on system equivalence this note establishes the relationship between strong system equivalence 3 and complete system equivalence 6 and deduces two sets of compact conditions for strong system equivalence of polynomial realizations

a hermite upwind weno scheme for solving hyperbolic conservation laws this paper proposes a new weno procedure to compute problems containing both discontinuities and a large disparity of characteristic scales in a one dimensional context the weno procedure is defined on a three points stencil and designed to be sixth order in regions of smoothness we define a finite volume discretization in which we consider the cell averages of the variable and its first derivative as discrete unknowns the reconstruction of their point values is then ensured by a unique sixth order hermite polynomial this polynomial is considered as a symmetric and convex combination by ideal weights of three fourth order polynomials a central polynomial defined on the three points stencil is combined with two polynomials based on the left and the right two points stencils the symmetric nature of such an interpolation has an important consequence the choice of ideal weights has no influence on the properties of the discretization this advantage enables to formulate the hermite interpolation for non uniform meshes following the methodology of the classic weno procedure nonlinear weights are then defined to deal with the peculiarities of the hermite interpolation near discontinuities we define a new procedure in order for the nonlinear weights to smoothly evolve between the ideal weights in regions of smoothness and one sided weights otherwise the resulting scheme is a sixth order weno method based on central hermite interpolation and tvd runge kutta time integration we call this scheme the hcweno6 scheme numerical experiments in the scalar and the 1d euler cases make it possible to check and to validate the options selected in these experiments we emphasize the resolution power of the method by computing test cases that model realistic aero acoustic problems

a chebyshev based rectangular polar integral solver for scattering by general geometries described by non overlapping patches this paper introduces a high order accurate strategy for integration of singular kernels and edge singular integral densities that appear in the context of boundary integral equation formulations of the problem of acoustic scattering in particular the proposed method is designed for use in conjunction with geometry descriptions given by a set of arbitrary non overlapping logically quadrilateral patches which makes the algorithm particularly well suited for treatment of cad generated geometries fejer s first quadrature rule is incorporated in the algorithm to provide a spectrally accurate method for evaluation of contributions from far integration regions while highly accurate precomputations of singular and near singular integrals over certain surface patches together with two dimensional chebyshev transforms and suitable surface varying rectangular polar changes of variables are used to obtain the contributions for singular and near singular interactions the overall integration method is then used in conjunction with the linear algebra solver gmres to produce solutions for sound soft open and closed surface scattering obstacles including an application to an aircraft described by means of a cad representation the approach is robust fast and highly accurate use of a few points per wavelength suffices for the algorithm to produce far field accuracies of a fraction of a percent and slight increases in the discretization densities give rise to significant accuracy improvements

an unconditionally stable fully conservative semi lagrangian method semi lagrangian methods have been around for some time dating back at least to 3 researchers have worked to increase their accuracy and these schemes have gained newfound interest with the recent widespread use of adaptive grids where the cfl based time step restriction of the smallest cell can be overwhelming since these schemes are based on characteristic tracing and interpolation they do not readily lend themselves to a fully conservative implementation however we propose a novel technique that applies a conservative limiter to the typical semi lagrangian interpolation step in order to guarantee that the amount of the conservative quantity does not increase during this advection in addition we propose a new second step that forward advects any of the conserved quantity that was not accounted for in the typical semi lagrangian advection we show that this new scheme can be used to conserve both mass and momentum for incompressible flows for incompressible flows we further explore properly conserving kinetic energy during the advection step but note that the divergence free projection results in a velocity field which is inconsistent with conservation of kinetic energy even for inviscid flows where it should be conserved for compressible flows we rely on a recently proposed splitting technique that eliminates the acoustic cfl time step restriction via an incompressible style pressure solve then our new method can be applied to conservatively advect mass momentum and total energy in order to exactly conserve these quantities and remove the remaining time step restriction based on fluid velocity that the original scheme still had

observability of structured linear systems in descriptor form a graph theoretic approach this paper deals with the right hand side observability of structured linear systems in descriptor form the method we propose is based on a graph theoretic approach it is applicable to a large class of descriptor systems including regular and nonregular systems even if they are square underdetermined or overdetermined after defining digraphs which represent such systems we express in graphic terms necessary and sufficient conditions to achieve the observability of the whole or of a given part of the state these conditions are easy to check because they are based on comparison of integers and on finding edges and subgraphs in a digraph therefore our approach is suited to study large scale and or uncertain systems

minimality of descriptor representations under external equivalence abstract necessary and sufficient conditions are derived for the minimality of descriptor representations under external equivalence these conditions are stated completely in terms of the matrices e a b c and d use is made of the close connection between the descriptor representation and the so called pencil representation this connection is further exploited to derive the transformation group for minimal descriptor representations it is shown that the transformations coincide with the operations of strong equivalence as introduced by verghese et al ieee trans aut control ac 26 811 831 1981

