h sub infinity optimal control with state feedback a h sub infinity optimal control problem in which the measured outputs are the states of the plant is considered the main result shows that the infimum of the norm of the closed loop transfer function using linear static state feedback equals the infimum of the norm of the closed loop transfer function over all stabilizing dynamic even nonlinear time varying state feedback controllers

equations for finite difference time domain simulation of sound propagation in moving inhomogeneous media and numerical implementation finite difference time domain fdtd calculations are typically performed with partial differential equations that are first order in time equation sets appropriate for fdtd calculations in a moving inhomogeneous medium with an emphasis on the atmosphere are derived and discussed in this paper two candidate equation sets both derived from linearized equations of fluid dynamics are proposed the first which contains three coupled equations for the sound pressure vector acoustic velocity and acoustic density is obtained without any approximations the second which contains two coupled equations for the sound pressure and vector acoustic velocity is derived by ignoring terms proportional to the divergence of the medium velocity and the gradient of the ambient pressure it is shown that the second set has the same or a wider range of applicability than equations for the sound pressure that have been previously used for analytical and numerical studies of sound propagation in a moving atmosphere practical fdtd implementation of the second set of equations is discussed results show good agreement with theoretical predictions of the sound pressure due to a point monochromatic source in a uniform high mach number flow and with fast field program calculations of sound propagation in a stratified moving atmosphere

optimal h robustness and the relationship to lqg design problems a solution to the hx optimal control problem is obtained by employing a standard lqg polynomial based solution procedure the derivation is straightforward and avoids many of the more abstract mathematical results usually employed the relationship between the lqg and hm design methods becomes transparent and the similarities and differences can be identified

schwarz lemma at the boundary of strongly pseudoconvex domain in mathbb c n in this paper we establish a new type of the classical boundary schwarz lemma for holomorphic self mappings of strongly pseudoconvex domain in mathbb c n

on positive definite solutions to the algebraic riccati equation abstract complete necessary and sufficient conditions for the existence of a positive definite solution to the algebraic riccati equation are given it is also shown that when a positive definite solution exists it is either unique or else there are uncountably many such solutions

optimal model matching control for time delay systems model matching control for time delay systems is formulated as an optimization problem in h2 norm space as well as h norm space wiener hopf techniques and the theory of optimal interpolation are successfully employed to treat this model matching problem including perfect and imperfect model matching cases prior to this work for time delay systems only the problem of perfect model matching control had been considered and no attempt had been made to examine that of imperfect model matching control with the optimization approach presented here an optimal model matching control scheme is constructed for the imperfect model matching case to produce perfect model matching results whenever possible

sampled data control of continuous time systems with an h optimality criterion abstract the synthesis of sampled data controllers for continuous time systems is studied in the context of h control theory the sampled data h optimal control problem consists of finding a sampled data controller which minimizes the l2 induced norm from the continuous time disturbance to the continuous time output the problem is here solved via a discrete system representation this is achieved by describing the closed loop system as a discrete system with finite state dimension and with a representation of the disturbance and the output signals of the discrete system as sequences of elements of certain infinite dimensional spaces via finite rank approximations of a compact integral operator associated with the system the sampled data h control problem can be solved to any degree of accuracy from the structure of the problem it follows that irrespective of the order of the approximation a feasible sampled data controller can be found which has the same order as the system

boundary jets of holomorphic maps between strongly pseudoconvex domains abstract in this paper we consider jets taken at a fixed boundary point of germs of holomorphic diffeomorphisms which send one strongly pseudoconvex domain into another we completely describe possible first and second jets and conditions of extremality in terms of the chern moser normal forms of the domains

finite difference time domain modeling of curved surfaces em scattering the finite difference time domain fdtd method is generalized to include the accurate modeling of curved surfaces this generalization the contour path cp method accurately models the illumination of bodies with curved surfaces yet retains the ability to model corners and edges cp modeling of two dimensional electromagnetic wave scattering from objects of various shapes and compositions is presented

vorticity and entropy boundary conditions for acoustical finite difference time domain simulations in this paper a time domain numerical model for describing the presence of vorticity and entropy boundary layers is introduced the boundary model can be inserted in acoustic time domain models such as the finite difference time domain fdtd model for studying the acoustic behavior of high quality resonator structures the main focus in deriving the model is on numerical efficiency boundary layer theory is reviewed to obtain a three dimensional formulation of its influence on fdtd equations that must be applied in boundary discretization cells the dependence that is encountered is approximated in time domain in such a way that no numerical convolution is required although this approximation is rather inaccurate it is sufficient for most applications and introduces almost no extra computational effort several numerical examples illustrate the applicability of the model

theoretical basis for numerically exact three dimensional time domain algorithms in a one dimensional 1d homogeneous space the classic yee finite difference timedomain fdtd algorithm is numerically exact when operated at the courant stability limit numerically exact is taken to mean that to within the sampling limit imposed by the discretization in space and time the only errors are due to the finite precision of digital computer arithmetic unfortunately the yee algorithm is not numerically exact in two or more dimensions however using the design shown here three dimensional 3d spatial differential operators can have 1d dispersion properties just as the space and time errors can be made to cancel in the 1d yee algorithm 3d algorithms for hyperbolic systems of coupled first order equations in an unbounded homogeneous space can be constructed which are in theory numerically exact the differential operators presented here extend over a localized non zero volume unlike the usual nabla or del operator which acts at a point our computer implementations are based on reconstruction methods producing global range operators thus our implementations of these operators are computationally expensive a sample implementation of an approximate electromagnetic algorithms is described and is shown to produce results that are superior to the classic yee algorithm for the cubic resonator problem

