preconditioning for dual time stepping simulations of the shallow water equations including coriolis and bed friction effects diagonal preconditioners for implicit unsteady and steady discretizations of the shallow water equations at low and high rossby and drag number limits are analyzed for each case sub and supercritical flow conditions are also considered based on the analysis a preconditioner is derived for use with a multigrid cycle that performs as well as possible under all conditions in addition a streamwise upwind petrov galerkin discretization of the system is presented that is derived from the preconditioned system using this discretization it is demonstrated that for most conditions the preconditioner gives rapid convergence that is independent of the grid resolution and the flow parameters practical tests including an equatorial rossby soliton and tide propagation over variable bathymetry are simulated to demonstrate the performance of this approach

non linear observer design by transformation into a generalized observer canonical form an observer design method for a certain class of non linear single output systems is introduced the characteristic feature of this method consists of the fact that it does not require any linearization in the way that the given non linear system is approximated by a linear one the present paper deals with the derivation of a transformation of the considered non linear system into a generalized observer canonical form gocf which enables a systematic observer design similar to the linear one based on the well known linear observer canonical form to assign conditions for its existence the transformation into the gocf is carried out in two steps via a generalized observability canonical form gobcf in contrast to previous forms used for linear systems the two non linear canonical forms presented here also depend on the time derivatives of the input variables this means that the resulting observer has to be supplied not only with the input and output variables of the given system but also with deri

large spaces of bounded rank matrices revisited let n p r be positive integers with n p r a rank r subset of n by p matrices with entries in a field is a subset in which every matrix has rank less than or equal to r a classical theorem of flanders states that the dimension of a rank r linear subspace must be less than or equal to nr and it characterizes the spaces with the critical dimension nr linear subspaces with dimension close to the critical one were later studied by atkinson lloyd and beasley over fields with large cardinality their results were recently extended to all fields 18 using a new method we obtain a classification of rank r affine subspaces with large dimension over all fields this classification is then used to double the range of large dimensions for which the structure of rank r linear subspaces is known for all fields

solution of the h sub infinity optimal linear filtering problem for discrete time systems the solution of l sub 2 minimum variance and h sub infinity estimation problems is considered using a polynomial systems approach the results for the l sub 2 filtering problem which corresponds with wiener or kalman filtering prediction are first presented in polynomial matrix form attention then turns to the solution of the h sub infinity estimation problem for scalar systems numerous examples are presented to illustrate the computational procedures the two types of estimator are appropriate to very different estimation problems and the new h sub infinity devices should be valuable in certain application areas

linear subspaces of matrices associated to a ferrers diagram and with a prescribed lower bound for their rank abstract fix a field k a subset p 1 k 1 m and an integer min k m let c m k p k be the vector space of all k m matrices with entries a i j 0 if i j p let k be the maximal dimension of a linear subspace v c m k p k such that all a v 0 have rank we show that known lower bounds for k for k one resp several resp almost all finite field give the same lower bounds for some resp many resp all number fields

a fully semi lagrangian discretization for the 2d incompressible navier stokes equations in the vorticity streamfunction formulation abstract a numerical method for the two dimensional incompressible navier stokes equations in vorticity streamfunction form is proposed which employs semi lagrangian discretizations for both the advection and diffusion terms thus achieving unconditional stability without the need to solve linear systems beyond that required by the poisson solver for the reconstruction of the streamfunction a description of the discretization of dirichlet boundary conditions for the semi lagrangian approach to diffusion terms is also presented numerical experiments on classical benchmarks for incompressible flow in simple geometries validate the proposed method

spaces of matrices of constant rank and uniform vector bundles abstract we consider the problem of determining l r a the maximal dimension of a subspace of a a matrices of rank r we first review in the language of vector bundles the known results then using known facts on uniform bundles we prove some new results and make a conjecture finally we determine l r a for every r 1 r a when a 10 showing that our conjecture holds true in this range

feedback and pole placement in descriptor variable systems the effects and uses of applying linear feedback to continuous time descriptor systems are studied structural changes resulting from feeding back the slow and fast parts of the trajectory separately are characterized it is shown that under certain conditions related to controllability the poles of the slow subsystem may be shifted arbitrarily and the impulsive behaviour of the fast subsystem may be eliminated

h control for descriptor systems a matrix inequalities approach abstract this paper considers the h control problem for descriptor systems that possibly have impulsive modes and or j axis zeros first we propose matrix inequalities that give a generalized stability condition and an h norm condition for descriptor systems using these matrix inequalities we show that the solvability of a set of matrix inequalities is necessary and sufficient to the existence of a proper controller that satisfies a prescribed h norm condition as well as stabilizing the closed loop system and eliminating all impulsive modes these inequalities are equivalent to certain linear matrix inequalities to which we can get solutions whenever they exist using efficient polynomial time algorithms

filtering for stochastic systems driven by poisson processes this paper investigates the filtering problem for stochastic systems driven by poisson processes by utilising the martingale theory such as the predictable projection operator and the dual predictable projection operator this paper transforms the expectation of stochastic integral with respect to the poisson process into the expectation of lebesgue integral then based on this this paper designs an filter such that the filtering error system is mean square asymptotically stable and satisfies a prescribed performance level finally a simulation example is given to illustrate the effectiveness of the proposed filtering scheme