the inverse distance weighted interpolation applied to a particular form of the path tubes method a simplified version of the inverse distance weighted interpolation formula was mathematically analyzed and employed in the context of a semi lagrangian scheme for the equation of advection the scheme used is a particular formulation of path tubes method a physically intuitive conservative method whose formulation is based on the theoretical foundations of the mechanics of continuous media which uses the so called reynolds s transport theorem to establish judiciously its main property written on the basis of a conservative integral equation the resulting algorithm is a five point explicit semi lagrangian scheme for incompressible flow from rigorous deductions based on the von neumann stability analysis it was proven that this explicit method is unconditionally stable the present algorithm was evaluated using test problems that are prototypes of more sophisticated mathematical models commonly employed in the prediction of intensity variations of weather fronts in addition our methodology was compared against two other methods available in the literature the proposed explicit semi lagrangian scheme was able to work with long time steps and proved to be accurate non oscillatory and non diffusive

transformations of matrix pencils and implications in linear systems theory a new transformation of matrix pencils is proposed and its theory formally developed its restriction to generalized state space system matrix pencils is shown to be an appropriate generalization of the usual state space transformation and to represent a closed form expression in system matrix terms of verghese s concept of strong equivalence of such pencils

the optimal p version approximation of singularities on polyhedra in the boundary element method we consider elliptic boundary value problems on three dimensional polyhedral domains we describe the three types of singular components that arise in the solution edge vertex and edge vertex singularities we analyze the approximation of the traces of each of each of these different types of singularities by polynomial subspaces on the boundary as the polynomial degree p tends to infinity the p version we establish asymptotic rates of convergence that are optimal in the h t norm over the boundary for 0 leq t leq 1 we apply these results to a galerkin boundary element method bem formulation for a model neumann problem obtaining the optimal convergence rate for the p version bem over polyhedral domains

restricted invariant factor assignment under state feedback abstract for a given matrix pair a b a square necessary and sufficient conditions are established for the existence of a state feedback matrix f such that a bf is in the same similarity class as a partially prescribed square matrix

a frequency domain approach to control of singular systems in this paper singular control systems are studied from the frequency domain point of view the proper stable factorization of a singular system is derived the stability of the closed loop system consisting of a singular system and controller is addressed most significantly all proper stabilizing controllers are parameterized for a given singular system

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

higher order schemes with cip method and adaptive soroban grid towards mesh free scheme a new class of body fitted grid system that can keep the third order accuracy in time and space is proposed with the help of the cip constrained interpolation profile cubic interpolated propagation method the grid system consists of the straight lines and grid points moving along these lines like abacus soroban in japanese the length of each line and the number of grid points in each line can be different the cip scheme is suitable to this mesh system and the calculation of large cfl 10 at locally refined mesh is easily performed mesh generation and searching of upstream departure point are very simple and almost mesh free treatment is possible adaptive grid movement and local mesh refinement are demonstrated

stationary lqg control of singular systems the stationary linear quadratic gaussian control problem is formulated and solved for single input single output singular systems the control system is required to be internally proper and stable in order to avoid both impulsive and unstable exponential behavior the set of all controllers resulting in such a control system is specified in parametric form all controllers that yield finite cost are identified once again in parametric form within this set necessary and sufficient conditions are then established for an optimal controller to exist all optimal controllers are shown to possess the same transfer function the problem is analyzed in the complex domain the transfer functions are expressed as quotients of proper strict hurwitz rational functions by means of this maneuver the powerful tools of algebra are made available the synthesis of the optimal controller is reduced to the solution of two linear diophantine equations whose coefficients are obtained by spectral factorization

block structured adaptive mesh refinement algorithms for vlasov simulation direct discretization of continuum kinetic equations like the vlasov equation are under utilized because the distribution function generally exists in a high dimensional 3d space and computational cost increases geometrically with dimension we propose to use high order finite volume techniques with block structured adaptive mesh refinement amr to reduce the computational cost the primary complication comes from a solution state comprised of variables of different dimensions we develop the algorithms required to extend standard single dimension block structured amr to the multi dimension case specifically algorithms for reduction and injection operations that transfer data between mesh hierarchies of different dimensions are explained in detail in addition modifications to the basic amr algorithm that enable the use of high order spatial and temporal discretizations are discussed preliminary results for a standard 1d 1v vlasov poisson test problem are presented results indicate that there is potential for significant savings for some classes of vlasov problems

robust stabilization of discrete generalized systems the robust stabilization problem for generalized discrete time systems described by polynomial or improper transfer function matrices subject to perturbations acting on the normalized coprime factors is solved the maximum achievable stability margin and the robust stabilizing controller are given in terms of realizations and solutions to appropriate riccati equations

boundary value descriptor systems well posedness reachability and observability in this paper we introduce the class of two point boundary value descriptor systems tpbvds discrete time systems described by possibly linear dynamics and a set of boundary conditions constraining the values of the system state at the two endpoints of the system s interval of definition by introducing a standard form for regular pencils we obtain a new and simple generalized cayley hamilton theorem that simplifies our investigation of well posedness green s function solutions and reachability and observability for tpbvds there are two distinct notions of reachability and observability that one can define for tpbvds associated with processes that propagate inward from and outward toward the boundaries we investigate each of these in detail obtaining among other things far simpler forms for the reachability and observability results than found previously in the literature in addition we describe several methods for the efficient solution of tpbvds one involving recursions from each end of t