exact computation of infimum for a class of continuous time h optimal control problem with a nonzero direct feedthrough term from the disturbance input to the controlled output a noniterative method for the computation of infimum for a class of continuous time h optimal control problem is considered in this paper the problem formulation is fairly general and does not place any restrictions on any direct feedthrough terms of the given systems the method is applicable to systems where i the transfer function from the disturbance input to the measurement output is free of imaginary axis invariant zeros and left invertible and ii the transfer function from the control input to the controlled output of the given system is free of imaginary axis invariant zeros and right invertible the result presented in this paper is a continuation of the previous work of the author and his co workers chen et al 1992 in which the direct feedthrough term from the disturbance input to the measurement output of the given system are required to be zero

generation of fdtd subcell equations by means of reduced order modeling adapted finite difference time domain fdtd update equations exist for a number of objects that are smaller than the grid step such as wires and thin slots we provide a technique that automatically generates new fdtd update equations for small objects our presentation focusses on 2d fdtd we start from the fdtd equations in a fine grid where the time derivative is not discretised this yields a large state space model that is drastically reduced with a reduced order modeling technique the reduced state space model is then translated into new fdtd update equations that can be used in an fdtd simulation in the same way as the existing update equations for wires and thin slots this technique is applied to a number of numerical problems showing the accuracy and versatility of the proposed method

the singular control problem with dynamic measurement feedback this paper is concerned with the h infty problem with measurement feedback the problem is to find a dynamic feedback from the measured output to the control input such that the closed loop system has an h infty norm strictly less than some a priori given bound gamma and such that the closed loop system is internally stable necessary and sufficient conditions are given under which such a feedback exists the only assumption that must be made is that there are no invariant zeros on the imaginary axis for two subsystems contrary to recent publications no assumptions are made on the direct feedthrough matrices of the plant it turns out that this problem can be reduced to an almost disturbance decoupling problem with measurement feedback and internal stability i e the problem in which we can make the h infty norm arbitrarily small

on the minimization of sensitivity to additive disturbances for linear distributed parameter mimo feedback systems the problem of minimizing the sensitivity of the output or input of a plant under a feedback control with respect to external additive disturbances is considered the mathematical model assumed for the plant is a rectangular matrix of transfer functions which can arise from both lumped parameter and distributed parameter systems including time delays the feedback controller is assumed to guarantee the closed loop stability it is shown that an arbitrarily small sensitivity function on a compact set of complex frequencies can be obtained by a suitable choice of feedback transfer function provided no zero of the plant transfer function is in this set additionally the sensitivity function can be designed to be bounded on an unbounded region containing the imaginary axis if there are no zeros of the plant in the right half plane and a certain hypothesis holds multiplicative delays are not excluded if there are zeros in the right half plane the latter design is not realizable since minimizing the sen

theory of ltr for non minimum phase systems recoverable target loops and recovery in a subspace part 1 analysis a complete analysis of loop transfer recovery problem using full order observer based controllers for general not necessarily left invertible and not necessarily minimum phase systems is considered the analysis here while showing that neither exact nor asymptotic loop transfer recovery is in general possible focuses on three fundamental issues the first issue is concerned with what can and what canot be achieved for a given system and for an arbitrarily specified target loop transfer function while the second issue is concerned with the development of necessary and or sufficient conditions a target loop has to satisfy so that it can be either exactly or asymptotically be recovered for a given system the third issue deals with the development of method s to test whether recovery is possible in a given subspace of the control space or not i e to test whether projections of target and achievable sensitivity and complimentary sensitivity functions onto a given subspace match each other or not such an

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

entropy minimizing and risk sensitive control rules abstract glover and doyle 4 have shown that the entropy minimising criterion is identical with the infinite horizon form of the leqg optimality criterion leqg linear exponential of quadratic gaussian whittle and kuhn 11 have given a hamiltonian formulation which provides a natural treatment of leqg optimisation this paper contains a direct proof that the control yielded by these hamiltonian methods is entropy minimising the conclusion would follow from the two assertions above but a simple adjoining of the proofs of these two assertions yields an argument so circuitous that a direct proof is of interest

the largest singular value of e sup x a sub 0 e sup x is convex on convex sets of commuting matrices a short and direct proof of the convexity property is given it is shown that the theorem applies to any convex commuting set of matrices in r sup nxn where a sub 0 in r sup nxn is fixed it is also shown that the result does not hold if x is permitted to be a general square matrix a counterexample is supplied for noncommuting matrices

exact computation of the infimum in h sub infinity optimization via output feedback the authors present a simple and noniterative procedure for the computation of the exact value of the infimum in the standard h sub infinity optimal control with output feedback the problem formulation is general and does not place any restrictions on the direct feedthrough terms between the control input and the controlled output variables and between the disturbance input and the measurement output variables the method is applicable to systems that satisfy the following conditions 1 the transfer function from the control input to the controlled output is right invertible and has no invariant zeros on the j omega axis and 2 the transfer function from the disturbance to the measurement output is left invertible and has no invariant zeros on the j omega axis

an algebraic approach to h output feedback control problems abstract we derive an output feedback controller which stabilizes a system and satisfies a prescribed h norm bound of the closed loop transfer function the proposed design method is available for any system i e there are no restrictions on d12 and d21 this approach utilizes only algebraic operations thus proofs are simple and clear

special coordinate basis for multivariable linear systems finite and infinite zero structure squaring down and decoupling abstract a special coordinate basis for multivariable linear systems is introduced here several fundamental properties of linear systems regarding controllability stabiliza bility observability detectability invariant zeros decoupling zeros infinite zero structure effect of feedback on zero structure squaring down diagonal and triangular decoupling etc can be directly displayed in terms of the special coordinate basis moreover connections between the special coordinate basis and the important invariant subspaces of the geometric theory of linear systems are established