interpolation approach to h estimation and its interconnection to loop transfer recovery abstract this paper proposes to solve the h optimal estimation problem via interpolation theory the advantages of this approach are the following i direct and simple solutions can be obtained for the optimal estimators ii frequency weightings on estimation error and disturbance can be easily incorporated and iii unnecessary high observer gains can be avoided we also show the interconnection between the h optimal estimation problem and the optimal loop transfer recovery problem the interpolation approach applies to both continuous time and discrete time systems

h sub spl infin state feedback control for discrete singular systems deals with the problem of state feedback h sub spl infin control for discrete singular systems it is not assumed that the singular system under consideration is necessarily regular the problem we address is the design of a state feedback controller such that the resulting closed loop system is not only regular causal and stable but also satisfies a prescribed h sub spl infin norm bound condition in terms of certain matrix inequalities a necessary and sufficient condition for the solution to this problem is obtained and a suitable state feedback control law is also given

multiblock multigrid grid generation algorithms overcoming multigrid anisotropy abstract the paper presents multiblock multigrid algorithms for the generation of boundary fitted grids bfgs able to avoid undesired multigrid anisotropy arises the algorithms combine a domain decomposition technique the elliptic grid generation and the multigrid computation and provide satisfactory numerical solutions and fast convergence block matching based on two surface overlapping saves grid characteristics through the block boundaries we assume two and three dimensional generation systems allowing line spacing control and we design block by block multigrid computation to solve the transformed finite difference systems we identify anisotropy as an undesirable multigrid effect and we overcome anisotropic behaviors by investigation over coefficients of the generating systems they can provide information to select appropriate relaxation algorithms a wide series of performance evaluation results is available one block and multiblock so as one grid and multi grid algorithms have been evaluated and meaningful results are collected in tables visualizations of 2d and 3d computed grids and displays of convergence histories comparing multigrid components are shown by figures

boundary fitted coordinate systems for numerical solution of partial differential equations a review a comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given some general mathematical framework and error analysis common to such coordinate systems is also included the general categories of generating systems are those based on conformal mapping orthogonal systems nearly orthogonal systems systems produced as the solution of elliptic and hyperbolic partial differential equations and systems generated algebraically by interpolation among the boundaries also covered are the control of coordinate line spacing by functions embedded in the partial differential operators of the generating system and by subsequent stretching transformation dynamically adaptive coordinate systems coupled with the physical solution and time dependent systems that follow moving boundaries are treated references reporting experience using such coordinate systems are reviewed as well as those covering the system development

observers for lipschitz nonlinear systems this paper presents some fundamental insights into observer design for the class of lipschitz nonlinear systems the stability of the nonlinear observer for such systems is not determined purely by the eigenvalues of the linear stability matrix the correct necessary and sufficient conditions on the stability matrix that ensure asymptotic stability of the observer are presented these conditions are then reformulated to obtain a sufficient condition for stability in terms of the eigenvalues and the eigenvectors of the linear stability matrix the eigenvalues have to be located sufficiently far out into the left half plane and the eigenvectors also have to be sufficiently well conditioned for ensuring asymptotic stability based on these results a systematic computational algorithm is then presented for obtaining the observer gain matrix so as to achieve the objective of asymptotic stability

kalman filtering and riccati equations for descriptor systems a general formulation of a discrete time filtering problem for descriptor systems is considered it is shown that the nature of descriptor systems leads directly to the need to examine singular estimation problems using a dual approach to estimation the authors derive a so called 3 block form for the optimal filter and a corresponding 3 block riccati equation for a general class of time varying descriptor models which need not represent a well posed system in that the dynamics may be either over or under constrained specializing in the time invariant case they examine the asymptotic properties of the 3 block filter and in particular analyze in detail the resulting 3 block algebraic riccati equation the noncausal nature of discrete time descriptor dynamics implies that future dynamics may provide some information about the present state a modified form for the descriptor kalman filter that takes this information into account is presented

a multigrid method for grid generation with line spacing control a multigrid method for grid generation on two dimensional regions and its applications to test problems are presented the multigrid algorithm deals with the solution of elliptic differential problems which occur in the computation of boundary fitted grids the solution of elliptic systems of partial differential equations which correspond to transformed poisson systems is carried out by a full approximation storage fas algorithm the components of the method such as the relaxation for error smoothing and the coarsening strategy are evaluated on problems in which sources of attractions are considered and the generated grids are shown by figures

impulse controllability and observability of rectangular descriptor systems the presence of impulsive responses in descriptor systems and how it relates to impulse controllability and impulse observability is considered it is shown that the equivalence between impulse controllability observability and the existence of an impulse eliminating semistate feedback output injection gain although true for square descriptor systems does not hold for rectangular descriptor systems in general hence necessary and sufficient conditions for the existence of an impulse eliminating semistate feedback output injection gain are presented

large affine spaces of matrices with rank bounded below abstract let k be an arbitrary commutative field with at least three elements and let n p and r be positive integers with r min n p in a recent work 11 we have proved that an affine subspace of m n p k containing only matrices of rank greater than or equal to r must have a codimension greater than or equal to r 1 2 here we classify up to equivalence these subspaces of minimal codimension r 1 2 this uses our recent classification 10 of the affine subspaces of m r k contained in gl r k which have the maximal dimension r 2