directional sparsity in optimal control of partial differential equations we study optimal control problems in which controls with certain sparsity patterns are preferred for time dependent problems the approach can be used to find locations for control devices that allow controlling the system in an optimal way over the entire time interval the approach uses a nondifferentiable cost functional to implement the sparsity requirements additionally bound constraints for the optimal controls can be included we study the resulting problem in appropriate function spaces and present two solution methods of newton type based on different formulations of the optimality system using elliptic and parabolic test problems we research the sparsity properties of the optimal controls and analyze the behavior of the proposed solution algorithms

a new notion of equivalence for discrete time ar representations we present a new equivalence transformation termed divisor equivalence that has the property of preserving both the finite and the infinite elementary divisor structures of a square non singular polynomial matrix this equivalence relation extends the known notion of strict equivalence which dealt only with matrix pencils to the general polynomial matrix case it is proved that divisor equivalence characterizes in a closed form relation the equivalence classes of polynomial matrices that give rise to fundamentally equivalent discrete time auto regressive representations

characteristics of the process zone at sharp notch roots the classical williams solution for the state of stress at the tip of a semi infinite notch is re visited and the two term singular solution re written in a form making the mode mixity and load magnitude explicit this is used to show that for a 270 solid angle the majority of notch problems exhibit a process zone which is entirely or substantially mode i in character which in turn means that the notch strength may practically be governed by a single elastic parameter a method for finding the practical limit on the load and stress intensity ratio where this holds is described

a high order time splitting method based on integral deferred correction for semi lagrangian vlasov simulations semi lagrangian schemes with various splitting methods and with different reconstruction interpolation strategies have been applied to kinetic simulations for example the order of spatial accuracy of the algorithms proposed in qiu and christlieb 2010 29 is very high as high as ninth order however the temporal error is dominated by the operator splitting error which is second order for strang splitting it is therefore important to overcome such low order splitting error in order to have numerical algorithms that achieve higher orders of accuracy in both space and time in this paper we propose to use the integral deferred correction idc method to reduce the splitting error specifically the temporal order accuracy is increased by r with each correction loop in the idc framework where r 1 2r 1 2 for coupling the first order splitting and the strang splitting respectively the proposed algorithm is applied to the vlasov poisson system the guiding center model and two dimensional incompressible flow simulations in the vorticity stream function formulation we show numerically that the idc procedure can automatically increase the order of accuracy in time we also investigate numerical stability of the proposed algorithm via performing fourier analysis to a linear model problem

solvability controllability and observability of continuous descriptor systems in this paper we investigate the properties of the continuous descriptor system e dot x t ax t bu t 0 leqt leqb where e a and b are complex and possibly singular matrices and u t is a complex function differentiable sufficiently many times the traditional approach to such systems is to separate the state equations from the algebraic equations however such algorithms usually destroy the natural physically based sparsity and structure of the original system therefore we consider descriptor systems in their original form such systems possess numerous properties not shared by the well known state variable systems first we relate classical theories of matrix pencils to the solvability of descriptor systems then we extend the concepts of reachability controllability and observability of state variable systems to descriptor systems and describe the set of reachable states for descriptor systems

inner outer factorization for strictly proper functions with j w axis zeros abstract this paper discussed the inner outer factorization for square real rational matrices which may have zeros on the j axis including infinity a factorization method is given in terms of the descriptor form representation of the rational matrix this method uses the solution of a generalized riccati equation we also propose an efficient computation algorithm for solving the generalized riccati equation

a framework for the solution of the generalized realization problem in this paper we present a novel way of constructing generalized state space representations e a b c d of interpolants matching tangential interpolation data the loewner and shifted loewner matrices are the key tools in this approach

analysis of descriptor systems using numerical algorithms in this paper we analyze numerical methods for the solution of the large scale dynamical system e dot y t ay t g t y t 0 y 0 where e and a are matrices possibly singular systems of this type have been referred to as implicit systems and more recently as descriptor systems since they arise from formulating system equations in physical variables special cases of such systems are algebraic differential systems we discuss the numerical advantages of this formulation and identify a class of numerical integration algorithms which have accuracy and stability properties appropriate to descriptor systems and which preserve structure detect nonsolvable systems resolve initial value consistency problems and are applicable to stiff descriptor systems we also present an algorithm for the control of the local truncation error on only the state variables

general edge asymptotics of solutions of second order elliptic boundary value problems i this is the first of two papers in which we study the singularities of solutions of second order linear elliptic boundary value problems at the edges of piecewise analytic domains in 3 when the opening angle at the edge is variable there appears the phenomenon of crossing of the exponents of singularities for this case we introduce the appropriate combinations of the simple tensor product singularities that allow us to give estimates in ordinary and weighted sobolev spaces for the regular part of the solution and for the coefficients of the singularities these combinations appear in a natural way as sections of an analytic bundle above the edge their behaviour is described with the help of divided differences of powers of the distance to the edge the class of operators considered includes second order elliptic operators with analytic complex valued coefficients with mixed dirichlet neumann or oblique derivative conditions with our description of the singularities we are able to remove some restrictive hypotheses that were previously made in other works in this first part we prove the basic facts in a simplified framework nevertheless the tools we use are essentially the same in the general situation