linear bicharacteristic schemes without dissipation this paper is concerned with developing methods for the propagation of linear waves in several space dimensions the methods are time reversible and hence are free from numerical dissipation they are based on bicharacteristic forms of the governing equations and are made possible by adopting forms of staggered storage that depend on the precise equations under consideration analysis is presented for the equations of acoustics electromagnetics and elastodynamics

road traffic noise shielding by vegetation belts of limited depth abstract road traffic noise propagation through a vegetation belt of limited depth 15 m containing periodically arranged trees along a road is numerically assessed by means of 3d finite difference time domain fdtd calculations the computational cost is reduced by only modeling a representative strip of the planting scheme and assuming periodic extension by applying mirror planes with increasing tree stem diameter and decreasing spacing traffic noise insertion loss is predicted to be more pronounced for each planting scheme considered simple cubic rectangular triangular and face centered cubic for rectangular schemes the spacing parallel to the road axis is predicted to be the determining parameter for the acoustic performance significant noise reduction is predicted to occur for a tree spacing of less than 3 m and a tree stem diameter of more than 0 11 m this positive effect comes on top of the increase in ground effect near 3 dba for a light vehicle at 70 km h when compared to sound propagation over grassland the noise reducing effect of the forest floor and the optimized tree belt arrangement are found to be of similar importance in the calculations performed the effect of shrubs with typical above ground biomass is estimated to be at maximum 2 dba in the uniform scattering approach applied for a light vehicle at 70 km h downward scattering from tree crowns is predicted to be smaller than 1 dba for a light vehicle at 70 km h for various distributions of scattering elements representing the tree crown the effect of the presence of tree stems shrubs and tree crowns is predicted to be approximately additive inducing some pseudo randomness in stem center location tree diameter and omitting a limited number of rows with trees seem to hardly affect the insertion loss these predictions suggest that practically achievable vegetation belts can compete to the noise reducing performance of a classical thin noise barrier on grassland with a height of 1 1 5 m in a non refracting atmosphere

paper adaptive controllers for discrete time systems with arbitrary zeros an overview the paper presents a comprehensive review of the problem of designing discrete time adaptive controllers for systems with arbitrary zeros minimum or non minimum phase systems being particular cases the authors have attempted to give a unified presentation of the various existing schemes by stripping away the technical details and highlighting their close interrelation through the use of a common framework both algorithmic and theoretical aspects are discussed with particular emphasis on the stability of the schemes

how much uncertainty can be dealt with by feedback feedback is used primarily for reducing the effects of the plant uncertainty on the performance of control systems and as such understanding the following questions is of fundamental importance how much uncertainty can be dealt with by feedback what are the limitations of feedback how does the feedback performance depend quantitatively on the system uncertainty how can the capability of feedback be enhanced if a priori information about the system structure is available as a starting point toward answering these questions a typical class of first order discrete time dynamical control systems with both unknown nonlinear structure and unknown disturbances is selected for our investigation and some concrete answers are obtained in the paper in particular we find that in the space of unknown nonlinear functions the generalized lipschitz norm is a suitable measure for characterizing the size of the structure uncertainty and that the maximum uncertainty that can be dealt with by the feedback mechanism is described by a ball with radius 3 2 spl radic 2 in this normed function space

h sub infinity control by state feedback and fast algorithms for the computation of optimal h sub infinity norms the suboptimality of some parameter for h sub infinity optimization by dynamic state feedback is characterized in terms of the solvability of riccati inequalities this is done without restricting the finite zero structure of the plant if there are no system zeros on the imaginary axis the h sub infinity problem can be treated in a complete and satisfactory way explicit characterizations optimum to be achieved are provided and a closed formula for the optimal value is derived in terms of the h sub infinity norm of some fixed transfer matrix if the optimum is not attained any sequence of controllers of bounded size which is constructed to approach the infimal norm must necessarily be high gain a globally and quadratically convergent algorithm to compute the optimal value is proposed this algorithm is generalized to the h sub infinity optimization problem by measurement feedback

boundary schwarz lemma for pluriharmonic mappings between unit balls abstract in this paper we get a schwarz lemma for pluriharmonic mappings between the unit balls of any dimensions which generalizes classical schwarz lemma for bounded harmonic functions to higher dimensions as an application of the schwarz lemma obtained a boundary schwarz lemma is established for pluriharmonic mappings between unit balls with any dimensions

locally conformal method for acoustic finite difference time domain modeling of rigid surfaces the finite difference time domain method is a simple but powerful numerical method for simulating full wave acoustic propagation and scattering however the method can demand a large amount of computational resources traditionally continuously curved boundaries are represented in a stair step fashion and thus accurately modeling scattering from a boundary will require a finer discretization than would otherwise be necessary for modeling propagation in a homogeneous medium however a fine discretization might not be practical due to limited computational resources a locally conformal technique is presented here for modeling acoustic scattering from continuously curved rigid boundaries this technique is low cost simple to implement and gives better results for the same grid discretization than the traditional stair step representation these improvements can be traded for a coarser discretization which reduces the computational burden the improved accuracy of this technique is demonstrated for a spherical scatterer

closed form solutions to a class of h optimization problems a closed form solution is presented to the h sub optimal control problem via state or output feedback the problem formulation is general and does not impose any restrictions on feedthrough terms between the control input and the controlled output or between the disturbance input and the measurement output variables it is however required that both the transfer function from the disturbance input to the measurement output and the transfer function from the control input to the controlled output have no invariant zeros on the jw axis and that they satisfy certain geometric conditions for the same class of systems the conditions under which the h optimal control problem via state feedback has a solution are given moreover explicit expressions for the optimal solutions are provided finally the pole zero cancellations in the closed loop system resulting from the h optimal or sub optimal state or output feedback are examined

