new results on composite control of singularly perturbed uncertain linear systems abstract we consider the problem of stabilizing uncertain singularly perturbed linear time varying systems whose fast dynamics can be unstable we propose a class of nonlinear composite controllers which assure global uniform ultimate boundedness of the trajectories of the closed loop system provided the singular perturbation parameter is sufficiently small these controllers consist of a fast controller which stabilizes the fast dynamics and a slow controller which yields the desired stability properties for the slow dynamics we consider the structure of the fast controller to be simpler than structures previously proposed in the literature to obtain these controllers we first develop some new results for singularly perturbed systems under output feedback in particular it is shown that the matching assumption which deals with the manner in which the uncertainties enter the system and is made on the reduced order system is invariant under linear feedback of the fast variable

utd diffraction coefficients for higher order wedge diffracted fields an asymptotic expansion of a multiple integral for knife edge diffraction is derived the expansion expresses the field in terms of single edge diffraction by considering this expression a similar expansion for higher order utd diffracted fields is proposed by means of a set of transition functions the result removes some of the shortcomings of the original set out of the utd when the incident field is not a ray optical field

diffraction by lossy dielectric wedges using both heuristic utd formulations and fdtd an improvement of the uniform theory of diffraction utd coefficient for the case of a lossy dielectric wedge when a transmitted ray exists is presented we elaborated two new terms that are added to the classical utd diffraction coefficient so that we obtain continuity of the total field this new utd formulation is compared to a numerical method based on finite difference time domain fdtd we outline the adaptation of the fdtd grid calculation which was necessary to isolate only one edge diffraction and to treat two dimensional 2 d structures with two infinite sides this comparison allows one to conclude that the new diffraction coefficient is relevant for the case of a lossy dielectric wedge then we present a comparison between two different versions of the utd diffraction coefficient based on single or multiple reflection in the case of a dielectric slab thus we can conclude to the significance of the multipaths for modeling dielectric structures finally we analyze the results obtained with two consecutive wedge vertices in order to show that the slope diffraction related to the doubly diffracted field allows one to predict the field behind the structure when the transmitted field does not exist

robust stabilization of discrete time linear systems with norm bounded time varying uncertainty abstract this paper presents an algorithm for the stabilization of a class of discrete time uncertain systems suffering from uncertainty of the norm bounded time varying type the stabilizing control gain matrix is obtained by solving a certain discrete riccati equation the solution of this riccati equation is also a lyapunov matrix which is used to establish the stability of closed loop system the results presented in this paper generalize those obtained in previous works for continuous time uncertain systems

on the essential spectrum of transport operators on l1 spaces in a recent article by the first author j math phys 35 6199 6212 1994 the essential spectrum of transport operator was analyzed in lp spaces for p 1 the purpose of the present work is to extend this analysis to the case of l1 spaces after establishing preliminary results we define the notion of the weak spectrum which we characterize by means of fredholm operators we show in particular that in l1 spaces the weak spectrum is nothing else but the essential spectrum using the same techniques as in the above mentioned work we prove the stability of the essential spectrum of a one dimensional transport operator with general boundary conditions where an abstract boundary operator relates the incoming and the outgoing fluxes sufficient conditions are given in terms of boundary and collision operators assuring the stability of the essential spectrum we show also that our results remain valid for neutron transport operators in arbitrary dimension

the guaranteed cost control problem of uncertain singularly perturbed systems abstract in this paper we study the algebraic riccati equation corresponding to the guaranteed cost control theory for an uncertain singularly perturbed system the construction of the controller involves solving the full order algebraic riccati equation with small parameter e under control oriented assumptions we first provide the sufficient conditions such that the full order algebraic riccati equation has a positive semi definite stabilizing solution next we propose an iterative algorithm based on the kleinman algorithm to solve the algebraic riccati equation which depends on the parameter e our new idea is to use the solutions of the reduced order algebraic riccati equations for the initial condition by using the iterative algorithm we can easily obtain a required solution of the algebraic riccati equation moreover using the initial conditions without e we show that there exists an e such that the proposed algorithm has quadratic convergence finally in order to show the effectiveness of the proposed algorithm numerical examples are included

a uniform gtd treatment of surface diffraction by impedance and coated cylinders in the context of the uniform geometrical theory of diffraction utd computation of the scattered fields near the shadow boundary of a smooth convex surface requires values for the pekeris integral function p spl xi q while in a small number of cases such as the case of perfect conductivity q 0 and q spl rarr spl infin tabulated values of the function are available in the general case these values must be obtained by some numerical method a procedure for approximating p spl xi q by residue series means is introduced in contrast with traditional residue series representations the new procedure requires only a limited knowledge of pole locations even in the shadow boundary transition region and thereby extends the regime of practical applicability of residue series methods beyond the deep shadow it is demonstrated that the new procedure can be combined with an earlier residue series representation derived by hussar and albus 1991 and with geometrical optics to provide a computationally efficient procedure for computing fields scattered by an impedance or coated cylinder