three dimensional eulerian method for large deformation of viscoelastic fluid toward plate mantle simulation toward the unified simulation of the large deformation of a rigid viscoelastic material plate and the convection of a viscous fluid mantle an eulerian scheme with a semi lagrangian method is developed the scheme adopts the cip cslr method for advection terms of staggered grid system in three dimensions the positive transported profile of a positive quantity is assured by flux corrections in the dimensional splitting method the jaumann co rotational effect of the stress tensor is also integrated into the semi lagrangian treatment this co rotated semi lagrangian method is combined with an exponential time differencing method in the time development of the maxwell constitutive model the large time step comparable to or larger than the maxwell relaxation time is successfully realized validation tests are performed for the three dimensional rayleigh taylor instability of a viscoelastic material with jump discontinuity of the mass density and other material properties

a survey of the maximum principles for optimal control problems with state constraints this paper gives a survey of the various forms of pontryagin s maximum principle for optimal control problems with state variable inequality constraints the relations between the different sets of optimality conditions arising in these forms are shown furthermore the application of these maximum principle conditions is demonstrated by solving some illustrative examples

barrier methods for optimal control problems with convex nonlinear gradient state constraints in this paper we are concerned with the application of interior point methods in function space to gradient constrained optimal control problems governed by partial differential equations we will derive existence of solutions together with first order optimality conditions afterwards we show continuity of the central path together with convergence rates depending on the interior point parameter

state feedback and transfer matrix in singular systems abstract the influence of state feedback on the transfer matrix in singular systems is considered we first discuss the problem for siso systems then by utilizing the time scale transformation the same problem is solved for mimo systems we also consider realizations of the feedback control strategies given here it is pointed out that the singular system is distinguished from the normal one by an important feature we can design a pure input prediction system for it finally the results are applied to the model matching problem

regularity of the solutions for elliptic problems on nonsmooth domains in r3 part 2 regularity in neighborhoods of edges this paper is the second in a series of three devoted to the analysis of the regularity of solutions of elliptic problems on nonsmooth domains in 3 the present paper concentrates on the regularity of solutions of the poisson equation in neighbourhoods of edges of a polyhedral domain in the framework of the weighted sobolev spaces and countably normed spaces these results can be generalised to elliptic problems arising from mechanics and engineering for instance the elasticity problem on polyhedral domains hence the results are not only important to understand comprehensively the qualitative and quantitative aspects of the behaviours of the solution and its derivatives of all orders in neighbourhoods of edges but also essential to design an effective computation and analyse the optimal convergence of the finite elements solutions for these problems

controllability and observability of second order descriptor systems we analyze controllability and observability conditions for second order descriptor systems and show how the classical conditions for first order systems can be generalized to this case we show that performing a classical transformation to first order form may destroy some controllability and observability properties as an example we demonstrate that the loss of impulse controllability in constrained multibody systems is due to the representation as a first order system to avoid this problem we will derive a canonical form and new first order formulations that do not destroy the controllability and observability properties

weighted norm least squares finite element method for poisson equation in a polyhedral domain this paper concerns poisson equation in a polyhedral domain with corners and edges we apply the least squares finite element method to the reformulated first order system of poisson equation to overcome the difficulties from boundary singularities a weighted norm technique is used to define the least squares functional the method prevents the loss of global accuracy numerical simulations are given to demonstrate the theoretical estimates

fundamental properties of the manifold of singular and regular linear systems abstract we construct a real analytic manifold l of systems of the form e x ax bu y cx and show that l is the completion with respect to solutions of the set of regular state space systems i e those systems with nonsingular e other geometric and analytic properties of l are established including genericity of the regular systems

new interpolation technique for the cip method on curvilinear coordinates we propose a new interpolation technique for the cip method applied to curvilinear coordinates the cip method can hardly maintain third order accuracy on curvilinear coordinates the reason for the degeneracy in accuracies has not been discussed in detail this paper reveals the problems of the cip method on curvilinear coordinates and presents an improved cip method to solve the advection equation accurately the features of the presented method are 1 the metric computation on the upwind stencil is defined in the same manner as in the advection phase of the cip method and 2 gradient values in the physical domain in the computation on the curvilinear coordinates are used various test problems show that the improved cip method has approximate third order accuracy

