energy conserving explicit local time stepping for second order wave equations locally refined meshes impose severe stability constraints on explicit time stepping methods for the numerical simulation of time dependent wave phenomena to overcome that stability restriction local time stepping methods are developed which allow arbitrarily small time steps precisely where small elements in the mesh are located when combined with a symmetric finite element discretization in space with an essentially diagonal mass matrix the resulting discrete numerical scheme is explicit is inherently parallel and exactly conserves a discrete energy starting from the standard second order leap frog scheme time stepping methods of arbitrary order of accuracy are derived numerical experiments illustrate the efficiency and usefulness of these methods and validate the theory

fundamental limits in sensitivity minimization multiple input multiple output mimo plants this paper provides a bridge between the h sub spl infin literature and that of fundamental limits by applying operator theoretic tools developed for the standard frequency domain model matching approach to sensitivity minimization explicit closed form expressions are given for tight bounds on the h sub spl infin norm of weighted sensitivity functions for output feedback control of linear multivariable systems

high order symplectic integration methods for finite element solutions to time dependent maxwell equations in this paper we motivate the use of high order integration methods for finite element solutions of the time dependent maxwell equations in particular we present a symplectic algorithm for the integration of the coupled first order maxwell equations for computing the time dependent electric and magnetic fields symplectic methods have the benefit a conserving total electromagnetic field energy and are therefore preferred over dissipative methods such as traditional runge kutta in applications that require high accuracy and energy conservation over long periods of time integration we show that in the context or symplectic methods several popular schemes can be elegantly cast in a single algorithm we conclude with some numerical examples which demonstrate the superior performance of high order time integration methods

a vector finite element time domain method for solving maxwell s equations on unstructured hexahedral grids in this paper the vector finite element time domain vfetd method is derived analyzed and validated the vfetd method uses edge vector finite elements as a basis for the electric field and face vector finite elements as a basis for the magnetic flux density the galerkin method is used to convert maxwell s equations to a coupled system of ordinary differential equations the leapfrog method is used to advance the fields in time the method is shown to be stable and to conserve energy and charge for arbitrary hexahedral grids a numerical dispersion analysis shows the method to be second order accurate on distorted hexahedral grids several computational experiments are performed to determine the accuracy and efficiency of the method

comments on robust tracking control for rigid robotic manipulators in the original paper by m zhihong and m palaniswami ibid vol 39 p 154 9 1994 a robust tracking control using a nominal feedback controller and a variable structure compensator for a rigid robotic manipulator with uncertain dynamics was presented it is assumed that the model uncertainty is bounded the author claims that this assumption is not necessarily correct and that the results obtained are therefore untenable

higher order triangular finite elements with mass lumping for the wave equation in this article we construct new higher order finite element spaces for the approximation of the two dimensional 2d wave equation these elements lead to explicit methods after time discretization through the use of appropriate quadrature formulas which permit mass lumping these formulas are constructed explicitly error estimates are provided for the corresponding semidiscrete problem finally higher order finite difference time discretizations are proposed and various numerical results are shown

dissipative terms and local time stepping improvements in a spatial high order discontinuous galerkin scheme for the time domain maxwell s equations in this paper we present some improvements in terms of accuracy and speed up for a particular well adapted discontinuous galerkin method devoted to the time domain maxwell equations first to reduce spurious modes on very distorted meshes the addition of dissipative terms as penalization in the numerical scheme is studied and compared on examples second in order to increase the efficiency of the method a multi class local time stepping strategy is presented and its validation and advantages are highlighted on different examples

fundamental design tradeoffs in filtering prediction and smoothing this paper examines fundamental design tradeoffs that apply to all linear filtering prediction and smoothing problems we introduce sensitivity functions that quantify filter performance and we show that their frequency response satisfies constraints imposed by unstable poles and nonminimum phase zeros of the system the constraints allow one to determine a priori whether or not a desired filter performance is attainable and how different arrangements of the measurement system influence the achievable performance

the cramer rao lower bound for directions of arrival of gaussian cyclostationary signals the cramer rao lower bound on the variance of estimates of directions of arrival signal strengths and carrier frequencies and phases of cyclostationary signals arriving at an array is considered numerical evaluations of the bound for the estimates of directions of arrival show that it can be orders of magnitude lower than the corresponding bound for stationary signals despite the great number of unknown parameters in the former case comparisons with the mean squared error of direction estimates obtained by the cyclic least squares algorithm show that the bound is not overly optimistic

nodal high order methods on unstructured grids we present a convergent high order accurate scheme for the solution of linear conservation laws in geometrically complex domains as our main example we include a detailed development and analysis of a scheme for the time domain solution of maxwell s equations in a three dimensional domain the fully unstructured spatial discretization is made possible by the use of a high order nodal basis employing multivariate lagrange polynomials defined on the triangles and tetrahedra while the equations themselves are satisfied in a discontinuous galerkin form with the boundary conditions being enforced weakly through a penalty term accuracy stability and convergence of the semidiscrete approximation to maxwell s equations is established rigorously and bounds on the growth of the global divergence error are provided concerns related to efficient implementations are discussed in detail this sets the stage for the presentation of examples verifying the theoretical results and illustrating the versatility flexibility and robustness when solving two and three dimensional benchmark problems in computational electromagnetics pure scattering as well as penetration is discussed and high parallel performance of the scheme is demonstrated