an improved heuristic utd solution for multiple edge transition zone diffraction this paper describes a new heuristic approach for multiple edge diffraction modeling based on the uniform theory of diffraction utd it incorporates the slope diffraction terms which can be realized as a second order diffraction process vital for accurate predictions when more than one edge exists the predictions of this approach are compared with the vogler 1982 solution and were found to be in very good agreement for many different geometrical arrangements with low computational complexity the solution is also extended to wedge diffraction

tabulated interaction method for uhf terrain propagation problems an integral equation ie solution to uhf terrain path loss computation is described that dramatically reduces computation times compared to both standard ie techniques and the fast far field method for typical propagation problems while maintaining the full wave accuracy associated with ie solutions results are provided which are in excellent agreement with published measured data

a stabilization algorithm for a class of uncertain linear systems abstract this paper presents an algorithm for the stabilization of a class of uncertain linear systems the uncertain systems under consideration are described by state equations which depend on time varying unknown but bounded uncertain parameters the construction of the stabilizing controller involves solving a certain algebraic riccati equation furthermore the solution to this riccati equation defines a quadratic lyapunov function which is used to establish the stability of the closed loop system this leads to a notion of quadratic stabilizability it is shown that the stabilization procedure will succeed if and only if the given uncertain linear system is quadratically stabilizable the paper also deals with a notion of overbounding for uncertain linear systems this procedure enables the stabilization algorithm to be applied to a larger class of uncertain linear systems also included in the paper are results which indicate the degree of conservativeness introduced by this overbounding process

analysis of the effects of irregular terrain on radio wave propagation based on a three dimensional parabolic equation the effects from lateral variations of irregular terrain on the propagation of radio waves are considered by the representation of the vector fields in terms of two scalar hertz potentials in spherical coordinates the combination of three dimensional parabolic equations for these potentials with an impedance boundary condition for the ground followed by a transformation of variables will define a boundary condition problem characterized by equations displaying coefficients that depend on the terrain height function and its partial derivatives the problem solution through the crank nicolson scheme will lead to a sparse system of linear equations which will be solved by a direct method the resulting numerical model will be applied to test cases to show similar features to those from examples described in the literature taken as references for validation purposes

stabilisation of polytopic singularly perturbed linear systems this article deals with two time scale polytopic linear systems in the singular perturbation form and in discrete time the aim is to propose well conditioned convex conditions for stability analysis and control design as the classical lti time scale separation based approach is not successful in the case of polytopic singularly perturbed systems our method leads to linear matrix inequality conditions independent of the singular perturbation parameter and offers an interesting solution from a numerical point of view in addition the conservatism of the proposed approach is limited as it is based on parameter dependent lyapunov functions a numerical example taken from the literature illustrates the effectiveness of the given stabilisation conditions

an efficient algorithm for the computation of the utd t transition function we present an efficient algorithm for the numerical calculation of the t canonical transition function which is encountered in the uniform geometrical theory of diffraction utd such a transition function allows the uniform ray field description of various high frequency diffraction mechanisms such as double wedge or vertex diffraction the proposed algorithm is valid for both real and imaginary arguments as required to deal with the general case in utd applications

comparison of lossy wedge diffraction coefficients with application to mixed path propagation loss prediction a heuristic lossy wedge diffraction coefficient is compared to the exact maliuzhinets diffraction coefficient for a 180 degrees wedge neglecting surface waves the comparison shows good agreement even for high incidence angles and greatly dissimilar wedge face materials this agreement provides justification for using the heuristic coefficient for the calculation of mixed path propagation loss since wedge angles are typically near 180 degrees for this application the heuristic coefficient has the advantages of being continuous at the reflection boundary and of being relatively simple to evaluate especially at angles other than 180 degrees

a utd solution for multiple rounded surfaces this paper describes the diffraction mechanism when a ray optical field is obstructed by a cascade of smooth convex obstructions a new formulation of the uniform theory of diffraction utd is presented that incorporates the slope diffraction term the solution follows a generic approach that can be applied to arbitrary placed convex structures it will be shown that the slope diffraction term provides the required accuracy in radio propagation predictions when more than one obstruction exists in the propagation path the proposed solution is then compared with measurements and other analytical models with excellent agreement it is also found that the presented slope utd solution seems to be superior in terms of computation time and complexity while achieving very accurate results in addition when the radius of the cylinder tends to be very small the solution approaches the utd solution for multiple knife edge predictions

h guaranteed cost control for uncertain continuous time linear systems abstract this paper deals with the h guaranteed cost control problems for continuous time uncertain systems it consist of the determination of a stabilizing state feedback gain which imposes on all possible closed loop models an h norm upper bound 0 assuming that the uncertain domain is convex bounded and the uncertain system is quadratic stabilizable with disturbance attenuation it is shown how to determine by means of a convex programming problem the global minimum of as a particular and important case for precisely known linear systems the last problem reduces to the classical h optimal control problem the results follow from the definition of a special parameter space on which the above mentioned problems are convex