on minimal order inverses of discrete time descriptor systems in this paper linear discrete time control systems of the form e k x k 1 a k x k b k u k y k c k x k d k u k are considered where e k and a k are not necessarily square matrices the problem to be solved is this find a system of the form e k v k 1 k v k bcirc k k u k kvk dcirc k k where k is a partitioned column vector whose blocks are linear combinations of some of the output vectors of the original system and which possesses either or both of the following properties i if the outputs of the original system are known then the output equation of the second system uniquely specifies the same inputs that generated the known outputs of the original system ii if the output vectors of the original system are desired outputs then the equation uk kvk dcirc k k yields one or more sequences of inputs for the original system that can generate the desired outputs we shall furthermore seek the system which among all systems having property i or ii or both has the sm

convergence in the boundary layer for singularly perturbed equations a singularly perturbed linear finite dimensional ordinary differential equation is considered on the half line 0 the reduced system is assumed to have a unique solution in the sense of distributions it is proved that under reasonable conditions the solution of the full system converges to that of the reduced in the distributional sense and the order of the limiting distribution is computed an application to the optimal linear quadratic regulator with cheap control is described

exactly conservative semi lagrangian scheme for multi dimensional hyperbolic equations with directional splitting technique abstract a new numerical method that guarantees exact mass conservation is proposed to solve multidimensional hyperbolic equations in semi lagrangian form the method is based on the constrained interpolation profile cip scheme and keeps the many good characteristics of the original cip scheme the cip strategy is applied to the integral form of variables although the advection and nonadvection terms are separately treated mass conservation is kept in the form of a spatial profile inside a grid cell therefore it retains various advantages of the semi lagrangian solution with exact conservation which has been beyond the capability of conventional semi lagrangian schemes

a jordan control canonical form for singular systems a canonical form for controllable singular systems modulo restricted system equivalence is presented the canonical form respects the decomposition of the singular system into a regular and an impulsive part the construction is based on popov s control canonical form and on the jordan canonical form recently developed by hinrichsen and pratzel wolters continuity properties are analysed and the cellular partition of the orbit space induced by the canonical form is briefly discussed

realizations in generalized state space form for polynomial system matrices and the definitions of poles zeros and decoupling zeros at infinity this paper contains three main results firstly a realization procedure is presented that brings a polynomial system matrix of a non proper multivariable system to generalized state space form such that all relevant properties including phenomena of redundancy associated with finite and infinite decoupling zeros are retained secondly new definitions are proposed for poles zeros and decoupling zeros at infinity of a general polynomial system matrix as a third result a theorem of rosenbrock 1974 e on the redundancy of lcr multiports is generalized to include the decoupling zeros at infinity

gradient augmented level set method for phase change simulations abstract a numerical method for the simulation of two phase flow with phase change based on the gradient augmented level set gals strategy is presented sharp capturing of the vaporization process is enabled by i identification of the vapor liquid interface t at the subgrid level ii discontinuous treatment of thermal physical properties except for and iii enforcement of mass momentum and energy jump conditions where the gradients of the dependent variables are obtained at t and are consistent with their analytical expression i e no local averaging is applied treatment of the jump in velocity and pressure at t is achieved using the ghost fluid method the solution of the energy equation employs the sub grid knowledge of t to discretize the temperature laplacian using second order one sided differences i e the numerical stencil completely resides within each respective phase to carefully evaluate the benefits or disadvantages of the gals approach the standard level set method is implemented and compared against the gals predictions the results show the expected trend that interface identification and transport are predicted noticeably better with gals over the standard level set this benefit carries over to the prediction of the laplacian and temperature gradients in the neighborhood of the interface which are directly linked to the calculation of the vaporization rate however when combining the calculation of interface transport and reinitialization with two phase momentum and energy the benefits of gals are to some extent neutralized and the causes for this behavior are identified and analyzed overall the additional computational costs associated with gals are almost the same as those using the standard level set technique

a weakly compressible scheme with a diffuse interface method for low mach number two phase flows abstract a weakly compressible scheme for gas liquid two phase flows with low mach number is proposed for a fully explicit time integration the scheme is based on the fractional step method with the euler equation solver and time integration for viscous surface tension and gravity terms for the efficient solution of the euler equation we introduce the directional splitting method and the method of characteristics which is applicable to semi lagrangian methods a reduction of the speed of sound is also taken into consideration to enlarge the time step intervals the primitive flow variables are time integrated on the node center configuration to capture the gas liquid interface the conservative phase field equation is solved by using the multi moment method it is computed as a conservative form for the volume averaged value defined at the cell center in which the flow velocities are given on the node we discard the exact momentum conservation however the total mass of gas and liquid is conserved by introducing a phase field variable several benchmark problems are examined and the results of the explicit scheme are in good agreement with the experimental and computational references

a generalized state space for singular systems systems of the form e dot x ax bu y cx with e singular are studied of particular interest are the impulsive modes that may appear in the free response of such systems when arbitrary initial conditions are permitted modes that are associated with natural system frequencies at infinity a generalized definition of system order that incorporates these impulsive degrees of freedom is proposed and concepts of controllability and observability are defined for the impulsive modes allowable equivalence transformations of such singular systems are specified the present framework is shown to overcome several difficulties inherent in other treatments of singular systems and to extend in a natural and satisfying way many results previously known only for regular state space systems

