almost invariant subspaces an approach to high gain feedback design part ii almost conditionally invariant subspaces in part i of this paper almost controlled invariant subspaces were studied in this part we will consider their duals the almost conditionally invariant subspaces these concepts give immediately by dualization of the almost disturbance decoupling control by state feedback the solution of the almost disturbance decoupled estimation problem finally we consider the problem of approximate disturbance decoupling by measurement feedback and it is shown that this problem is solvable to any arbitrary degree of accuracy if and only if 1 almost disturbance decoupling by state feedback and 2 almost disturbance decoupled estimation of the to be controlled output are both possible

time domain transfer coupled response of antennas reciprocity theorem approach a complete time domain network representation of a transmit receive two port perfect electric conducting antenna system in an arbitrary distance is presented we utilize a scattering matrix setting which as the impedance matrix formulation is a proper setting for the time domain formulation in antenna system representations the formulation is derived directly in the time domain using both the convolution type and the correlation type reciprocity relations we derive the general expressions for the matrix in particular the transfer coupled coefficients between the antennas transfer coupled response followed by closed form example of parallel staggered dipole antennas that provides a clear and transparent physical interpretation for the time domain phenomenology

estimation of states and parameters for linear systems with nonlinearly parameterized perturbations we consider systems that can be described by a linear part with a nonlinear perturbation where the perturbation is parameterized by a vector of unknown constant parameters under a set of technical assumptions about the perturbation and its relationship to the outputs we present a modular design technique for estimating the system states and the unknown parameters the design consists of a high gain observer that estimates the states of the system together with the full perturbation and a parameter estimator constructed by the designer to invert a nonlinear equation we illustrate the technique on a simulated dc motor with friction

fast evaluation of transient acoustic fields the efficient computation of transient fields radiated by non harmonic source distributions is a problem relevant in numerous areas of acoustics this paper presents an efficient easily implemented method for the generation of time dependent spherical harmonic expansions for arbitrary sources which can be used to compute the transient radiated field at arbitrary points outside the source domain the method depends on the theory of time domain spherical harmonic expansions and the solution of vandermonde systems results are presented demonstrating the efficiency and accuracy of the method with respect to full evaluation of the field radiated by a randomized source distribution

an iterative method for the computation of nonlinear wide angle pulsed acoustic fields of medical diagnostic transducers the development and optimization of medical ultrasound transducers and imaging modalities require a computational method that accurately predicts the nonlinear acoustic pressure field a prospective method should provide the wide angle pulsed field emitted by an arbitrary planar source distribution and propagating in a three dimensional large scale domain holding a nonlinear acoustic medium in this paper a method is presented that is free of any assumed wavefield directionality the nonlinear acoustic wave equation is solved by treating the nonlinear term as a contrast source this formulation leads to an iterative scheme that involves the repetitive solution of a linear wave problem through green s function method it is shown that accurate field predictions may be obtained within a few iterations moreover by employing a dedicated numerical convolution technique the method allows for a discretization down to two points per wavelength or period of the highest frequency of interest the performance of the method is evaluated through a number of nonlinear field predictions for pulsed transducers with various geometries the results demonstrate the directional independence of the method moreover comparison with results from several existing methods shows that the method accurately predicts the nonlinear field for weak to moderate nonlinearity

construction and parameterization of all static and dynamic h 2 optimal state feedback solutions for discrete time systems abstract this paper considers an h 2 optimization problem via state feedback for discrete time systems the class of problems dealt with here has a left invertible transfer matrix function from the control input to the controlled output the paper constructs and parameterizes all the static and dynamic h 2 optimal state feedback solutions moreover all the eigenvalues of an optimal closed loop system are characterized all optimal closed loop systems share a set of eigenvalues which are termed the optimal fixed modes every h 2 optimal controller must assign among the closed loop eigenvalues the set of optimal fixed modes this set of optimal fixed modes includes a set of optimal fixed decoupling zeros which shows the minimum absolutely necessary number and locations of pole zero cancellations present in any h 2 optimal design most of the results presented here are analogous to but not quite the same as those for continuous time systems in fact there are some fundamental differences between the continuous and discrete time systems reflecting mainly the inherent nature and characteristics of these systems