feedback and optimal sensitivity model reference transformations multiplicative seminorms and approximate inverses in this paper the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras and then specialized to a class of multivariable time invariant systems characterized by n times n matrices of h infty frequency response functions either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity and on the concept of an approximate inverse approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility called a measure of singularity is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure in particular if there are no right half plane zeros sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties and methods of constructing them in special cases are presented

an efficient realization of frequency dependent boundary conditions in an acoustic finite difference time domain model abstract the finite difference time domain fdtd method provides a simple and accurate way of solving initial boundary value problems however most acoustic problems involve frequency dependent boundary conditions and it is not easy to include such boundary conditions in an fdtd model although solutions to this problem exist most of them have high computational costs and stability cannot always be ensured in this work a solution is proposed based on mixing modelling strategies this involves separating the fdtd mesh and the boundary conditions a digital filter representation of the impedance and combining them into a global solution this solution is based on an interaction model that involves wave digital filters the proposed method is validated with several test cases

time domain wave equations for lossy media obeying a frequency power law for attenuation described by a slowly varying power law function of frequency 0 y classical lossy time domain wave equations exist only for the restricted cases where y 0 or y 2 for the frequently occurring practical situation in which attenuation is much smaller than the wave number a lossy dispersion characteristic is derived that has the desired attenuation general power law dependence in order to obtain the corresponding time domain lossy wave equation time domain loss operators similar in function to existing derivative operators are developed through the use of generalized functions three forms of lossy wave equations are found depending on whether y is an even or odd integer or a noninteger a time domain expression of causality analogous in function to the kramers kronig relations in the frequency domain is used to derive the causal wave equations final causal versions of the time domain wave equations are obtained even for the cases where y 1 which according to the paley wiener th

h control with transients in h infty or uniformly optimal control problems it is usually assumed that the system initial conditions are zero in this paper an h infty like control problem that incorporates uncertainty in initial conditions is formulated this is done by defining a worst case performance measure both finite and infinite horizon problems are considered necessary and sufficient conditions are derived for the existence of controllers that yield a closed loop system for which the above mentioned performance measure is less than a prespecified value state space formulae for the controllers are also presented

application of the fourier pseudospectral time domain method in orthogonal curvilinear coordinates for near rigid moderately curved surfaces the fourier pseudospectral time domain method is an efficient wave based method to model sound propagation in inhomogeneous media one of the limitations of the method for atmospheric sound propagation purposes is its restriction to a cartesian grid confining it to staircase like geometries a transform from the physical coordinate system to the curvilinear coordinate system has been applied to solve more arbitrary geometries for applicability of this method near the boundaries the acoustic velocity variables are solved for their curvilinear components the performance of the curvilinear fourier pseudospectral method is investigated in free field and for outdoor sound propagation over an impedance strip for various types of shapes accuracy is shown to be related to the maximum grid stretching ratio and deformation of the boundary shape and computational efficiency is reduced relative to the smallest grid cell in the physical domain the applicability of the curvilinear fourier pseudospectral time domain method is demonstrated by investigating the effect of sound propagation over a hill in a nocturnal boundary layer with the proposed method accurate and efficient results for sound propagation over smoothly varying ground surfaces with high impedances can be obtained

direct computation of infimum in discrete time h optimization using measurement feedback a direct and non iterative method for the computation of the infimum for a class of discrete time h optimal control problem is considered in this paper the problem formulation is fairly general and does not place any restrictions on any direct feedthrough terms of the given systems the method is applicable to systems where i the transfer function from the disturbance input to the measurement output is free of unit circle invariant zeros and left invertible and ii the transfer function from the control input to the controlled output of the given system is free of the unit circle invariant zeros and right invertible

conjugation interpolation and model matching in h abstract the notion of conjugation is introduced to give a unified framework of algebraic operations connected to the analytic aspects of transfer functions two classes of conjugations are shown to be important one is the lossless conjugation that performs inner outer factorization and the other is the j lossless conjugation that solves the model matching problem related to h 8 control the solution of the model matching problem obtained by j lossless conjugation is regarded as the state space version of the directional interpolation theory and is much simpler than those obtained via the nehari approximation

modeling of the seat dip effect using the finite difference time domain method in this paper the use of the finite difference time domain technique for the modeling of the seat dip effect in concert halls is demonstrated the linear time domain acoustic partial differential equations are discretized using a finite difference technique the second order accurate differencing scheme is time space centered and the velocity and pressure are solved on an interlaced mesh first and second order mur absorbing boundary conditions originally formulated for electromagnetic problems are adapted to the acoustics case and used to truncate the numerical grid the technique is first verified by comparing the numerical results to the analytic solution of a simple point source results from computer simulations of the seat dip phenomena are compared with the findings of previous studies where measurements had been made on scale models and in real concert halls the computer model successfully predicts the effects associated with the source receiver distance the height of the receiver and the h

state space formulae for all stabilizing controllers that satisfy and h norm bound and relations to risk sensitivity abstract given a linear system all stabilizing controllers such that a specified closed loop transfer function has h norm less than a given scalar are parametrized this characterization involves the solution to two algebraic riccati equations each with the same order as the system and further gives gives feasible controllers also with this order the relationship to the risk sensitive lqg stochastic control problem is established giving an equivalence between robust and stochastic control

squaring down of non strictly proper systems in an earlier work a procedure for squaring down proper systems by static and dynamic compensators has been developed the compensators designed there have the following properties a they are asymptotically stable b the additional finite zeros induced by them are assignable to the open left half complex plane and c they preserve the fundamental properties such as stabilizability detectability infinite zero structure and minimum phase nature of the original system the earlier design procedure is extended to non strictly proper systems while retaining all the above mentioned properties