a fundamental notion of equivalence for linear multivariable systems a fundamental form of equivalence of polynomial matrix descriptions of linear multivariable systems is defined based on the existence of a bijective map between the finite and infinite solution sets of the differential equations describing the two systems the connection with the system matrix relationship of full system equivalence is established

infinite frequency structure preserving transformations for general polynomial system matrices a recent transformation proposed for polynomial matrices is extended to the systems theory case of general polynomial system matrices two such extensions are proposed depending on whether the system matrix or its normalized form is used the relationship between both these transformations is established and under them all finite and infinite frequency system zero and pole structure is shown to be invariant

conservative semi lagrangian schemes for vlasov equations conservative methods for the numerical solution of the vlasov equation are developed in the context of the one dimensional splitting in the case of constant advection these methods and the traditional semi lagrangian ones are proven to be equivalent but the conservative methods offer the possibility to add adequate filters in order to ensure the positivity in the non constant advection case they present an alternative to the traditional semi lagrangian schemes which can suffer from bad mass conservation in this time splitting setting

fundamental equivalence of generalized state space systems this paper defines a fundamental form of equivalence between two generalized state space systems in terms of mappings of the solution sets of the describing differential equations together with mappings of the sets of restricted initial conditions properties of this equivalence relation are discussed and it is shown to be an alternative characterization of the system matrix relationship of complete system equivalence

extracting edge flux intensity functions for the laplacian the solution to the laplace operator in three dimensional domains in the vicinity of straight edges is presented as an asymptotic expansion involving eigenpairs with their coefficients called edge flux intensity functions efifs the eigenpairs are identical to their two dimensional counterparts over a plane perpendicular to the edge extraction of efifs however cannot be obtained in a straightforward manner over this two dimensional plane a method based on l 2 projection and richardson extrapolation is presented for point wise extraction of efifs from p finite element solutions and illustrated by examples a similar but more efficient method based on energy projection for extracting efifs is proposed

a canonical parameterization of the kronecker form of a matrix pencil abstract the kronecker form is the classical canonical form for matrix pencils under strict equivalence transformation consider a matrix pencil whose entries are smooth functions of a parameter vector the kronecker form of the parameterized pencil will in general be a discontinuous function of the parameters for a linear time invariant control system these discontinuities correspond to a change in the finite and infinite invariant zero structure since many control strategies require knowledge of or place restrictions on the zero structure these points of discontinuity are of considerable interest in this paper a general approach to the study of such points is developed in the framework of singularity theory we derive a miniversal parameterization of a given pencil that is a parameterized family of pencils that i includes the given pencil ii is locally equivalent to any other family up to a change of parameters and iii uses the fewest number of parameters to achieve this property all nearby zero structures can be obtained by varying parameter values in the miniversal parameterization from all miniversal parameterizations one having a particularly uncluttered representation is selected as canonical however some restrictions on the finite elementary divisors are then required

some results on system equivalence simple necessary and sufficient conditions for system equivalence at infinity and strong system equivalence of systems in the form t s b c d are established a necessary condition for system equivalence at infinity of systems in the general form t s u s v s w s is also established

the cubic interpolated pseudo particle cip method application to nonlinear and multi dimensional hyperbolic equations abstract the basic of cip as a method to solve hyperbolic equations is re examined from a different viewpoint and the scheme is modified into an explicit finite difeerence form the method gives a stable and less diffusive result for square wave propagation compared with fct and a better result for propagation of a sine wave with a discontinuit the scheme is extended to nonlinear and multi dimensional problems

matrix pencil equivalents of a general 2 d polynomial matrix a two level algorithm which reduces a general 2 d polynomial matrix to an equivalent matrix pencil form is presented the exact nature of the equivalence transformation connecting the matrix with its associated pencil is established

the algorithm for computing nonmonic second order multivariable systems abstract an efficient method for computing impulse response matrices of nonmonic multivariable second order systems is proposed a procedure has been developed which uses some properties of regular matrix polynomials p s s 2 a 2 sa 1 a 0 with a 2 identically singular an algorithm suitable for computer use is established and its applications can be effectively controlled via the newly introduced special graphical scheme it produces simultaneously the adjoint and determinant of the matrix polynomial p s and avoids the inversion of any matrix moreover all computations can be performed on constant matrices and coefficients only it is shown that substantial economy may be achieved in computation time and storage when solving large order problems characteristic of many physical plants and engineering structures

h infinity kalman estimation for rectangular descriptor systems with unknown inputs this note considers h filtering and prediction for rectangular descriptor systems with unknown inputs that affect both the system and the output an optimal h descriptor kalman estimator hdke which can simultaneously solve the h filtering and prediction problems for rectangular descriptor systems with unknown inputs is developed based on the maximum likelihood descriptor kalman filtering method the hdke serves as a unified solution to solve h and kalman filtering for descriptor systems and standard systems with or without unknown inputs to reduce the computational complexity problem some efficient alternatives to the developed hdke are further proposed the relationship between the hdke and the existing literature results is also addressed an illustrative example is given to show the usefulness of the proposed results