numerical methods for convection dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures finite element and finite difference methods are combined with the method of characteristics to treat a parabolic problem of the form cu t bu x au x x f optimal order error estimates in l 2 and w 1 2 are derived for the finite element procedure various error estimates are presented for a variety of finite difference methods the estimates show that for convection dominated problems b gg a these schemes have much smaller time truncation errors than those of standard methods extensions to n space variables and time dependent or nonlinear coefficients are indicated along with applications of the concepts to certain problems described by systems of differential equations

determination of bed elevation in the enhanced lattice boltzmann method for the shallow water equations the bed slope in the shallow water equations reflects the bed topography it is not a flow variable and cannot be determined in the solution to the flow equations an immovable nonflat bed affects a flow as a force term but the flow has no effect on it only when the bed term is correctly represented in a numerical method can it generate an accurate solution in the enhanced lattice boltzmann method for the shallow water equations elabswe using an individual chapman enskog analysis it is found that such a correct representation can be achieved by retaining c 2 in which c is the coefficient for bed elevation in the lattice boltzmann equation and is that for the water depth in the local equilibrium distribution function the finding has been validated through simulations of a water at rest in a dish shaped lake a wind induced shallow flow in the same lake and a steady flow over a two dimensional bed hump

a domain decomposition and overlapping method for the generation of three dimensional boundary fitted coordinate systems abstract a new method is presented for numerically generating boundary fitted coordinate systems for arbitrarily shaped three dimensional regions in the method the three dimensional region of interest is decomposed into several hexahedrons each of which has two grid surfaces overlapped with each of the neighboring hexahedrons based on this method a new computer program grid 3d has been developed which allows the generation of an unlimitted number of different types of coordinate systems application to a variety of geometries confirms that grid 3d is a convenient and efficient tool in the generation of boundary fitted coordinate systems even for a considerably complicated configuration consisting of many different components

h filtering for a class of uncertain nonlinear systems abstract this paper investigates the problem of h filtering for a class of uncertain continuous time nonlinear systems with real time varying parameter uncertainty and unknown initial state we develop an infinite horizon h filtering methodology which provides both robust stability and a guaranteed h performance for the filtering error irrespective of the parameter uncertainty

the hilbert null cone on tuples of matrices and bilinear forms we describe the null cone of the representation of g on m p where either g sl w sl v and m hom v w linear maps or g sl v and m is one of the representations s 2 v symmetric bilinear forms 2 v skew bilinear forms or v otimes v arbitrary bilinear forms here v and w are vector spaces over an algebraically closed field k of characteristic zero and m p is the direct sum of p of copies of m more specifically we explicitly determine the irreducible components of the null cone on m p results of kraft and wallach predict that their number stabilises at a certain value of p and we determine this value we also answer the question of when the null cone in m p is defined by the polarisations of the invariants on m typically this is only the case if either dim v or p is small a fundamental tool in our proofs is the hilbert mumford criterion for nilpotency also known as unstability

euler s predictor corrector technique for solving the depth integrated shallow water equations abstract euler s predictor corrector technique combined with finite analysis method is applied to solve 2d advection diffusion shallow water equations in this algorithm the momentum equations are calculated by the finite analysis method based on a single mesh while the continuity equation is solved by euler s predictor corrector technique to verify the performance of this approach the simulation of tidal flow in the huangpu estuary is carried out the numerical results are found to be consistent with the field results implying that this proposed method is effective and applicable

stability accuracy and efficiency of a semi implicit method for three dimensional shallow water flow abstract the stability analysis the accuracy and the efficiency of a semi implicit finite difference scheme for the numerical solution of a three dimensional shallow water model are presented and discussed the governing equations are the three dimensional reynolds equations in which pressure is assumed to be hydrostatic the pressure gradient in the momentum equations and the velocities in the vertically integrated continuity equation are discretized with the method with being an implicitness parameter it is shown that the method is stable for 1 2 1 unstable for 1 2 and highest accuracy and efficiency is achieved when 1 2 the resulting algorithm is mass conservative and naturally allows for the simulation of flooding and drying of tidal flats

nonlinear observers with linearizable error dynamics we present a new method for designing asymptotic observers for a class of nonlinear systems the error between the state of the system and the state of the observer in appropriate coordinates evolves linearly and can be made to decay arbitrarily exponentially fast

h sub infinity minimum error state estimation of linear stationary processes a state estimator is derived which minimizes the h sub infinity norm of the estimation error power spectrum matrix two approaches are presented the first achieves the optimal estimator in the frequency domain by finding the filter transfer function matrix that leads to an equalizing solution the second approach establishes a duality between the problem of h sub infinity filtering and the problem of unconstrained input h sub infinity optimal regulation using this duality previously published results for the latter regulation problem are applied which lead to an optimal filter that possess the structure of the corresponding kalman filter the two approaches usually lead to different results they are compared by a simple example which also demonstrates a clear advantage of the h sub infinity estimate over the conventional l sub 2 estimate