time domain uniform geometrical theory of diffraction for a curved wedge a time domain version of the uniform geometrical theory of diffraction td utd is developed to describe in closed form the transient electromagnetic scattering from a perfectly conducting arbitrarily curved wedge excited by a general time impulsive astigmatic wavefront this td utd impulse response is obtained by a fourier inversion of the corresponding frequency domain utd solution an analytic signal representation of the transient fields is used because it provides a very simple procedure to avoid the difficulties that result when inverting frequency domain utd fields associated with rays that traverse line or smooth caustics the td utd response to a more general transient wave excitation of the wedge may be found via convolution a very useful representation for modeling a general pulsed astigmatic wave excitation is also developed which in particular allows its convolution with the td utd impulse response to be done in closed form some numerical examples illustrating the utility of these developments are presented

a characterization of some subsets of schechter s essential spectrum and application to singular transport equation the purpose of this paper is to provide a detailed treatment of some subsets of schechter s essential spectrum of closed densely defined linear operators subjected to additive perturbations our results are used to describe the essential approximate point spectrum and the essential defect spectrum of singular neutron transport operators in bounded geometries

a heuristic utd slope diffraction coefficient for rough lossy wedges heuristic wedge diffraction coefficients for computing propagation path loss over finitely conducting earth are extended to include slope diffraction with the assumption that propagation of energy through the wedge is negligible the slope diffraction terms for the lossy wedge are obtained in an analogous manner as for the perfectly conducting case except that special care must be taken with the factor multiplying the incident field for grazing incidence results given show that the slope diffraction term produces continuous results that behave reasonably when compared with results for perfectly conducting wedges

a slope utd solution for a cascade of multishaped canonical objects the case of multiple diffraction from a cascade of two dimensional multi shaped canonical objects such as wedges knife edges and cylinders is investigated a heuristic slope uniform theory of diffraction utd solution is presented that can give accurate and uniform field predictions at any area point and for any kind of environment the solution is then compared against measurements taken in an anechoic chamber and a very good agreement is observed furthermore an algorithm for implementing the proposed utd solution to rural area field predictions is also presented based on a novel algorithm for optimum fit of canonical shapes to the terrain irregularities comparisons between the model and measurements taken in real terrain profile show a very good agreement and uniform field predictions the importance of the choice of the used canonical object to terrain modeling is also discussed since different diffraction patterns are observed for different combination of the canonical objects

on essential spectra of operator matrices and their feshbach maps abstract a connection between the essential spectrum of certain operator matrices and essential spectra of the corresponding feshbach maps is discussed and applied to some concrete rational operator valued functions

essential spectra of some matrix operators and application to two group transport operators with general boundary conditions abstract in this article we investigate the essential spectra of a 2 2 block operator matrix on a banach space furthermore we apply the obtained results to determine the essential spectra of two group transport operators with general boundary conditions in the banach space l p a a 1 1 l p a a 1 1 a 0

near optimum regulators for stochastic linear singularly perturbed systems this paper presents a new approach to the decomposition and approximation of linear quadratic gaussian estimation and control problems for singularly perturbed systems the kalman filter is decomposed into separate slow mode and fast mode filters via the use of a decoupling transformation a near optimal control law is derived by approximating the coefficients of the optimal control law the order of approximation of the optimal performance is 0 mu n where n is the order of approximation of the coefficients

a utd triple diffraction coefficient for straight wedges in arbitrary configuration a new utd solution is presented for the description of the ray triply diffracted by straight wedges in arbitrary configuration illuminated by a spherical wavefront field the proposed utd coefficient permits to uniformly describe the field at any aspect in particular including the case of overlapping transition regions where the subsequent application of utd single wedge diffraction coefficient fails the triple diffracted ray field is expressed in an analytical form providing physical insight into the triple diffraction mechanism and a new effective engineering tool within the utd framework as required in a modern ray based code

algorithm for the computation of the generalized fresnel integral the generalized fresnel integral appears as a canonical function in the uniform ray field representation of several high frequency diffraction mechanisms such as double wedge or vertex diffraction here we propose an algorithm for its calculation which is valid both for real and imaginary arguments as required for treating the general case in the uniform geometrical theory of diffraction framework