a priori error estimates for optimal control problems with pointwise constraints on the gradient of the state we analyze a finite element approximation of an elliptic optimal control problem with pointwise bounds on the gradient of the state variable we derive convergence rates if the control space is discretized implicitly by the state equation in contrast to prior work we obtain these results directly from classical results for the w 1 error of the finite element projection without using adjoint information if the control space is discretized directly we first prove a regularity result for the optimal control to control the approximation error based on which we then obtain analogous convergence rates

matrix fractions and strict system equivalence unimodular equivalence ue is defined for matrix fraction decompositions mfds it is shown that if an mfd is regarded as a quadruple d s n s i then uni modular equivalence and fuhrmann strict system equivalence coincide it is thus established that ue for mfds and system similarity for state space representations are exact counterparts a brief discussion on extended unimodular equivalence eue of polynomial matrices is included and a short polynomial matrix proof that the invariant factors of the smith form are preserved under eue is given

conservative form of interpolated differential operator scheme for compressible and incompressible fluid dynamics the proposed scheme which is a conservative form of the interpolated differential operator scheme ido cf can provide high accurate solutions for both compressible and incompressible fluid equations spatial discretizations with fourth order accuracy are derived from interpolation functions locally constructed by both cell integrated values and point values these values are coupled and time integrated by solving fluid equations in the flux forms for the cell integrated values and in the derivative forms for the point values the ido cf scheme exactly conserves mass momentum and energy retaining the high resolution more than the non conservative form of the ido scheme a direct numerical simulation of turbulence is carried out with comparable accuracy to that of spectral methods benchmark tests of riemann problems and lid driven cavity flows show that the ido cf scheme is immensely promising in compressible and incompressible fluid dynamics studies

an optimization approach for well targeted transcranial direct current stimulation transcranial direct current stimulation tdcs is a noninvasive brain stimulation technique which modifies neural excitability by providing weak currents through scalp electrodes the aim of this study is to introduce and analyze a novel optimization method for safe and well targeted multiarray tdcs for optimization we consider an optimal control problem for a laplace equation with neumann boundary conditions with control and pointwise gradient state constraints we prove well posedness results for the proposed methods and provide computer simulation results in a highly realistic six compartment geometry adapted hexahedral head model for discretization of the proposed minimization problem the finite element method is employed and the existence of at least one minimizer to the discretized optimization problem is shown for numerical solution of the corresponding discretized problem we employ the alternating direction method of multipliers and comprehensively examine the cortical current flow field with regard to focality target intensity and orientation the numerical results reveal that the optimized current flow fields show significantly higher focality and in most cases higher directional agreement to the target vector in comparison to standard bipolar electrode montages

optimal control of elliptic equations with pointwise constraints on the gradient of the state in nonsmooth polygonal domains this article is concerned with optimal control problems subject to a second order elliptic pde and additional pointwise constraints on the gradient of the state in particular the existence of solutions on nonsmooth polygonal or polyhedral domains is analyzed in this situation the solution operator for the pde does not provide enough regularity to state the pointwise constraint for any right hand side due to the appearance of singularities associated to the corners edges and vertices of the domain further necessary optimality conditions for the solution of the optimization problem in two and three space dimensions are derived however in the three dimensional case certain critical angles along the edges of the domain have to be circumvented in the derivation of the optimality conditions finally the derived optimality conditions are utilized to deduce additional regularity for the control variable

algebraic and dynamic characterizations of poles and zeros at infinity abstract the presence of infinite frequency poles and zeros in a rational transfer function matrix is considered and certain algebraic characterizations for their occurrence are given one such characterization is shown to enable the transmission effects due to infinite poles and zeros to be ascertained in an extremely simple and direct way

numerical methods for extracting edge stress intensity functions in anisotropic three dimensional domains the solution to elasticity problems in three dimensional 3 d polyhedral domains in the vicinity of an edge is represented by a family of eigen functions similar to 2 d domains complemented by shadow functions and their associated edge stress intensity functions esifs which are functions along the edge these are of major engineering importance because failure theories directly or indirectly involve them in isotropic materials one may compute analytically the eigen functions and their shadows z yosibash n omer m costabel m dauge edge stress intensity functions in polyhedral domains and their extraction by a quasi dual function method int j fract 136 2005 37 73 used in conjunction with the quasi dual function method m costabel m dauge z yosibash a quasi dual function method for extracting edge stress intensity functions siam j math anal 35 5 2004 1177 1202 for extracting esifs from finite element solutions however in anisotropic materials and multi material interfaces the analytical derivation becomes intractable and numerical methods are mandatory herein we use p finite element methods p fem for the computation of the eigen pairs and shadow functions together with their duals having computed these the p fem is used again to obtain a fe solution from which we extract approximations of the esifs based on a family of adaptive hierarchical jacobi polynomials of increasing order numerical examples for 3 d isotropic and anisotropic materials are provided for which the eigen pairs and shadow functions are numerically computed and esifs extracted these examples show the efficiency and high accuracy of the numerical approximations 2007 elsevier b v all rights reserved