nondegenerate piecewise linear systems a finite newton algorithm and applications in machine learning we investigate newton type optimization methods for solving piecewise linear systems plss with nondegenerate coefficient matrix such systems arise for example from the numerical solution of linear complementarity problem which is useful to model several learning and optimization problems in this letter we propose an effective damped newton method pls dn to find the exact up to machine precision solution of nondegenerate plss pls dn exhibits provable semiiterative property that is the algorithm converges globally to the exact solution in a finite number of iterations the rate of convergence is shown to be at least linear before termination we emphasize the applications of our method in modeling from a novel perspective of plss some statistical learning problems such as box constrained least squares elitist lasso kowalski torreesani 2008 and support vector machines cortes vapnik 1995 numerical results on synthetic and benchmark data sets are presented to demonstrate the effectiveness and efficiency of pls dn on these problems

h_ infty unbiased filtering for linear descriptor systems via lmi this note concerns the optimal h infin unbiased filtering problem for linear descriptor systems it unifies the design of reduced order minimal order and full order filters for continuous and discrete time systems necessary and sufficient conditions for the solvability of the problem are obtained in terms of a set of linear matrix inequalities lmis the parametrization of all h infin unbiased filters is presented application to standard systems with or without unknown inputs is given a numerical example is given to show the applicability of the presented approach

semi implicit semi lagrangian modelling for environmental problems on staggered cartesian grids with cut cells in this paper we propose an extension of semi implicit models for the shallow water or euler equations on staggered cartesian meshes to handle the presence of cut cells at the boundaries of the computational domain semi lagrangian advection algorithms are also extended to staggered cartesian meshes with cut boundary cells a linear reconstruction algorithm and radial basis function interpolation are used respectively to compute approximate trajectories and to recover an accurate velocity field in cells intersected by the boundary the effective accuracy of radial basis function interpolators for semi lagrangian algorithms is assessed by simple numerical experiments timestep control techniques in the computation of the semi lagrangian trajectories are also discussed the accuracy of the resulting models for environmental flows is demonstrated by a number of test cases simulating nonlinear open channel flows and baroclinic flows over an isolated obstacle

linear spaces of matrices of constant rank and instanton bundles abstract we present a new method to study 4 dimensional linear spaces of skew symmetric matrices of constant co rank 2 based on rank 2 vector bundles on p 3 and derived category tools the method allows one to prove the existence of new examples of size 10 10 and 14 14 via instanton bundles of charge 2 and 4 respectively and it provides an explanation for what used to be the only known example westwick 1996 25 we also give an algorithm to construct explicitly a matrix of size 14 of this type

vector spaces of skew symmetric matrices of constant rank abstract we study the orbits of vector spaces of skew symmetric matrices of constant rank 2 r and type n 1 n 1 under the natural action of sl n 1 over an algebraically closed field of characteristic zero we give a complete description of the orbits for vector spaces of dimension 2 relating them to some 1 generic matrices of linear forms we also show that for each rank two vector bundle on p 2 defining a triple veronese embedding of p 2 in g 1 7 there exists a vector space of 8 8 skew symmetric matrices of constant rank 6 whose kernel bundle is the dual of the given rank two vector bundle

tripartite to bipartite entanglement transformation by stochastic local operations and classical communication and the structure of matrix spaces we study the problem of transforming a tripartite pure state to a bipartite one using stochastic local operations and classical communication slocc it is known that the tripartite to bipartite slocc convertibility is characterized by the maximal schmidt rank of the given tripartite state i e the largest schmidt rank over those bipartite states lying in the support of the reduced density operator in this paper we further study this problem and exhibit novel results in both multi copy and asymptotic settings utilizing powerful results from the structure of matrix spaces in the multi copy regime we observe that the maximal schmidt rank is strictly super multiplicative i e the maximal schmidt rank of the tensor product of two tripartite pure states can be strictly larger than the product of their maximal schmidt ranks we then provide a full characterization of those tripartite states whose maximal schmidt rank is strictly super multiplicative when taking tensor product with itself notice that such tripartite states admit strict advantages in tripartite to bipartite slocc transformation when multiple copies are provided in the asymptotic setting we focus on determining the tripartite to bipartite slocc entanglement transformation rate computing this rate turns out to be equivalent to computing the asymptotic maximal schmidt rank of the tripartite state defined as the regularization of its maximal schmidt rank despite the difficulty caused by the super multiplicative property we provide explicit formulas for evaluating the asymptotic maximal schmidt ranks of two important families of tripartite pure states by resorting to certain results of the structure of matrix spaces including the study of matrix semi invariants these formulas turn out to be powerful enough to give a sufficient and necessary condition to determine whether a given tripartite pure state can be transformed to the bipartite maximally entangled state under slocc in the asymptotic setting applying the recent progress on the non commutative rank problem we can verify this condition in deterministic polynomial time

multicolor iccg methods for vector computers this paper considers the incomplete choleski conjugate gradient method for symmetric positive definite linear systems the goal is to obtain implementations of this method suitable for vector computers which require long vectors for efficiency this is achieved by a multicoloring strategy which allows efficient solution of the triangular systems of the preconditioning as well as efficient matrix vector multiplication numerical results are given for three model problems on a cyber 205