a modified diffraction coefficient for imperfect conducting wedges and buildings with finite dimensions multiple building diffraction loss calculation is often based on the assumption that their dimensions are infinite in the direction perpendicular to the propagation path even though in reality this assumption is not valid in this paper a modified diffraction coefficient model for the calculation of a more realistic diffraction loss caused by a single building with finite dimensions is proposed the overall diffraction loss is calculated for a group of buildings in a row by using the proposed model in addition after carrying out the field measurements it is shown that for some particular cases where the transmitter and diffracting obstacles are not far away from each other i e microcells or picocells spherical wave modeling produces a better accuracy than the plane wave approximation it is also demonstrated that the theoretical results can further be improved by considering the higher order terms in the calculation of diffraction coefficients lastly excess path loss obtained for a row of buildings with spherical wave assumption is compared with our measurement data this comparison shows reasonable correspondence between our theoretical model and measurements therefore our proposed model can successfully be used for improving the theoretical methods for predicting path loss in urban environments where diffraction from a number of buildings has to be considered

a hybrid finite difference surface green s function method for computing transmission losses in an inhomogeneous atmosphere over irregular terrain a standard parabolic equation spe is used to approximate the helmholtz equation for electromagnetic propagation in an inhomogeneous atmosphere an implicit finite difference ifd scheme to solve the spe is applied between the irregularly shaped ground and an altitude z z sub h below which all inhomogeneities of the medium are assumed localized the boundary condition at z z sub h is obtained by matching the ifd solution to a surface green s function sgf solution within the uniform region above z z sub h for ground slopes above about 1 degrees the ifd implementation of the impedance boundary condition at the ground is shown to maintain the validity of the approximation only for vertically polarized waves predictions using this hybrid finite difference fd sgf method agree well with results obtained using other computational methods

radiowave propagation analysis with a bidirectional 3 d vector parabolic equation method a 3 d bidirectional solution to the parabolic approximation of the wave equation is investigated by using a vector field representation the backward propagating wave is integrated to the classical parabolic equation approach which represents the forward propagating wave propagation over flat terrain in the presence of knife edges is considered as well as over irregular terrain consisting of hills modeled by the succession of knife edges at each knife edge appropriate boundary conditions are enforced and the wave is partly reflected in the backward direction the wave is marched in both directions by using the split step algorithm different tests are conducted in order to analyze and validate the results obtained by the proposed algorithm comparisons with results from both 2 d parabolic equation based algorithm and 3 d finite difference time domain based algorithm are presented in this paper

output feedback control of linear two time scale systems output feedback control of linear time invariant singularly perturbed systems is studied the set of all compensators that stabilize a singularly perturbed system while preserving its two time scale structure is parameterized the parameterization is used to show that any two frequency scale stabilizing compensator can be asymptotically approximated by a compensator designed via a sequential procedure in this procedure a fast high frequency compensator is designed first to stabilize the fast model of the system then a strictly proper slow low frequency compensator is designed to stabilize a modified slow model the parallel connection of the two compensators forms a two frequency scale stabilizing compensator for the singularly perturbed system

wide angle shift map pe for a piecewise linear terrain a finite difference approach a wide angle parabolic wave equation solution is presented using shift map and finite difference techniques the corresponding split step fourier solution is well known the solution using finite difference technique where the standard parabolic wave equation is modified into the so called claerbout equation allowing propagation angles up to 45deg from the paraxial direction is also well known here we present an extension to that solution in which the shift map technique is incorporated into the finite difference scheme allowing a varying terrain to be considered the result is a solution that corresponds to the well known split step solution which is believed to perform well for terrain slopes up to 10deg 15deg and discontinuous slope changes on the order of 15deg 20deg this solution is a first order one with respect to the terrain slope however when using the finite difference technique it is also possible to find a second order solution with respect to the terrain slope this new solution performs well for slopes up to about 15deg and discontinuous slope changes up to about 30deg which is an improvement

robust semiglobally practical stabilization for nonlinear singularly perturbed systems in this work the problem of semiglobally practical stabilization is considered for nonlinear singularly perturbed systems with unknown parameters the composite lyapunov function for the full systems is established by both that of the slow subsystem and the boundary layer system a state feedback control law for the linear part of the slow subsystem and boundary layer system is proposed which renders the whole closed loop system semiglobally stable the upper bound expression of e is given to obtain the condition of asymptotic stability for the system a simulation example is given to demonstrate the effectiveness and feasibility of the controller

time domain diffraction by a right angled penetrable wedge the electromagnetic diffraction by a right angled dielectric wedge normally illuminated by a plane wave is considered in the time domain the proposed approach exploits the knowledge of uniform asymptotic diffraction coefficients in the frequency domain and uses the inverse laplace transform for obtaining the response to an impulse plane wave then the response to an arbitrary function plane wave is determined in the dielectric material and the surrounding space via a convolution integral comparisons with fdtd data prove the validity of the approach at best authors knowledge time domain solutions are not available to date for the considered diffraction problem

a characterization of the schechter essential spectrum on banach spaces and applications abstract in a recent article by the author c r acad sci paris ser i 331 2000 525 530 boll un mat ital 2002 to appear the schechter spectrum of closed densely defined linear operators has been characterized on spaces which possess the dunford pettis property or which are isomorphic to one of the spaces l p p 1 the purpose of the present work is to extend this analysis to the case of banach spaces further we apply the obtained results to investigate the schechter essential spectrum of one dimensional transport equations with different boundary conditions