formulation of probe corrected planar near field scanning in the time domain probe corrected planar near field formulas in the time domain are derived for both acoustic and electromagnetic fields so that a single set of near field measurements in the time domain yields the fields of the test antenna directly in the time domain the time domain probe corrected formulas are first derived by taking the inverse fourier transform of the corresponding frequency domain formulas and then by using a time domain expansion for the fields of the test antenna and a time domain receiving characteristic of the probe because these general formulas which involve a double integral over the scan plane and an infinite time convolution integral are rather complicated we consider a special probe whose output due to an incoming time domain plane wave is proportional to the time derivative of the field of that plane wave for this special d dot probe the probe corrected formulas simplify to give the time domain far held pattern as a double spatial integral of the time domain output of the probe over the scan plane multiplied by the angular dependence of the inverse receiving characteristic of the probe time domain reciprocity relations are derived for reciprocal probes and their time domain receiving characteristics are related to their far fields finally a time domain sampling theorem is derived and a numerical example illustrates the use of the time domain probe corrected formulas

a note on the calculation and placing of finite zeros the finite zeros of a transfer function matrix are defined as the finite points on the complex plane to which the multivariable root loci converge as the loop gain increases infinitely in this paper an example is given where the finite zeros arc not obtained by the algorithm of kouvaritakis and macfarlane 1976 then a modification is suggested for the theorem which states a necessary and sufficient condition that the finite zeros are placed at stipulated n m points

the sampling window corresp the concept of the sampling window is introduced for the central interpolation of finite energy band limited functions the sampling window does not increase the rate of convergence of the truncation error series as do various convergence factors but does significantly reduce the truncation error bound

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

semi global stabilization of partially linear composite systems via feedback of the state of the linear part abstract we consider the problem of semi global stabilization of a class of partially linear composite systems we show by explicit construction of the control laws that a cascade of linear stabilizable and nonlinear asymptotically stable subsystems is semi globally stabilizable by a dynamic feedback of the state of the linear subsystem if a the linear subsystem is right invertible and has all its invariant zeros in the closed left half s plane and b the only linear variables entering the nonlinear subsystem are the output of the linear subsystem our work generalizes previous results by c i byrnes and a isidori 1991 h j sussmann and p v kokotovic 1991 and a r teel 1992

a singular perturbation canonical form of invertible systems determination of multivariate root loci a new canonical form of multivariable invertible systems is given this form is suitable for the singular perturbation analysis of such singular problems as multi variable asymptotic root loci under high gain feedback cheap control state variable estimation with weak measurement noise etc appropriate selection and decomposition of state variables into slow and fast changing groups is a key feature that loads to well defined singular perturbation models the selection of state variables is accomplished without explicitly calculating any eigenvalues of the given system but by knowing the direct relationship of the output and its differential coefficients with the input the use of the canonical form to characterize the multivariable root loci under high gain feedback is demonstrated

iterative computational techniques in scattering based upon the integrated square error criterion an iterative technique is developed to rigorously compute the electromagnetic time and frequency domain scattering problems the method is based upon a wave function expansion technique this also includes the integral representation techniques in which the electromagnetic field equations and causality conditions are satisfied analytically while the boundary conditions or the constitutive relations have to be satisfied in a computational manner the latter is accomplished by an iterative minimization of the integrated square error for the solution of an integral equation it is shown how to obtain optimum convergence some numerical results pertaining to a number of representative problems illustrate the numerical advantages and disadvantages of the iterative method

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

two alternative expressions for the spherical wave expansion of the time domain scalar free space green s function and an application scattering by a soft sphere the importance of expanding green s functions particularly free space green s functions in terms of orthogonal wave functions is practically self evident when frequency domain scattering problems are of interest with the relatively recent and widespread interest in time domain scattering problems similar expansions of green s functions are expected to be useful in the time domain in this paper two alternative expressions expanded in terms of orthogonal spherical wave functions for the free space time domain scalar green s functions are presented although the two expressions are equivalent one of them is seen to be more convenient for the calculation of the scattered field for a known equivalent source density whereas the second expression is more suitable for setting up an integral equation for the equivalent source density such an integral equation may be setup for example by the application of a time domain equivalent of the t matrix extended boundary condition method