h filter design for a class of nonlinear discrete time singular systems this paper deals with the h filter design problem for a class of discrete time lipschitz nonlinear singular systems the approach is based on the parameterisation of the obtained algebraic constraints from the estimation errors sufficient conditions for the existence of the filters which guarantee stability and the worst case filter error energy over all bounded energy disturbances is minimised are given the method also unifies the design for the full order reduced order minimal order filters for discrete time systems the presented results are less conservative than those existing in the literature this is due to the introduction of new slack variables application to systems with unknown input is presented via a numerical example

design of observers for descriptor systems in this note simple and straightforward methods to design full and reduced order observers for linear time invariant descriptor systems are presented the approach for the reduced order observer design is based on the generalized sylvester equation sufficient conditions for the existence of the observers are given an illustrative example is included

third order conservative sign preserving and steady state preserving time integrations and applications in stiff multispecies and multireaction detonations abstract in this paper we develop third order conservative sign preserving and steady state preserving time integrations and seek their applications in multispecies and multireaction chemical reactive flows in this problem the density and pressure are nonnegative and the mass fraction for the ith species denoted as z i 1 i m should be between 0 and 1 where m is the total number of species there are four main difficulties in constructing high order bound preserving techniques for multispecies and multireaction detonations first of all most of the bound preserving techniques available are based on euler forward time integration therefore for problems with stiff source the time step will be significantly limited secondly the mass fraction does not satisfy a maximum principle and hence it is not easy to preserve the upper bound 1 thirdly in most of the previous works for gaseous denotation the algorithm relies on second order strang splitting methods where the flux and stiff source terms can be solved separately and the extension to high order time discretization seems to be complicated finally most of the previous ode solvers for stiff problems cannot preserve the total mass and the positivity of the numerical approximations at the same time in this paper we will construct third order conservative sign preserving rugne kutta and multistep methods to overcome all these difficulties the time integrations do not depend on the strang splitting i e we do not split the flux and the stiff source terms moreover the time discretization can handle the stiff source with large time step and preserves the steady state numerical experiments will be given to demonstrate the good performance of the bound preserving technique and the stability of the scheme for problems with stiff source terms

a fully implicit domain decomposition algorithm for shallow water equations on the cubed sphere popular approaches for solving shallow water equations swes for climate modeling are explicit and semiimplicit methods and both have certain constraints on the time step size in this paper we propose and study a fully implicit method which imposes no limit on the time step size but requires the solution of a large sparse nonlinear system of equations at every time step the focus of the paper is a parallel fully coupled newton krylov ras algorithm with a jacobian matrix explicitly calculated on a weakly nonmatching cubed sphere mesh here ras is a restricted additive schwarz method we show numerically that with such a preconditioned nonlinearly implicit method the time step size is no longer constrained by the cfl condition and we report superlinear speedup of the algorithm on machines with thousands of processors for problems with smooth and nonsmooth solutions

state and input simultaneous estimation for a class of nonlinear systems this paper addresses the problem of estimating simultaneously the state and input of a class of nonlinear systems here the systems nonlinear part comprises a lipschitz nonlinear function with respect to the state and input and a state dependent unknown function including additive disturbance as well as uncertain nonlinear time varying terms upon satisfying some conditions the observer design problem can be solved via a riccati inequality or a lmi based technique with asymptotic estimation guaranteed a numerical example is included for illustration

a barely implicit correction for flux corrected transport abstract the barely implicit correction bic removes the stringent limit on the timestep imposed by the sound speed in explicit methods this is done by adding one elliptic equation which has to be solved implicitly bic is combined with the flux corrected transport algorithm in order to represent sharp gradients in subsonic flows accurately the resultant conservative algorithm costs about the same per timestep as a single explicit timestep calculated using an optimized fct module several examples show the technique s ability to solve nearly incompressible flows very economically

dirichlet fundamental domains and topology of projective varieties we prove that for every finitely presented group g there exists a 2 dimensional irreducible complex projective variety w with the fundamental group g so that all singularities of w are normal crossings and whitney umbrellas

reduced order h filtering for singular systems abstract this paper solves the problem of reduced order h filtering for singular systems the purpose is to design linear filters with a specified order lower than the given system such that the filtering error dynamic system is regular impulse free or causal stable and satisfies a prescribed h performance level one major contribution of the present work is that necessary and sufficient conditions for the solvability of this problem are obtained for both continuous and discrete singular systems these conditions are characterized in terms of linear matrix inequalities lmis and a coupling non convex rank constraint moreover an explicit parametrization of all desired reduced order filters is presented when these inequalities are feasible in particular when a static or zeroth order h filter is desired it is shown that the h filtering problem reduces to a convex lmi problem all these results are expressed in terms of the original system matrices without decomposition which makes the design procedure simple and directly last but not least the results have generalized previous works on h filtering for state space systems an illustrative example is given to demonstrate the effectiveness of the proposed approach