characteristic basis function method for solving electromagnetic scattering problems over rough terrain profiles a computationally efficient algorithm which combines the characteristic basis function method cbfm the physical optics po approach when applicable with the forward backward method fbm is applied for the investigation of electromagnetic scattering from and propagation over large scale rough terrain problems the algorithm utilizes high level basis functions defined on macro domains blocks called the characteristic basis functions cbfs that are constructed by aggregating low level basis functions i e conventional sub domain basis functions the fbm as well as the po approach when applicable are used to construct the aforementioned cbfs the conventional cbfm is slightly modified to handle large terrain problems and is further embellished by accelerating it as well as reducing its storage requirements via the use of an extrapolation procedure numerical results for the total fields as well as for the path loss are presented and compared with either measured or previously published reference solutions to assess the efficiency and accuracy of the algorithm

a fredholm integral equation method for propagation predictions over small terrain irregularities two dimensional propagation of vertical line source fields over lossy irregular terrain is considered using the magnetic field integral equation the terrain is characterized by its elevation profile and the local surface impedance both of which may vary with distance for treatment via the fredholm integral equation the domain under consideration is made finite by enclosing the terrain irregularity and the source within an arbitrary outer boundary absorbing boundary conditions are imposed on the outer boundary to reduce unwanted reflections from it the integral equation is solved by the boundary element method with quadratic elements substantial comparison is made with specific canonical problems with previously published results of other workers and with measurements to validate the method

multiple time domain diffraction for uwb signals the time domain td solution of the two dimensional multiple diffraction case is investigated the proposed td solution is based on the representation of the inverse fourier transform of the corresponding frequency domain fd solution in closed form as it is given by the uniform theory of diffraction utd and it incorporates the td representation of the higher order diffraction coefficients an algorithm to predict the td diffracted field after an arbitrary number of objects is also presented in the proposed algorithm different types of objects along the propagation path can be applied as well such as absorbing knife edges and metallic or nonperfectly conducting wedges the comparison between the td solution and the numerical inverse fast fourier transform of the fd solution proves the validity of the proposed solution

direct solution of current density induced on a rough surface by forward propagating waves a new volterra integral equation of the second kind with square integrable kernel is derived for paraxial propagation of radiowaves over a gently varying perfectly conducting rough surface the integral equation is solved exactly in terms of a infinite series and the necessary and sufficient conditions for the solution to exist and converge are established super exponential convergence of the neumann series for arbitrary surface slope is established through asymptotic analysis expressions are derived for the determination of the number of terms needed to achieve a given accuracy the latter depending on the parameters of the rough surface the frequency of operation and the maximum range numerical results with truncated series are compared with that obtained by solving the integral equation numerically for a sinusoidal surface gaussian hill and a random rough surface with pierson moskowitz spectrum

fresnel kirchhoff integral for 2 d and 3 d path loss in outdoor urban environments a deterministic model for propagation in outdoor urban environments based on the fresnel kirchhoff integral is presented both two dimensional 2 d and three dimensional 3 d formulations considering reflection and diffraction are given the theoretical predictions are compared with 2 d and 3 d measurements and good agreement is achieved the 3 d experiments conducted in an anechoic chamber with scaled models representing buildings are described in detail and provide a benchmark for comparisons with other methods

a general uniform double wedge diffraction coefficient the uniform theory of diffraction utd is extended to include double diffraction by an arbitrary configuration of two wedges a scalar double diffraction coefficient is defined which is uniform throughout space while reducing to the product of single diffraction coefficients outside overlapping transition regions the result is formulated in terms of double fresnel integrals which can be rapidly evaluated

h sub 2 guaranteed cost control for singularly perturbed uncertain systems the h sub 2 guaranteed cost control problem for a singularly perturbed norm bounded uncertain system is addressed using the quadratic stabilizability framework after defining the corresponding slow and fast uncertain subsystems the set of quadratic stabilizing composite controls is characterized two riccati equations have to be solved one for the slow subsystem and the other for the fast subsystem choosing appropriately the weighting matrices it is shown how to pick up in the set of quadratic stabilizing composite controls a control minimizing an upper bound on the h sub 2 norm of a certain transfer matrix the case of the guaranteed cost control problem for the reduced system is also investigated

h optimal control for singularly perturbed systems part i perfect state measurements we study the h optimal control of singularly perturbed linear systems under perfect state measurements for both finite and infinite horizons using a differential game theoretic approach we show that as the singular perturbation parameter approaches zero the optimal disturbance attenuation level for the full order system under a quadratic performance index converges to a value that is bounded above by the maximum of the optimal disturbance attenuation levels for the slow and fast subsystems under appropriate slow and fast quadratic cost functions furthermore we construct a composite controller based on the solution of the slow and fast games which guarantees a desired achievable performance level for the full order plant as approaches zero a slow controller however is not generally robust in this sense but still under some conditions which are delineated in the paper the fast dynamics can be totally ignored the paper also studies optimality when the controller includes a feedforward term in the disturbance and presents some numerical examples to illustrate the theoretical results

