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

transfer matrices and partition function zeros for antiferromagnetic potts models iii triangular lattice chromatic polynomial we study the chromatic polynomial pg q for m n triangular lattice strips of widths m 12p 9f with periodic or free transverse boundary conditions respectively and arbitrary lengths n with free longitudinal boundary conditions the chromatic polynomial gives the zero temperature limit of the partition function for the q state potts antiferromagnet we compute the transfer matrix for such strips in the fortuin kasteleyn representation and obtain the corresponding accumulation sets of chromatic zeros in the complex q plane in the limit n we recompute the limiting curve obtained by baxter in the thermodynamic limit m n and find new interesting features with possible physical consequences finally we analyze the isolated limiting points and their relation with the beraha numbers

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

the global artificial boundary conditions for numerical simulations of the flow around a submerged body we consider the numerical approximations of the two dimensional steady potential flow around a body moving in a liquid of finite constant depth at constant speed and distance below a free surface one vertical segment is introduced as the upstream artificial boundary and two vertical segments are introduced as the downstream artificial boundaries on the artificial boundaries a sequence of high order global artificial boundary conditions are given then the original problem is reduced to a problem defined on a finite computational domain which is equivalent to a variational problem after solving the variational problem by the finite element method we obtain the numerical approximation of the original problem the numerical examples show that the artificial boundary conditions given in this paper are very effective

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 fast iterative method to compute the flow around a submerged body the authors develop an efficient iterative method for computing steady linearized potential flow around a submerged body moving in a liquid of finite constant depth in this paper they restrict the presentation to the two dimensional problem but the method is readily generalizable to the three dimensional case i e the flow in a canal the problem is indefinite which makes the convergence of most iterative methods unstable to circumvent this difficulty the authors decompose the problem into two more easily solvable subproblems and form a schwarz type iteration to solve the original problem the first subproblem is definite and can therefore be solved by standard iterative methods the second subproblem is indefinite but has no body it is therefore easily and efficiently solvable by separation of variables the authors prove that the iteration converges for sufficiently small froude numbers in addition they present numerical results for a second order accurate discretization of the problem they demonstrate that the iterative method converges rapidly and that the convergences rate improves when the froude number decreases they also verify numerically that the convergence rate is essentially independent of the grid size 20 refs 6 figs 10 tabs

the three state square lattice potts antiferromagnet at zero temperature we study the 3 state square lattice potts antiferromagnet at zero temperature by a monte carlo simulation using the wang swendsen koteck cluster algorithm on lattices up to 1024 1024 we confirm the critical exponents predicted by burton and henley based on the height representation of this model

computing the flow around a submerged body using composite grids the subject of this paper is an accurate numerical method for solving the linear two dimensional steady potential flow around a body which moves in a liquid of finite constant depth at constant speed and distance below the free surface the differential equation is discretized by a second order accurate finite difference scheme on a composite grid the composite grid consists of two overlapping component grids one curvilinear grid close to the body and one cartesian grid which covers the surrounding liquid to solve the problem numerically the infinite domain is truncated to finite length the inflow and outflow boundary conditions are formed by making an eigenfunction expansion of the solution ahead of and behind the body each eigenfunction is required to be bounded and satisfy the upstream condition at infinity this is imposed by functional relations between the solution and its normal derivative at the inflow and outflow boundaries the method is carefully validated and the computed solutions are found to be in very good agreement with existing results

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

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

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

the artificial boundary conditions for computing the flow around a submerged body in this paper we consider the numerical simulations of the steady linearized potential flow around a body which moves in a liquid of finite constant depth at constant speed and distance below a free surface two vertical segments are introduced as the artificial boundary to limit the unbounded physical domain to a bounded computational domain a series of approximate artificial boundary conditions at the given artificial boundary are designed by imposing the continuity of the solution and its normal derivative then the original problem is reduced to a problem defined in a bounded computational domain which is solved numerically by the finite element method the numerical examples show that our artificial boundary conditions are very effective

composite overlapping meshes for the solution of partial differential equations abstract we discuss the generation of curvilinear composite overlapping grids and the numerical solution of partial differential equations on them a composite overlapping grid consists of a set of curvilinear component grids that cover a region and overlap where they meet continuity conditions interpolation are imposed at the overlapping boundaries the principal advantage of composite grids is in the generation of grids for regions with complicated geometries the grid construction program cmpgrd is used to create composite grids with any number of component grids we describe some techniques for the solution of elliptic and time dependent pdes on composite meshes applications to the solution of the compressible navier stokes equations are presented

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