eulerian lagrangian solution of the convection dispersion equation in natural coordinates the vast majority of numerical investigations of transport phenomena use an eulerian formulation for the convenience that the computational grids are fixed in space an eulerian lagrangian method elm of solution for the convection dispersion equation is discussed and analyzed the elm uses the lagrangian concept in an eulerian computational grid system the values of the dependent variable off the grid are calculated by interpolation when a linear interpolation is used the method is a slight improvement over the upwind difference method at this level of approximation both the elm and the upwind difference method suffer from large numerical dispersion however if second order lagrangian polynomials are used in the interpolation the elm is proven to be free of artificial numerical dispersion for the convection dispersion equation the concept of the elm is extended for treatment of anisotropic dispersion in natural coordinates in this approach the anisotropic properties of dispersion can be conveniently related to the properties of the flow field several numerical examples are given to further substantiate the results of the present analysis

reduced order observer design for descriptor systems with unknown inputs a new method for the design of reduced order observers for descriptor systems with unknown inputs is presented the approach is based on the generalized constrained sylvester equation sufficient conditions for the existence of the observer are given

nonlinear observer design by observer error linearization this paper studies the observer design problem by the observer error linearization approach for nonlinear systems with and without inputs necessary and sufficient conditions for the existence of the linearization transformation are derived for nonlinear systems without inputs the conditions are shown to be corrections to an existing result a computation procedure and a different set of necessary and sufficient conditions based on the computation procedure are presented

a staggered semi implicit spectral discontinuous galerkin scheme for the shallow water equations a spatially arbitrary high order semi implicit spectral discontinuous galerkin dg scheme for the numerical solution of the shallow water equations on staggered control volumes is derived and discussed the free surface elevation and the momentum are expressed in terms of the same polynomials that are used as basis and as test functions each unknown is however defined on a different set of control volumes that are spatially staggered with respect to each other a semi implicit time integration yields a stable and efficient mass conservative algorithm the use of a staggered mesh has the advantage that after substitution of the momentum equations into the mass conservation equation only one single block penta diagonal system must be solved for the new free surface location which is a scalar quantity subsequently the new momentum components are directly obtained the staggered semi implicit approach makes the present dg scheme different from other published dg schemes the sparse linear system of the resulting discrete wave equation for the free surface can be conveniently solved by a matrix free gmres algorithm furthermore for the shallow water equations the proposed scheme can be written as a quadrature free method where all surface and volume integrals can be precomputed once and for all on the reference element and assembled into universal matrices and tensors for the special case n 0 the proposed method reduces to a classical semi implicit finite difference scheme the proposed semi implicit scheme is particularly well suited for low froude number flows the method is validated on some typical academic benchmark problems using polynomial degrees of up to n 20

enhancement of the labswe for shallow water flows in the lattice boltzmann method for the shallow water equations labswe the force term involves the first order derivative related to a bed slope which has to be determined using the centred scheme for an accurate solution however such calculation contradicts the spirit of only simple arithmetic calculations required in the lattice boltzmann method this paper shows how to remove this drawback from the labswe by incorporating the bed level into the lattice boltzmann equation in a consistent manner with the lattice boltzmann approach three numerical tests have been presented to verify the proposed method

kalman filtering for general discrete time linear systems recursive state estimation problems for explicit and implicit time invariant linear systems both for systems with and without unknown inputs can be formulated as a single problem usually referred to as descriptor kalman filtering solutions to this problem have been proposed in the literature however these solutions either neglect possible contributions of future dynamics to the current estimate or make unnecessary assumptions on the structure of the system in this paper the authors propose a solution to this problem which leads to a constructive method lifting these unnecessary assumptions this method uses a generalization of the shuffle algorithm

semi global robust output regulation for a class of singular nonlinear systems via nonlinear internal model abstractmost of existing results on robust output regulation problem of singular nonlinear systems are limited to local solutions in this paper the semi global robust output regulation problem for a class of singular nonlinear systems is investigated by using a nonlinear internal model attaching a nonlinear internal model to the singular nonlinear system yields an augmented singular nonlinear system whose semi global robust stabilisation solution leads to the solution of the semi global robust output regulation problem of the original singular nonlinear system the solvability conditions of the semi global output regulation problem are established by addressing the solvability of the robust stabilisation problem of augmented singular nonlinear system finally a numerical simulation example is used to illustrate the design of the semi global regulator for the singular nonlinear systems

a high order semi implicit discontinuous galerkin method for the two dimensional shallow water equations on staggered unstructured meshes a well balanced spatially arbitrary high order accurate semi implicit discontinuous galerkin scheme is presented for the numerical solution of the two dimensional shallow water equations on staggered unstructured non orthogonal grids the semi implicit method is derived in such a fashion that all relevant integrals can be precomputed and stored in a preprocessing stage so that the extension to curved isoparametric elements is natural and does not increase the computational effort of the simulation at runtime for p 0 the resulting scheme becomes a generalization of the classical semi implicit finite volume finite difference scheme of casulli and walters 2000 25 but with less conditions on the grid geometry the method proposed in this paper allows large time steps with respect to the surface wave speed gh and is thus particularly suitable for low froude number flows the approach is validated on some typical academic benchmark problems using polynomial degrees up to p 6