the fractional representation approach to synthesis problems an algebraic analysis viewpoint part i weakly doubly coprime factorizations in this paper we show how to reformulate the fractional representation approach to analysis and synthesis problems within an algebraic analysis framework in terms of modules we give necessary and sufficient conditions so that a system admits weakly left right doubly coprime factorizations moreover we explicitly characterize the integral domains a such that every plant defined by means of a transfer matrix whose entries belong to the quotient field of a admits weakly doubly coprime factorizations finally we show that this algebraic analysis approach allows us to recover on the one hand the approach developed in m c smith ieee trans automat control 34 1989 pp 1005 1007 and on the other hand the ones developed in k mori and k abe siam j control optim 39 2001 pp 1952 1973 v r sule siam j control optim 32 1994 pp 1675 1695 and 36 1998 pp 2194 2195 m vidyasagar h schneider and b a francis ieee trans automat control 27 1982 pp 880 894 m vidyasagar control system synthesis a factorization approach mit press cambridge ma 1985

a finite difference time domain solution to scattering from a rough pressure release surface the finite difference time domain fdtd method is a numerical technique that makes no explicit physical approximations to the underlying problem the quality of a fdtd based solution typically is determined by the discretization of the computational domain the smaller the spacing the more accurate the solution unfortunately for large computational domains i e ones spanning many wavelengths the small spatial step size needed to obtain a high fidelity solution may lead to a prohibitively large number of unknowns here it is shown how the fdtd method can be used to model accurately scattering from pressure release surfaces above a homogeneous water column to keep the computational cost manageable a number of enhancements to the standard fdtd algorithm are employed these enhancements include correcting for numerical dispersion along the specular direction of the incident insonification using locally conformal cells at the pressure release boundary and propagating the field through the homogeneous water column via an analytic method the accuracy of the fdtd approach is demonstrated by comparison with an integral equation based reference solution to the same rough surface scattering problem thorsos proceedings of the reverberation and scattering workshop pp 3 2 3 20 1994 naval research laboratory book contribution nrl be 7181 96 001

disturbance attenuation and h optimization a design method based on the algebraic riccati equation this note presents a method for designing a state feedback control law to reduce the effect of disturbances on the output of a given linear system the problem under consideration involves attenuating the disturbances to a prespecified level the construction of the state feedback control law requires the solution of a certain algebraic riccati equation by applying the procedure with successively smaller values of the prespecifled disturbance level the result also provides an approach to the h infty optimization problem for the state feedback case

p sv wave propagation in heterogeneous media velocity stress finite difference method i present a finite difference method for modeling p sv wave propagation in heterogeneous media this is an extension of the method i previously proposed for modeling sh wave propagation by using velocity and stress in a discrete grid the two components of the velocity cannot be defined at the same node for a complete staggered grid the stability condition and the p wave phase velocity dispersion curve do not depend on the poisson s ratio while the s wave phase velocity dispersion curve behavior is rather insensitive to the poisson s ratio therefore the same code used for elastic media can be used for liquid media where s wave velocity goes to zero and no special treatment is needed for a liquid solid interface typical physical phenomena arising with p sv modeling such as surface waves are in agreement with analytical results the weathered layer and corner edge models show in seismograms the same converted phases obtained by previous authors this method gives stable results for step discontinuities as shown for a liquid layer above an elastic half space the head wave preserves the correct amplitude finally the corner edge model illustrates a more complex geometry for the liquid solid interface as the poisson s ratio v increases from 0 25 to 0 5 the shear converted phases are removed from seismograms and from the time section of the wave field

a non iterative method for computing the infimum in h optimization this paper presents a simple and non iterative procedure for the computation of the exact value of the infimum in the singular h optimization problem and is an extension of our earlier work the problem formulation is general and does not place any restriction on the direct feedthrough terms between the control input and the controlled output variables and between the disturbance input and the measurement output variables our method is applicable to a class of singular h optimization problems for which the transfer functions from the control input to the controlled output and from the disturbance input to the measurement output have no invariant zeros on the jw axis and also satisfy certain geometric conditions the computation of the infimum in our method involves solving two well defined riccati and two lyapunov equations

the simulation of piano string vibration from physical models to finite difference schemes and digital waveguides a model of transverse piano string vibration second order in time which models frequency dependent loss and dispersion effects is presented here this model has many desirable properties in particular that it can be written as a well posed initial boundary value problem permitting stable finite difference schemes and that it may be directly related to a digital waveguide model a digital filter based algorithm which can be used for musical sound synthesis techniques for the extraction of model parameters from experimental data over the full range of the grand piano are discussed as is the link between the model parameters and the filter responses in a digital waveguide simulations are performed finally the waveguide model is extended to the case of several coupled strings

numerical simulations of piano strings i a physical model for a struck string using finite difference methods the first attempt to generate musical sounds by solving the equations of vibrating strings by means of finite difference methods fdm was made by hiller and ruiz j audio eng soc 19 462 472 1971 it is shown here how this numerical approach and the underlying physical model can be improved in order to simulate the motion of the piano string with a high degree of realism starting from the fundamental equations of a damped stiff string interacting with a nonlinear hammer a numerical finite difference scheme is derived from which the time histories of string displacement and velocity for each point of the string are computed in the time domain the interacting force between hammer and string as well as the force acting on the bridge are given by the same scheme the performance of the model is illustrated by a few examples of simulated string waveforms a brief discussion of the aspects of numerical stability and dispersion with reference to the proper choice of sampling parameters is also included