mixed discontinuous galerkin approximation of the maxwell operator we introduce and analyze a discontinuous galerkin discretization of the maxwell operator in mixed form here all the unknowns of the underlying system of partial differential equations are approximated by discontinuous finite element spaces of the same order for piecewise constant coefficients the method is shown to be stable and optimally convergent with respect to the mesh size numerical experiments highlighting the performance of the proposed method for problems with both smooth and singular analytical solutions are presented

generalization of integral constraints on sensitivity to time delay systems extends results on integral constraints to time delay systems key technical issues in this extension include properties of nonminimum phase zeros the convergence of blaschke products and the poisson integral the results have implications for scalar and multivariable control system design as well as in filtering problems

conservative space time mesh refinement methods for the fdtd solution of maxwell s equations a new variational space time mesh refinement method is proposed for the fdtd solution of maxwell s equations the main advantage of this method is to guarantee the conservation of a discrete energy that implies that the scheme remains l 2 stable under the usual cfl condition the only additional cost induced by the mesh refinement is the inversion at each time step of a sparse symmetric positive definite linear system restricted to the unknowns located on the interface between coarse and fine grid the method is presented in a rather general way and its stability is analyzed an implementation is proposed for the yee scheme in this case various numerical results in 3 d are presented in order to validate the approach and illustrate the practical interest of space time mesh refinement methods

integral constraints on sensitivity vectors for multivariable linear systems this paper develops integral constraints on sensitivity vectors for multivariable feedback systems due to either unstable poles or non minimum phase zeros of the plant the results presented cover the continuous rational or distributed case and are based on the use of directions corresponding to zeros or poles of the plant the integral constraints are in vector form and give new insights into the inherent trade offs in sensitivity reduction for multivariable systems and the cost of decoupling

crossover frequency limitations in mimo nonminimum phase feedback systems this paper investigates limitations and design tradeoffs of the closed loop sensitivity performance of linear time invariant nonminimum phase uncertain multiple input multiple output plants with i inputs and m outputs where m spl les l it is shown that if rows i sub 1 i sub k of the plant transfer function form a k spl times l nonminimum phase transfer matrix and if the design is such that the sensitivity gain of k 1 rows among the rows i sub 1 i sub k of the closed loop transfer function is low then by necessity the sensitivity gain of the remaining row is high this sensitivity constraint is quantified with the help of the crossover frequency restriction of a specially constructed single input single output transfer function that includes the right half plane zeros and poles of the k spl times l transfer matrix

technical communique cheap decoupled control requiring a controlled system to be decoupled may increase some performance costs however decoupling may be desirable from an applied perspective this paper gives an explicit quantification of decoupling costs in terms of the average quadratic tracking error the analysis exploits the parametrisation of all decoupling controllers together with wiener hopf frequency domain techniques

right half plane poles and zeros and design tradeoffs in feedback systems this paper expresses limitations imposed by right half plane poles and zeros of the open loop system directly in terms of the sensitivity and complementary sensitivity functions of the closed loop system the limitations are determined by integral relationships which must be satisfied by these functions the integral relationships are interpreted in the context of feedback design

a new family of mixed finite elements in ir 3 we introduce two families of mixed finite element on conforming inh div and one conforming inh curl these finite elements can be used to approximate the stokes system

brief fundamental limitations due to jω axis zeros in siso systems this paper shows that fundamental limitations arise from the presence of stable zeros on or near the j w axis the stability of the closed loop system is used in conjunction with the laplace transform to show that time domain integral constraints must be satisfied by the system response the presence of stable zeros near the j w axis together with upper limits on the permissible overshoot of the output signal place an effective lower bound on the settling time of the closed loop system the constraints are illustrated by an application to the control of a single stand reversing mill

explicit local time stepping methods for maxwell s equations explicit local time stepping methods are derived for time dependent maxwell equations in conducting and non conducting media by using smaller time steps precisely where smaller elements in the mesh are located these methods overcome the bottleneck caused by local mesh refinement in explicit time integrators when combined with a finite element discretisation in space with an essentially diagonal mass matrix the resulting discrete time marching schemes are fully explicit and thus inherently parallel in a non conducting source free medium they also conserve a discrete energy which provides a rigorous criterion for stability starting from the standard leap frog scheme local time stepping methods of arbitrarily high accuracy are derived for non conducting media numerical experiments with a discontinuous galerkin discretisation in space validate the theory and illustrate the usefulness of the proposed time integration schemes

interior penalty discontinuous galerkin method for maxwell s equations energy norm error estimates we develop the symmetric interior penalty discontinuous galerkin dg method for the time dependent maxwell equations in second order form we derive optimal a priori error estimates in the energy norm for smooth solutions we also consider the case of low regularity solutions that have singularities in space

decoupling linear multiinput multioutput plants by dynamic output feedback an algebraic theory this paper presents an algebraic theory for the design of a decoupling compensator for linear time invariant multiinput multioutput systems the design method uses a two input one output compensator which gives a convenient parametrization of all diagonal input output i o maps and all disturbance to output d o maps achievable by a stabilizing compensator for a given plant it is shown that this method has two degrees of freedom any achievable diagonal i o map and any achievable d o map can be realized simultaneously by a choice of an appropriate compensator the difference between all achievable diagonal and nondiagonal i o maps and the cost of decoupling is discussed for some particular algebraic settings

a conservative space time mesh refinement method for the 1 d wave equation part ii analysis we introduced in 2 a new method for space time refinement for the 1 d wave equation this method is based on the conservation of a discrete energy through two different discretization grids which guarantees the stability of the scheme in this second part we analyse the accuracy of this scheme in a detailed way by means of a plane wave analysis and numerical experiments that permit us to point out spurious numerical phenomena and explain how to control them