linear spaces of symmetric nilpotent matrices abstract in 1958 gerstenhaber showed that if l is a subspace of the vector space of the square matrices of order n over some field f consisting of nilpotent matrices and the field f is sufficiently large then the maximal dimension of l is n n 1 2 and if this dimension is attained then the space l is triangularizable linear spaces of symmetric matrices seem to be first studied by meshulam in 1989 in view of the bound of their rank although it seems unnatural to ask when a linear space of symmetric matrices is made of nilpotents and when it is triangular we find a way to do so by going to an equivalent notion for symmetric matrices i e persymmetric matrices we develop a theory that enables us to prove extensions of some beautiful classical triangularizability results to the case of symmetric matrices not only the gerstenhaber s result but also engel jacobson and radjavi theorems can be extended we also study maximal linear spaces of symmetric nilpotents of smaller dimension

vector spaces of matrices of low rank in this paper we study vector spaces of matrices all of whose elements have rank at most a given number the problem of classifying such spaces is roughly equivalent to the problem of classifying certain torsion free sheaves on projective spaces we solve this problem in case the sheaf in question has first chern class equal to 1 the characterization of the vector spaces of matrices of rank d 3 due to m d atkinson j ausfral math sot 34 1983 306 315 follows we speculate on the situation for higher rank and chern class free resolutions are used to verify some properties of the low rank examples and to produce an abundance of examples of somewhat higher rank connected with the theory of curves 0 1988 academic

a semi implicit semi lagrangian p adaptive discontinuous galerkin method for the shallow water equations a semi implicit and semi lagrangian discontinuous galerkin method for the shallow water equations is proposed for applications to geophysical scale flows a non conservative formulation of the advection equation is employed in order to achieve a more treatable form of the linear system to be solved at each time step the method is equipped with a simple p adaptivity criterion that allows to adjust dynamically the number of local degrees of freedom employed to the local structure of the solution numerical results show that the method captures well the main features of gravity and inertial gravity waves as well as reproducing correct solutions in nonlinear test cases with analytic solutions the accuracy and effectiveness of the method are also demonstrated by numerical results obtained at high courant numbers and with automatic choice of the local approximation degree

filtering and smoothing in an h sup infinity setting the problems of filtering and smoothing are considered for linear systems in an h sup infinity setting i e the plant and measurement noises have bounded energies are in l sub 2 but are otherwise arbitrary two distinct situations for the initial condition of the system are considered the initial condition is assumed known in one case while in the other the initial condition is not known but the initial condition the plant and measurement noise are in some weighted ball of r sup n xl sub 2 finite horizon and infinite horizon cases are considered necessary and sufficient conditions are presented for the existence of estimators both filters and smoothers that achieve a prescribed performance bound and algorithms that result in performance within the bounds are developed in case of smoothers the optimal smoother is also presented the approach uses basic quadratic optimization theory in a time domain setting as a consequence of which both linear time varying and time invariant systems can be considered with equal ease in the smoothing problem for linear time varying systems one considers only the finite horizon case

state and input estimation for a class of uncertain systems we consider here the problem of state and input estimation for a class of uncertain systems which consist of a nominally linear part and an uncertain nonlinear time varying part which can be regarded as a state dependent time varying input we obtain a lyapunov type characterization of the assumptions commonly found in the literature on this problem using this characterization we obtain estimators which using only a measured output can asymptotically estimate to any desired accuracy the system state and the input

optimal unbiased filtering via linear matrix inequalities abstract solutions to the optimal h and l2 l unbiased reduced order filtering problems are obtained in terms of linear matrix inequalities lmis the order of the optimal filter is equal to the number of measurements both continuous and discrete time results are presented an explicit parametrization of all optimal unbiased filters is provided in terms of a free contractive matrix

semi implicit finite difference methods for the two dimensional shallow water equation abstract in this paper a semi implicit finite difference method for the 2 dimensional shallow water equations is derived and discussed a characteristic analysis of the governing equations is carried out first in order to determine those terms to be discretized implicitly so that the stability of the method will not depend upon the celerity such terms are the gradient of the water surface elevation in the momentum equations and the velocity divergence in the continuity equation the convective terms are discretized explicitly the simpler explicit discretization for the convective terms is the upwind discretization which is conditionally stable and introduces some artificial viscosity it is shown that the stability restriction is eliminated and the artificial viscosity is reduced when an eulerian lagrangian approach with large time steps is used to discretize the convective terms this method at each time step requires the solution of a linear symmetric 5 diagonal system such a system is diagonally dominant with positive elements on the main diagonal and negative ones elsewhere thus existence and uniqueness of the numerical solution is assured the resulting algorithm is mass conservative and fully vectorizable for an efficient implementation on modern vector computers the performance of this method is further improved when used in combination with an adi technique which results in two sets of simpler linear 3 diagonal systems and maintains all the properties described above

steady state and sign preserving semi implicit runge kutta methods for odes with stiff damping term in this paper we develop a family of second order semi implicit time integration methods for systems of ordinary differential equations odes with stiff damping term the important feature of the new methods resides in the fact that they are capable of exactly preserving the steady states as well as maintaining the sign of the computed solution under the time step restriction determined by the nonstiff part of the system only the new semi implicit methods are based on the modification of explicit strong stability preserving runge kutta ssp rk methods and are proven to have a formal second order of accuracy a alpha stability and stiff decay we illustrate the performance of the proposed ssp rk based semi implicit methods on both a scalar ode example and a system of odes arising from the semi discretization of the shallow water equations with stiff friction term the obtained numerical results clearly demonstrate that the ability of the introduced ode solver to exactly preserve equilibria plays