efficient computation of nonparaxial surface fields excited on an electrically large circular cylinder with an impedance boundary condition an alternative numerical approach is presented for the evaluation of the fock type integrals that exist in the uniform geometrical theory of diffraction utd based asymptotic solution for the nonparaxial surface fields excited by a magnetic or an electric source located on the surface of an electrically large circular cylinder with an impedance boundary condition ibc this alternative approach is based on performing numerical integration of the fock type integrals on a deformed path on which the integrands are nonoscillatory and rapidly decaying comparison of this approach with the previously developed one presented in which is based on invoking the cauchy s residue theorem by finding the pole singularities numerically reveals that the alternative approach is considerably more efficient

a scheme for automatic computation of fock type integrals the evaluation of fock type integrals i e integrals that are formally the fourier transform of a slowly varying factor comprising a quotient of terms containing airy functions and their derivatives is developed in a computationally efficient way the integrals are evaluated by use of a simple extension of a fourier quadrature method that is related to the discrete fourier transform the resulting quadrature is applicable to both surface field and reflected field fock integrals for a lossy impedance surface the computation is believed to be efficient enough to allow the use of these functions in field computations codes where the fock integrals must be computed on an as needed basis

h control for fuzzy singularly perturbed systems in this paper both the state feedback and static output feedback h controllers for fuzzy singularly perturbed systems are investigated we give sufficient conditions for the existence of h controller such that the closed loop fuzzy control system is globally stable and achieves a prescribed level of disturbance attenuation for sufficiently small perturbation parameters the linear matrix inequality lmi approach is proposed to obtain the state feedback gains and a homotopy based iterative lmi algorithm is developed to get the static output feedback gains simulation results for two examples are included to demonstrate the effectiveness of the proposed approaches

frequency scale decomposition of h disk problems time and frequency scale decomposition methods have been used extensively for the sim plification of automatic control problems this paper considers the problem of parametrizing all functions in a specified h infty function disk over the unit ball in h infty this problem arises in the design of stabilizing feedback compensators to minimize a weighted sensitivity matrix in the h infty norm sense it is shown that an h infty disk problem whose data has two frequency scale behavior can be broken down into slow and fast subproblems if solutions can be found for both subproblems then the solutions can be combined to give an approximate solution for the original problem

on a characterization of the essential spectra of some matrix operators and application to two group transport operators in this paper we investigate the essential approximate point spectrum and the essential defect spectrum of a 2 2 block operator matrix on a banach space furthermore we apply the obtained results to two group transport operators in the banach space l p a a 1 1 l p a a 1 1 a 0 p 1

terrain based propagation model for rural area an integral equation approach a terrain based propagation model for vertically polarized radio waves is described based on the field integral equation for a smooth surface the model is simplified from a 3d integral equation model to a one dimensional integral equation by assuming that the surface is magnetically perfectly conducting a soft surface with no transverse variations by assuming no back scattering the integral equation is turned into a simple integral the method is tested numerically with known solutions the integral equation model is also applied to actual terrain profiles at four frequencies 144 435 970 1900 mhz and the results are compared with results from the hata model and measurements the standard deviation std of the error is a growing function of frequency from 3 to 9 db

bibo stabilization of time delayed system with nonlinear perturbation time delayed control system with the nonlinear perturbation is considered novel bibo stabilization criteria are established by the lyapunov functional and formulated in terms of existence of a positive definite solution to an auxiliary algebraic riccati matrix equation the robust quadratic stability for such systems is also discussed a numerical example is given to illustrate the effectiveness of our result

a uniform gtd formulation for the diffraction by a wedge with impedance faces a uniform high frequency solution is presented for the diffraction by a wedge with impedance faces illuminated by a plane wave perpendicularly incident on its edge arbitrary uniform isotropic impedance boundary conditions may be imposed on the faces of the wedge and both the transverse electric te and transverse magnetic tm cases are considered this solution is formulated in terms of a diffraction coefficient which has the same structure as that of the uniform geometrical theory of diffraction utd for a perfectly conducting wedge its extension to the present case is achieved by introducing suitable multiplying factors which have been derived from an asymptotic evaluation of the exact solution given by maliuzhinets when the field point is located on the surface near the edge a more accurate asymptotic evaluation is employed to obtain a high frequency expression for the diffracted field which is suitable for several specific applications the formulation described in this paper may provide a useful rigorous basis to search for a more numerically efficient but yet accurate approximation