cubic interpolated pseudo particle method cip for solving hyperbolic type equations abstract a new cubic polynomial interpolation method where the gradient of the quantity is a free parameter is proposed for solving hyperbolic type equations various choices of the gradient are investigated and a stable and less diffusive scheme is made possible without the clipping or the flux correction procedure

a geometric approach to eigenstructure assignment for singular systems moore s well known result on the feedback assignment of eigenstructure in linear state space systems 5 was generalized to descriptor systems in 9 in this note we make some useful extensions to fill out the theory to begin with we do not assume controllability of the plant it is shown that the maximum number of finite closed loop eigenvalues is equal to dim el where l is the supremal a e r b invariant subspace in order to relate the possible closed loop structure to the open loop plant structure we define a set of indexes for descriptor systems which are in many respects similar to the controllability indexes of state space systems in terms of these controllability indexes we give a systematic approach to selecting the closed loop eigenvectors a major contribution of this note is the fact that it is geometric in nature and hence avoids any decomposition of the system matrices into a special form e g weierstrass form 1 the geometric setting introduced here should constitute a basis for further research in generalizing the well known results in geometric system theory disturbance decoupling input output decoupling etc to singular systems

weighted regularization of maxwell equations in polyhedral domains we present a new method of regularizing time harmonic maxwell equations by a bf grad div term adapted to the geometry of the domain this method applies to polygonal domains in two dimensions as well as to polyhedral domains in three dimensions in the presence of reentrant corners or edges the usual regularization is known to produce wrong solutions due the non density of smooth fields in the variational space we get rid of this undesirable effect by the introduction of special weights inside the divergence integral standard finite elements can then be used for the approximation of the solution this method proves to be numerically efficient

observers for singular systems the following three major aspects of the design of observers for linear time invariant singular systems are resolved the necessary and sufficient conditions for the problem to have a solution the order of the minimal observer and the properties of the closed loop system separation principle an algorithm is presented for the construction of the minimal order observer

a numerical procedure for the determination of certain quantities related to the stress intensity factors in two dimensional elasticity abstract this work is devoted to the investigation of corner and interface singularities in linear elasticity and to the development of a numerical code that computes certain quantities associated with those singularities we compute several terms of the asymptotic expansion of the solution of the elasticity system near the corner or interface which is of the form knr nfn in particular the n and fn we treat our problem as a non linear eigenvalue problem and we use an approach based on the shooting method for boundary value problems to create an analytic function whose zeros are the n above the zeros of this function are then found using an iteration method and a global method to make sure that no zero was overlooked the program works for the general case of anisotropic non homogeneous wedge with general boundary conditions as well as in the case of crossing interfaces in an internal point we test the convergence accuracy robustness efficiency and reliability of the code from those tests it can be seen that the code works quite well for the majority of the applications

dirichlet to neumann map for domains with corners and approximate boundary conditions we present in this paper the dirichlet to neumann operator for the wave equation on a straight wedge in r 2 using fourier integral operators as a consequence we recover the classical approximate boundary conditions of orders 1 and 2

an extension of wolovich s definition of equivalence of linear systems wolovich s classical definition of equivalence for linear systems 1974 is extended to the generalized study of linear systems it is shown that the resulting equivalence is an alternative characterization of the notion of full system equivalence underlying its fundamental role in the generalized study of linear systems

observers for discrete singular systems the author considers the design of observers for the discrete singular system ex k 1 ax k bu k y k cx k placing special emphasis on the problems of state reconstruction and minimal time state reconstruction it is shown that for a singular system finite poles can be moved to infinity by state feedback and the state can be reconstructed by causal observers

a geometric approach to proportional plus derivative feedback using quotient and partitioned subspaces abstract in this paper a new characterization of invariant subspaces is presented using the notions of partitioned and quotient subspaces this classification is based on a feedback approach that exhibits the importance of these subspaces for the problem of proportional plus derivative feedback it also provides the ability to decompose the closed loop system into two subsystems that completely characterize the closed loop behavior a feedback free formulation is also considered which opens new horizons for the problem of general semistate feedback by utilizing nonsquare pencils for spectrum assignability the importance of this technique arises from the fact that we deal with reduced order pencils therefore the computational methods are more stable in order to accomplish this we use two generalized lyapunov equations and exploit the generalized hessenberg form

multi dimensional conservative semi lagrangian method of characteristics cip for the shallow water equations a new characteristic approach that guarantees conservative property is proposed and is applied to the shallow water equations cip csl constrained interpolation profile conservative semi lagrangian interpolation is applied to the cip method of characteristics in order to enhance the mass conservation of the numerical result although the characteristic formulation is originally derived from non conservative form present scheme achieves complete mass conservation by solving mass conservation simultaneously and reflecting conserving mass in interpolation profile present method has less height error compared to the cip method of characteristics by several orders of magnitude by the enhanced conservation property present scheme is applicable to nonlinear problem such as shock furthermore application to two dimensions including the coriolis term is straightforward with directional splitting technique