prior knowledge on infinite dimensional control theory a numerical example is given to illustrate the result