a note on observers for lipschitz nonlinear systems this note deals with the design of reduced order observers for lipschitz nonlinear systems it shows that the conditions under which a full order observer exists also guarantee the existence of a reduced order observer a design method of the reduced order observer that is dependent on the solution of the riccati equation is then presented and an example is given to illustrate effects of the design method

linear rank and corank preserving maps on b h and an application to semigroup isomorphisms of operator ideals abstract we characterize linear rank k nonincreasing rank k preserving and corank k preserving maps on b h the algebra of all bounded linear operators on the hilbert space h this unifies and extends finite dimensional results and results on linear rank 1 non increasing and rank 1 preserving maps in the infinite dimensional case we conclude with an application to semigroup isomorphisms of operator ideals

full order observers for linear systems with unknown inputs this note presents a simple method to design a full order observer for linear systems with unknown inputs the necessary and sufficient conditions for the existence of the observer are given

h sub spl infin filtering for singular systems this note considers the h sub spl infin filtering problem for linear continuous singular systems the purpose is the design of a linear filter such that the resulting error system is regular impulse free and stable while the closed loop transfer function from the disturbance to the filtering error output satisfies a prescribed h sub spl infin norm bound constraint without decomposing the original system matrices a necessary and sufficient condition for the solvability of this problem is obtained in terms of a set of linear matrix inequalities lmis when these lmis are feasible an explicit expression of a desired filter is given finally an illustrative example is presented to demonstrate the applicability of the proposed approach

technical communique robust admissibility of time varying singular systems with commensurate time delays this paper addresses the problem of admissibility of time varying singular systems with commensurate time delays by introducing a new method to study the convergence of the fast sub system an admissibility condition is obtained in terms of linear matrix inequalities which guarantees the considered time varying singular delay system to be regular impulse free and stable furthermore a robust admissibility condition is proposed for the case when the time varying system matrices admit the usual constant plus norm bounded structure it is theoretically established that the proposed robust admissibility condition is less conservative than the existing one in the literature one of the important features of the results is that the inferred admissibility condition coincides with the usual stability condition for state space delay systems moreover the results are also applicable to the multiple rational delay case

on newton type approach for piecewise linear systems we investigate effective newton type methods for solving piecewise linear systems we prove that under certain relaxed conditions the proposed newton type methods converge monotonically and have a finite termination property moreover we give some conclusions on the existence of solution for the piecewise linear systems

two results on the size of spectrahedral descriptions a spectrahedron is a set defined by a linear matrix inequality given a spectrahedron we are interested in the question of the smallest possible size r of the matrices in the description by linear matrix inequalities we show that for the n dimensional unit ball r is at least frac n 2 if n 2 k 1 then we actually have r n the same holds true for any compact convex set in mathbb r n defined by a quadratic polynomial furthermore we show that for a convex region in mathbb r 3 whose algebraic boundary is smooth and defined by a cubic polynomial we have that r is at least five more precisely we show that if a b c in sym r mathbb r are real symmetric matrices such that f x y z det i r a x b y c z is a cubic polynomial then the surface in complex projective three space with affine equation f x y z 0 is singular

robust h infinity filtering for a class of non linear systems with state delay and parameter uncertainty this paper deals with the problem of robust h infinity filtering for a class of state delayed non linear systems with normbounded parameter uncertainty appearing in all the matrices of the linear part of the system model the non linearities are assumed to satisfy the global lipschitz conditions and appear in both the state and measured output equations attention is focused on the design of a non linear filter which ensures both the robust stability and a prescribed h infinity performance of the filtering error dynamics for all admissible uncertainties a sufficient condition for the existence of such a filter is given in terms of a linear matrix inequality lmi when this lmi is feasible the expression of a desired h infinity filter is also presented a numerical example is provided to demonstrate the applicability of the proposed approach

observers for a class of nonlinear singular systems this technical note considers the observers design for a class of nonlinear singular systems the approach is based on the new parameterization of the generalized sylvester equations solutions the conditions for the existence of these observers are given and sufficient conditions for their stability are derived using linear matrix inequalities lmis formulation reduced order minimal order and full order observers are designed by a unified method a numerical example is presented to demonstrate the effectiveness of the developed method

nonlinear observers a circle criterion design and robustness analysis globally convergent observers are designed for a class of systems with monotonic nonlinearities the approach is to represent the observer error system as the feedback interconnection of a linear system and a time varying multivariable sector nonlinearity using lmi software observer gain matrices are computed to satisfy the circle criterion and hence to drive the observer error to zero in output feedback design the observer is combined with control laws that ensure input to state stability with respect to the observer error robustness to unmodeled dynamics is achieved with a small gain assignment design as illustrated on a jet engine compressor example

robust normalization and stabilization of uncertain descriptor systems with norm bounded perturbations this note is concerned with the problem of the so called quadratic normalization and stabilization via both proportional and derivative state feedback pdsf and proportional and derivative output feedback pdof for uncertain descriptor systems with norm bounded perturbations necessary and sufficient conditions are presented in terms of linear matrix inequalities lmis or quadratic matrix inequalities qmis by using a simple idea of changing the problem to the corresponding stabilization problem of an augmented uncertain system