a k space method for coupled first order acoustic propagation equations a k space method for large scale simulation of ultrasonic pulse propagation is presented the present method which solves the coupled first order differential equations for wave propagation in inhomogeneous media is derived in a simple form analogous to previous finite difference methods with staggered spatial and temporal grids like k space methods based on second order wave equations the present method is exact for homogeneous media unconditionally stable for slow c r c0 media and highly accurate for general weakly scattering media in addition unlike previous k space methods the form of the method allows straightforward inclusion of relaxation absorption and perfectly matched layer pml nonreflecting boundary conditions numerical examples illustrate the capabilities of the present k space method for weakly inhomogeneous media accurate results are obtained using coarser temporal and spatial steps than possible with comparable finite difference and pseudospectral methods the low dispers

a filtered convolution method for the computation of acoustic wave fields in very large spatiotemporal domains the full wave computation of transient acoustic fields with sizes in the order of 100x100x100 wavelengths by 100 periods requires a numerical method that is extremely efficient in terms of storage and computation iterative integral equation methods offer a good performance on these points provided that the recurring spatiotemporal convolutions are computed with a coarse sampling and relatively few computational operations this paper describes a method for the numerical evaluation of very large scale four dimensional convolutions that employs a fast fourier transformation and that uses a sampling rate close to or at the limit of two points per wavelength and per period to achieve this the functions involved are systematically filtered windowed and zero padded with respect to all relevant coordinates prior to sampling the method is developed in the context of the neumann iterative solution of the acoustic contrast source problem for an inhomogeneous medium the implementation of the method on a parallel computer is discussed the obtained numerical results have a relative root mean square error of a few percent when sampling at two points per wavelength and per period further the results prove that the method enables the computation of transient fields in the order of the indicated size

morava modules and brown comenetz duality fix a prime number p and let x be a finite spectrum whose n 1 st morava k theory is trivial but whose n th morava k theory is nontrivial n 0 we prove following a method outlined to us by m j hopkins that if 2 p n 2 n 2 the morava module of the brown comenetz dual of the e n localization of x is isomorphic to a suspension of the pontryagin dual of the morava module of x to complete this proof we found it necessary to develop a more canonical construction of certain modified adams spectral sequences this construction should be of independent interest

spherical expansions of time domain acoustic fields application to near field scanning this paper addresses the problem of formulating spherical near field scanning for time domain acoustic fields two basic spherical expansions for time domain acoustic fields are derived that determine the field outside a scan sphere enclosing the source region the first expansion is obtained with the help of green s second identity the scalar free space green s function and the fourier transform this expansion expresses the time domain acoustic field outside the scan sphere in terms of the time domain acoustic field and its normal derivative on the scan sphere the second expansion is a spherical eigenfunction expansion that expresses the time domain acoustic field outside the scan sphere directly in terms of the time domain acoustic field on the scan sphere then a probe corrected formula is presented that expresses the field outside the scan sphere in terms of the output of a known axis symmetric probe on the scan sphere sampling theorems that determine the distance between spatial sample points on the scan sphere and the distance between time sample points are also derived the sampling theorems show how to compute the field everywhere outside the scan sphere in terms of space time samples of the field on the scan sphere or in terms of the probe output on the scan sphere finally a numerical example illustrates the use of the eigenfunction expansion and the corresponding sampling theorem

the receiving antenna as a linear differential operator application to spherical near field scanning the general receiving antenna is represented as a linear differential operator converting the incident field and its spatial derivatives at a single point in space to an output voltage the differential operator is specified explicitly in terms of the multipole coefficients of the antenna s complex receiving pattern when the linear operator representation is applied to the special probes used in spherical near field measurements a probe corrected spherical transmission formula is revealed that retains the form applicability and simplicity of the nonprobe corrected equations the new spherical transmission formula is shown to be consistent with the previous transmission formula derived from the rotational and translational addition theorems for spherical waves

fast computation of time dependent acoustic fields a method for the fast evaluation of time dependent acoustic fields from complex sources is presented the technique is based on a fast integration method for the boundary integral arising in a kirchhoff formulation and requires a small and roughly constant computation time to compute a transient signal at the expense of a pre processing stage in the calculations in this paper based on test cases for a single rotor a counter rotating open rotor and a broadband volume source it is found that transient field calculations require an order of magnitude less computational time for the field from an array of 16 384 sources a computational advantage that increases with source number