absorbing boundary condition for the elastic wave equation velocity stress formulation this paper describes an absorbing boundary condition for finite difference modeling of elastic wave propagation in two and three dimensions the boundary condition is particularly effective for obliquely incident waves typically quite troublesome for absorbing boundaries analytical predictions of the boundary reflection coefficients of a few percent or less for angles of incidence up to 89 are verified in example finite difference applications the algorithm is appropriate for use in a velocity stress finite difference vs fd formulation it is computationally simpler than a similar absorbing boundary given previously for the standard displacement formulation a second algorithm is presented which may be advantageous when the boundary of interest is exposed to strong evanescent waves both algorithms require that the adjacent elastic medium be locally homogeneous

almost disturbance decoupling with internal stability the almost disturbance decoupling problem with internal stability is solved in terms of the geometric concepts of linear systems theory the solution gives necessary and sufficient conditions for the existence of a dynamic output feedback controller such that in the closed loop system the disturbances are quenched say in the h sup infinity sense up to any degree of accuracy while maintaining a stable system matrix

output feedback decentralized control of large scale systems using weighted sensitivity functions minimization this paper considers the problem of achieving stability and desired dynamical transient behavior for linear large scale systems by decentralized control it can be done by making the effects of the interconnections between the subsystems arbitrarily small sufficient conditions for stability and diagonal dominance of the closed loop system are introduced these conditions are in terms of decentralized subsystems and directly make a constructive h control design possible a mixed h pole region placement is suggested such that by assigning the closed loop eigenvalues of the isolated subsystems appropriately the eigenvalues of the overall closed loop system are assigned in desirable range the designs are illustrated by an example

brief paper reliable stabilization using a multi controller configuration given a plant p we consider the problem of designing a pair of controllers c 1 and c 2 such that their sum stabilizes p and in addition each of them also stabilizes p should the other one fail this is referred to as the reliable stabilization problem it is shown that every strongly stabilizable plant can be reliably stabilized moreover one of the two controllers can be specified arbitrarily subject only to the constraint that it should be stable the stabilization technique is extended to reliable regulation

h2 optimal control of linear systems with tracking disturbance rejection constraints this paper considers the design of two degree of freedom linear multivariable controllers for four block matrix transfer functions with objectives pertaining to both random and deterministic signals the former are taken into account in the cost functional whereas the latter entail that the controller is constrained to solve a servomechanism problem involving a class of reference signals and two classes of disturbances the cost functional is set up by adding quadratic terms to the usual lqg wiener hopf cost in such a way as to ensure the existence of unique solutions even when the signals to be tracked rejected as well as models have poles on the imaginary axis the solutions of the servomechanism problem are explicitly parametrized by free stable rational and proper parameters under two sets of assumptions one which is necessary and sufficient for the existence of solutions and another stronger set which avoids kronecker products and the associated higher dimensional factorizations involved in

frequency dependent fdtd methods using z transforms the frequency dependent finite difference time domain method fd sup 2 td method has been shown to be capable of correctly calculating electromagnetic propagation through media whose dielectric properties are frequency dependent however as researchers search for more elaborate applications the formulation of the fd sup 2 td methods becomes more complex in this work the mathematics of the fd sup 2 td method is developed using z transform theory this has the advantages of presenting a clearer formulation and allowing researchers to draw on the literature of systems analysis and signal processing disciplines

linear feedback systems and the graph topology it is established for general linear systems that the gap metric induces the coarsest topology with respect to which both closed loop stability and closed loop performance are robust properties in earlier works similar topological results were obtained by exploiting the existence of particular coprime factor system representations not known to exist in general by contrast the development here does not rely on any specific system representations systems are simply characterized as subspaces of norm bounded input output pairs and the analysis hinges on the underlying geometric structure of the feedback stabilization problem unlike other work developed within such a framework fundamental issues concerning the causality of feedback interconnections are discussed explicitly the key result of this paper concerns the difference between linear feedback interconnections with identical controllers in terms of a performance robustness related closed loop mapping upper and lower bounds on the induced norm of this difference are derived allowing for possibly infinite dimensional input output spaces and time varying behavior the bounds are both proportional to the gap metric distance between the plants which clearly demonstrates the gap to be an appropriate measure of the difference between open loop systems from the perspective of closed loop behavior to conclude an example is presented to show that bounds of the form derived here for linear systems do not hold in a general nonlinear setting

further results on limitations to the capability of feedback in this paper we study the limitations of the capability of the feedback mechanism in dealing with structural uncertainty for a class of pth order non linear autoregressive control systems the size of the structural uncertainty is characterized by multiple lipschitz constants say l 1 l 2 lp of the uncertain non linear function it is shown that if l 1 l 2 lp satisfy certain algebraic conditions then there exists no globally stabilizing feedback control law for the corresponding uncertain systems the result here is an extension of the previous result obtained by zhang and guo 2002

optimal sensitivity theory for multivariate distributed plants in this note we generalized the results of foias and tannenbaum 1986 a and foias et al 1987 on optimal sensitivity minimization to a much broader class of distributed plants we relate our results to certain kinds of hankel norm approximation problems that frequently appear in control engineering applications

an approach to h control of a class of nonlinear systems this paper considers robust h control of a class of nonlinear systems that can be represented by a heterogeneous model a new controller design method using both state feedback is proposed based on quadratic stability theory a number of necessary and sufficient conditions are derived for quadratic stabilizability with disturbance attenuation of the control system concerned an example is also given to demonstrate the performance of the proposed controller design methods

brief the weighted incremental norm approach from linear to nonlinear h control weighted induced norms can be used to handle robustness and sensitivity requirements in the linear context as shown by zames in its seminal work this paper deals with an attempt to extend linear h control concepts to the nonlinear context making use of a weighted incremental norm it is shown how these concepts make it possible to handle basic requirements such as robust stability disturbance attenuation and steady state behaviors