a curvilinear coordinate based split step parabolic equation method for propagation predictions over terrain propagation of radiowaves over irregular terrain and in an inhomogeneous atmosphere is solved by the parabolic equation method using the split step fourier algorithm on a terrain conformal mesh a piecewise continuous coordinate system is generated by the specification of 1 the terrain profile shape at discrete points and 2 an upper height the resulting mesh is conformal to the terrain at the lower boundary and gradually flattens off at the maximum height in addition to preserving the number of points on any vertical line between the terrain and the maximum height from one range step to another the coordinate transformation used in the paper produces a correction term in the refractive index whose gradient diminishes with height as a result the sampling requirements over steep terrain are relaxed when compared to the beilis tappert transformation formulation and results are given both for the horizontal and vertical polarizations

path loss predictions in the presence of buildings on flat terrain a 3 d vector parabolic equation approach starting from a parabolic approximation to the helmholtz equation a three dimensional 3 d vector parabolic equation technique for calculating path loss in an urban environment is presented the buildings are assumed to be polygonal in cross section with vertical sides and flat rooftops and the terrain is assumed to be flat both buildings and ground are allowed to be lossy and present impedance type boundary condition to the electromagnetic field vector fields are represented in terms of the two components of hertzian potentials and depolarization of the fields is automatically included in the formulation a split step algorithm is presented for marching the aperture fields along the range boundary conditions on the building surfaces are treated by using a local fourier representation of the aperture fields several test cases are considered to check the boundary treatment used in the technique as well as to validate the overall approach comparison is shown with uniform theory of diffraction utd exact solutions as well as with measurements

generalization of utd double diffraction to the case of impenetrable wedges with relatively general boundary conditions in the framework of the uniform geometrical theory of diffraction utd a novel high frequency solution is provided which allows the description of the rays doubly diffracted by a pair of impenetrable straight wedges with relatively general boundary conditions under a spherical wave illumination such a utd solution is heuristically derived by imposing the continuity of the total field at the shadow boundaries of the first order i e geometrical optics utd wedge single diffracted ray field utd solution it is the extension to the case of double diffraction of the first order solutions proposed by luebbers and by burnside and burgener it allows a uniform description of the field at any observation point including those aspects where transition regions overlap and the cascading of utd single wedge diffraction coefficients fails the proposed solution does not consider surface wave effects and for the special case of two perfectly conducting wedges it reduces to the formulation present in the literature of which it can be considered a generalization indeed it requires the same special functions involved in utd double diffraction by two perfectly conducting wedges the double diffracted ray field is expressed in analytical closed form providing a deeper understanding of the physics involved in double diffraction and a new powerful tool to be employed in any modern ray based code

a hybrid asymptotic solution for the scattering by a pair of parallel perfectly conducting wedges the overlapping transition regions of the double diffraction by a pair of parallel wedge edges are considered for the hybrid case where the gap between the edges is small compared to the distances from the source and the observation point plane wave far field limit and the scatterer as a whole is large or infinite a closed form asymptotic solution for the scattered field continuous at all angles of incidence and scattering is constructed for this case the peculiar feature of this solution is a hybrid representation of the field singly diffracted by the first wedge a part of it is described by a nonuniform geometrical theory of diffraction gtd expression while the other part is described in terms of the uniform theory of diffraction utd the rest of the diffracted ray fields are described by nonuniform expressions with singularities mutually canceling on summation this solution is applied to the scattering by a perfectly conducting rectangular cylinder with appropriate geometrical parameters and agreement with moment method calculation is demonstrated

forward backward method with spectral acceleration for scattering from layered rough surfaces a fast method of moments is presented to calculate electromagnetic wave scattering from layered one dimensional rough surfaces the formulation is provided for m stratified homogeneous regions separated by m 1 rough surfaces and solved using point matching and pulse basis functions compared to the single surface case the solution of scattering from m 1 surfaces requires significantly more memory and computational time to facilitate the solution the forward backward method with spectral acceleration is applied as an example a dielectric layer on a perfect electric conductor surface is studied the numerical results are compared with the analytical solution for layered flat surfaces to partly validate the formulation the accuracy efficiency and convergence of the method are then studied for various rough surfaces and layer permittivities

robust stabilization of uncertain linear systems quadratic stabilizability and h sup infinity control theory the problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time domain results on the quadratic stabilization of uncertain systems and the frequency domain results on h sup infinity optimization a complete solution to a certain quadratic stabilization problem in which uncertainty enters both the state and the input matrices of the system is given relations between these robust stabilization problems and h sup infinity control theory are explored it is also shown that in a number of cases if a robust stabilization problem can be solved via lyapunov methods then it can be also be solved via h sup infinity control theory based methods