simple conformal methods for finite difference time domain modeling of pressure release surfaces the finite difference time domain fdtd method provides a simple and accurate means of simulating a wide range of acoustic wave propagation problems unfortunately the method has a voracious appetite for computational resources for example to accurately model scattering from a continuously varying pressure release boundary an fdtd grid is typically required that has a much finer discretization than is necessary to model propagation in a homogeneous space such a fine discretization can become prohibitive when considering large scale problems two simple conformal techniques are presented for acoustic fdtd simulations of problems involving pressure release boundaries these techniques which rely upon splitting velocity cells adjacent to the pressure release boundary significantly improve the accuracy of the results over those of the standard staircase representation of the boundary these methods permit the use of a coarser fdtd grid than would otherwise be practical and yet add negligible computa

a schwarz lemma at the boundary using the julia wolff caratheodory type condition on finite dimensional irreducible bounded symmetric domains abstract in this paper we prove a schwarz lemma at the boundary for holomorphic self mappings f of finite dimensional irreducible bounded symmetric domains without assuming the boundary regularity of f our result generalizes the previous results obtained for holomorphic self mappings f of the euclidean unit ball or of the classical cartan domains of type i and of type ii which are smooth up to the boundary

numerical model for moderately nonlinear sound propagation in three dimensional structures a three dimensional numerical model is presented that is capable of handling moderately nonlinear sound propagation the model is based on a finite difference time domain fdtd discretization of a set of equations that approximate the navier stokes equations and that include molecular relaxation processes the mathematical model and numerical discretization focus on compatibility with earlier linear fdtd models in this way combining both models in a single simulation is trivial and optimum efficiency is obtained for acoustic propagation a staggered grid is used for the discretization nonlinear effects heat conduction and damping are treated to a lower order of accuracy two examples illustrate the use of the model the first example is the nonlinear resonance of a finite length duct typical waveform steepening and frequency shift broadening and skewing of the resonance peak that are also observed in experiments are found the second example is a tuned reactive muffler installed on a duct the dec

an algebraic riccati equation approach to h optimization abstract this paper considers the general so called four block h optimal control problem with the assumption that system states are available for feedback it is shown that infimization of the h norm of the closed loop transfer function over all linear constant i e nondynamic stabilizing state feedback laws can be completely characterized via an algebraic riccati equation it is further shown that the optimal norm is not improved by allowing feedback to be dynamic thus the general state feedback h optimal control problem can be solved by iteratively solving one are and the controller can be chosen to be static gain

on the numerical computation of a structural decomposition in systems and control in this paper we develop a new numerical method for a special coordinate basis of a linear time invariant system such a special coordinate basis is essentially a structural decomposition which explicitly displays the finite and infinite zero structures as well as the invertibility structures of the given system the technique is playing important roles in numerous topics in system and control theory such as robust control h sub spl infin and h sub 2 optimal control almost disturbance decoupling and zero placement of linear systems just to name a few our method consists of three steps reduction by orthogonal transformations reduction by generalized sylvester equations and extraction of infinite zero structure the performance of our method is illustrated by some numerical examples

the complementary operators method applied to acoustic finite difference time domain simulations the complementary operators method com has recently been introduced as a mesh truncation technique for open domain radiation problems in electromagnetics the com entails the construction of two solutions that employ absorbing boundary conditions abcs with complementary behavior i e the reflection coefficients associated with the two abcs are exactly opposite each other the average of these solutions then yields a new solution in which the errors caused by artificial reflections from the termination of grid are nearly eliminated in this work com is introduced for the finite difference time domain fdtd solution of acoustics problems the development of com is presented in terms of higdon s absorbing boundary operators but generalization to non higdon operators is straightforward the effectiveness of com in comparison to other absorbing boundary conditions is demonstrated with numerical experiments in two and three dimensions

all optimal hankel norm approximations of linear multivariable systems and their l error bounds the problem of approximating a multivariable transfer function g s of mcmillan degree n by s of mcmillan degree k is considered a complete characterization of all approximations that minimize the hankel norm is derived the solution involves a characterization of all rational functions s f s that minimize where s has mcmillan degree k and f s is anticavisal the solution to the latter problem is via results on balanced realizations all pass functions and the inertia of matrices all in terms of the solutions to lyapunov equations it is then shown that where k 1 g s is the k l st hankel singular value of g s and for one class of optimal hankel norm approximations the method is not computationally demanding and is applied to a 12 state model

the quadratic matrix inequality in singular h control with state feedback in this paper the standard h infty control problem using state feedback is considered given a linear time invariant finite dimensional system this problem consists of finding a static state feedback such that the resulting closed loop transfer matrix has h infty norm smaller than some a priori given upper bound in addition it is required that the closed loop system is internally stable conditions for the existence of a suitable state feedback are formulated in terms of a quadratic matrix inequality reminiscent of the dissipation inequality of singular linear quadratic optimal control where the direct feedthrough matrix of the control input is injective the results presented here specialize to known results in terms of solvability of a certain indefinite algebraic riccati equation

sh wave propagation in heterogeneous media velocity stress finite difference method a new finite difference fd method is presented for modeling sh wave propagation in a generally heterogeneous medium this method uses both velocity and stress in a discrete grid density and shear modulus are similarly discretized avoiding any spatial smoothing therefore boundaries will be correctly modeled under an implicit formulation standard problems quarter plane propagation sedimentary basin propagation are studied to compare this method with other methods finally a more complex example a salt dome inside a two layered medium shows the effect of lateral propagation on seismograms recorded at the surface a corner wave always in phase with the incident wave and a head wave will appear which will pose severe problems of interpretation with the usual vertical migration methods

pseudospectra of linear operators if a matrix or linear operator a is far from normal its eigenvalues or more generally its spectrum may have little to do with its behavior as measured by quantities such as an or exp ta more may be learned by examining the sets in the complex plane known as the pseudospectra of a defined by level curves of the norm of the resolvent zi a 1 five years ago the author published a paper that presented computed pseudospectra of thirteen highly nonnormal matrices arising in various applications since that time analogous computations have been carried out for differential and integral operators this paper a companion to the earlier one presents ten examples each chosen to illustrate one or more mathematical or physical principles

acoustical finite difference time domain simulations of subwavelength geometries accurate simulation of wave propagation around subwavelength geometries using standard finite difference time domain fdtd techniques require a fine spatial and temporal sampling resulting in high computational costs in this paper an extension to this standard fdtd technique is proposed by means of quasi stationary solutions on a subwavelength scale the fdtd equations in the region near the subwavelength geometry are extended with some correction terms of which the magnitude is extracted from the quasi stationary pressure distribution around these geometries these pressure distributions can be calculated from the laplace equation using this new technique fdtd simulations can be based on a more coarse grid thus reducing computational cost considerably the accuracy of this technique is mainly determined by the accuracy of the laplace solutions this technique was tested with success on the simulation of resonators it was also shown that the new fdtd equations can be extended to include viscosity ef

stabilization of time domain acoustic boundary element method for the interior problem with impedance boundary conditions the time domain boundary element method bem is associated with numerical instability that typically stems from the time marching scheme in this work a formulation of time domain bem is derived to deal with all types of boundary conditions adopting a multi input multi output infinite impulse response structure the fitted frequency domain impedance data are converted into a time domain expression as a form of an infinite impulse response filter which can also invoke a modeling error in the calculation the response at each time step is projected onto the wave vector space of natural radiation modes which can be obtained from the eigensolutions of the single iterative matrix to stabilize the computation unstable oscillatory modes are nullified and the same decay rate is used for two nonoscillatory modes as a test example a transient sound field within a partially lined parallelepiped box is used within which a point source is excited by an octave band impulse in comparison with the results

complementary boundary operators for wave propagation problems the complementary operators method com has been shown to be an effective mesh terminator when solving open region scattering and radiation problems this study presents the theory of com and extends it to include general analytical absorbing boundary conditions abcs the com is applied to the finite difference time domain simulation of electromagnetic problems the application of com to elastic and acoustic waves follows in a similar manner the numerical adaptations of com to the discretized domain is then discussed to show that careful numerical adaptation is needed to ensure full complementariness of the discretized equations numerical experiments will be presented to show the effectiveness of com in predicting accurate time domain response as well as critical frequency domain response in particular an experiment is detailed that demonstrates how com can be effective in treating evanescent fields which traditionally have been a major challenge for abcs in general

weight selection in feedback design with degree constraints we present an approach for feedback design which is based on recent developments in analytic interpolation with a degree constraint performance is cast as an interpolation problem with bounded analytic functions minimizers of a certain weighted entropy functional provide interpolants having degree less than the number of constraints the choice of weight parameterizes all such bounded degree solutions however the relationship between the weights and the shape of corresponding transfer functions is not direct thus in this paper we develop a formalism that guides weight selection

effects of sources on time domain finite difference models recent work on excitation mechanisms in acoustic finite difference models focuses primarily on physical interpretations of observed phenomena this paper offers an alternative view by examining the properties of models from the perspectives of linear algebra and signal processing interpretation of a simulation as matrix exponentiation clarifies the separate roles of sources as boundaries and signals boundary conditions modify the matrix and thus its modal structure and initial conditions or source signals shape the solution but not the modal structure low frequency artifacts are shown to follow from eigenvalues and eigenvectors of the matrix and previously reported artifacts are predicted from eigenvalue estimates the role of source signals is also briefly discussed

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

two properties of l sub 1 optimal controllers the solution of the l sub 1 sensitivity minimization problem is shown to have two properties which contrast markedly with properties of the solutions to the better known h infinity sensitivity minimization problem or the lqg linear quadratic gaussian problem is given of a one parameter family of first order plants where the order of the l sub 1 optimal compensator can be arbitrarily large and thus it is impossible to bound the order of an l sub 1 optimal compensator in terms of the order of the plant a plant is considered which has a continuous one parameter family of l sub 1 optimal compensators and thus l sub 1 optimal compensators need not be unique the author s two examples are considered to answer two questions left open by m a daleh and j b pearson ibid vol 32 p 314 23 1987

delay dependent stability and h control for a class of fuzzy descriptor systems with time delay this paper addresses issues of stability analysis and h control for a class of fuzzy time delay descriptor systems described by an extended takagi sugeno t s fuzzy model a delay dependent stability criterion is first presented and a h control synthesis approach is then developed both the stability criterion and the h controller synthesis are based on the solutions of linear matrix inequalities lmis finally two examples are given to illustrate the effectiveness of the approaches proposed in this paper

infinite horizon h control for nonlinear stochastic markov jump systems with x u v dependent noise via fuzzy approach in this paper the h control problem is studied for nonlinear stochastic markov jump systems with state control and external disturbance dependent noise x u v dependent noise for short a sufficient condition is derived for the infinite horizon h control of such systems in terms of a set of coupled second order hamilton jacobi inequalities hjis in general it is difficult to solve these coupled hjis by using fuzzy approach the infinite horizon h control design for nonlinear stochastic markov jump systems is developed via solving a set of linear matrix inequalities lmis instead of hjis two numerical examples are presented to illustrate the effectiveness of the proposed design methods