two level tabulated interaction method for electromagnetic scattering from lossy irregular terrain profiles incorporating back scattering an efficient method is proposed for computing electromagnetic wave propagation over lossy terrain profiles using a coupled surface integral equation formulation the proposed method uses a set of basis functions which can produce a linear system with much fewer unknowns than that created using pulse basis functions in addition the matrix entries can be computed very rapidly using precomputed tabulated values the method improves upon the original tabulated interaction method tim by extending it to lossy profiles allowing for back scatter and by introducing increased accuracy for near field interactions the complexity and numerical analysis demonstrates that the proposed method has an extremely low computational complexity and storage requirement moreover the accuracy of the proposed method is demonstrated by comparing the pathloss against numerically precise solutions and measured data

some remarks on the essential spectrum of transport operators with abstract boundary conditions this article deals with the analysis of the essential spectrum of the one dimensional transport operator with general boundary conditions where an abstract boundary operator relates the incoming and the outgoing fluxes after a complete description of the spectrum of the transport equation with vacuum boundary conditions sufficient conditions are given in terms of boundary and collision operators assuring the stability of the essential spectrum the article ends with an analysis of the essential spectrum of the neutron transport operator in arbitrary dimension finally some open problems are indicated

a uniform geometrical theory of diffraction for an imperfectly conducting half plane diffraction tensors are presented in the context of the uniform geometrical theory of diffraction utd for the high frequency scattering by an impedance half plane at normal and oblique skew incidence these are based on the exact wiener hopf solution and were derived according to the utd ansatz in addition unlike previous uniform diffraction coefficients the ones given here reduce to the known utd diffraction coefficients for the perfectly conducting case the coefficients are explicit and therefore appropriate for practical applications several scattering patterns are also presented and compared to a previous heuristic solution

robust stability of two time scale systems with nonlinear uncertainties this note is concerned with the robust stability problem of uncertain two time scale systems where the only information available for system uncertainties is their norm upper bounds the stability bound spl epsiv sup is derived via a state transformation and the constructive use of a lyapunov function finally examples are given to illustrate the applications of the proposed results

noise attenuation by a hard wedge shaped barrier this paper is concerned with the problem of sound screening by a wedge like barrier the sound source is assumed to be point like and the receiver is located in the shadow of the source sound field so that according to geometrical optics only the field diffracted by the edge of the barrier is considered first for the hard wedge in space three models are used for calculating the amplitude of the edge diffracted field these are the uniform theory of diffraction utd the hadden pierce model both in the frequency domain and the biot tolstoy theory of diffraction which is a time domain formulation it is first shown that even at relatively low frequencies the frequency domain models perform quite satisfactorily as compared to the exact time domain theory hence and due to its relative simplicity the utd is proposed as an accurate calculation scheme for solving problems with edge diffraction by hard wedges it is also proved from theoretical calculations that the amplitude of the edge diffracted field increases for an increasing angle of the wedge and consequently the hard half plane gives the lowest field amplitude in the shadow zone some applications are then considered for evaluating the performance of a barrier on a flat ground either completely hard or with mixed homogeneous boundary conditions an improvement of the scheme for calculating the sound field in the all hard case is achieved through considering the multiple diffraction in this case only to the second order between the top of the wedge barrier and its base the results show that for usually occurring situations increasing the angle of the hard wedge barrier affects negatively its efficiency through diminishing its insertion loss these conclusions are also supported by the results of some experimental measurements conducted at a scale model level

calculation of higher order diffracted fields for multiple edge transition zone diffraction a well known problem in conventional uniform theory of diffraction utd is multiple edge transition zone diffraction here higher order diffracted fields have to be used in order to improve the result and these fields are added by means of a series unfortunately this series will converge slowly for many edges which means that a good enough result might require a large number of terms however by summing up the series properly the computation time can be kept reasonable which will be shown for knife edges the summation technique is though valid for wedges as well

some remarks on the schechter essential spectrum and applications to transport equations abstract the purpose of this article is to provide an extension of the work a jeribi j math anal appl 271 2002 343 358 where a detailed treatment of the schechter essential spectrum of a closed densely defined linear operators a subjected to additive perturbations k such that a 1k or k a 1 belonging to arbitrary subsets of l x where x denotes a banach spaces contained in the ideal of fredholm perturbations our approach consists principally in considering the class of a closable not necessarily bounded which contained in the set of a resolvent fredholm perturbations see definition 1 12 they are used to describe the schechter essential spectrum of singular neutron transport equations in bounded geometries

time domain utd po solution for the multiple diffraction of spherical waves for uwb signals the time domain td solution for the multiple diffraction of spherical waves after an arbitrary number of obstacles with different shapes such as knife edges and wedges is presented the proposed td solution is based on the representation of the inverse laplace transform of the corresponding frequency domain solution in closed form as it is given by a hybrid of the uniform theory of diffraction utd physic optics po solution the proposed formulation validated with the results from technical literature does not need to incorporate the td version of the higher order diffraction coefficients due to a recursive relation thus significantly reducing both the mathematical complexity and computation time of the formulation when compared with other td solutions