modeling of nonlinear ultrasound propagation in tissue from array transducers a computationally efficient model capable of simulating finite amplitude ultrasound beam propagation in water and in tissue from phased linear arrays and other transducers of arbitrary quasiplanar geometry is described it is based on a second order operator splitting approach tavakkoli et al j acoust soc am 104 2061 2072 1998 with a fractional step marching scheme whereby the effects of diffraction attenuation and nonlinearity can be computed independently over incremental steps this approach is an extension to that of christopher and parker j acoust soc am 90 507 521 90 488 499 1991 wherein linear and nonlinear effects are propagated separately over incremental steps and the computation of the diffractive substeps are based on an angular spectrum technique with a modified sampling scheme for accurate and efficient implementation of diffractive propagation from nonradially symmetric sources results of the model are compared with published data predicted field profiles for nonlinear propagation in tissue from realistic array transducers using the pulse inversion method are presented

the generating hypothesis for the stable module category of a p group freyd s generating hypothesis interpreted in the stable module category of a finite p group g is the statement that a map between finite dimensional kg modules factors through a projective if the induced map on tate cohomology is trivial we show that freyd s generating hypothesis holds for a non trivial finite p group g if and only if g is either c2 or c3 we also give various conditions which are equivalent to the generating hypothesis

direct singular perturbation analysis of high gain and cheap control problems a new and direct approach to the analysis and design of high gain feedback and cheap control problems is developed transformation of such singular problems to singular perturbation models of conventional type early at the onset of analysis or design allows a direct application of the readily available singular perturbation literature the approach permits a simple characterization of a multivariable root loci under a high gain feedback and b asymptotic behavior of optimal closed loop poles state and control trajectories performance index and optimal transfer function as the control cost coefficient in the performance index goes to zero

generalization of the k space formulation to elastodynamic scattering problems a generalized k space gks formulation is presented for vectorial elastodynamic scattering problems it represents a generalization of bojarski s scalar k space formulation from the basic second order partial differential equation or its integral representation in the space frequency r f domain a local equation is derived for the displacement field in the spectral frequency k f domain this equation together with the constitutive equation in the r f domain reduces the original scattering problem into two simultaneous local equations with two unknowns displacement field and the induced source which are then solved by the conjugate gradient cg method the connection between the k f domain and r f domain is obtained by the spatial fast fourier transform fft algorithm the number of complex multiply add operations per cg iteration is o n log2 n and the storage requirement is only o n where n is the number of spatial discretization points this is much more efficient than the conventional m

on the structure at infinity of linear square decoupled systems the purpose of this note is to demonstrate that a square invertible linear system c a b is decouplable by static state feedback if and only if its infinite zero orders are respectively equal to the infinite zero orders of the subsystems c i a b where c i denotes the i th row of c until now only the necessity of this condition has been established 1

homogeneous networks of non introspective agents under external disturbances h almost synchronization this paper addresses the problem of h almost synchronization for homogeneous networks of general linear agents subject to external disturbances and under directional communication links agents are presumed to be non introspective i e agents are not aware of their own states or outputs and the only available information for each agent is a network measurement that is a linear combination of relative outputs under a certain set of conditions a family of dynamic protocols is developed such that the impact of disturbances on the synchronization error dynamics expressed in terms of the h norm of the corresponding closed loop transfer function is reduced to any arbitrarily small value

strictly observable linear systems a theory of strictly observable linear systems is developed in a module theoretic framework which is consistent with the classical algebraic theory of linear time invariant realization the theory incorporates in a unified framework the reduction of linear systems through precompensation through state feedback and through dynamic output feedback

near field scanning in the time domain on a spherical surface a formulation using the free space green s function two formulations for determining the characteristics of an unknown source of acoustic waves using the measurement of its field at its near zone are presented the measurement in both cases is to be performed on a spherical scan surface which encapsulates the source the first is for an ideal probe which measures the field at its location the knowledge of the field is sufficient its normal derivative is not required in the second formulation a realistic probe is considered this time it is required only that the probe has an axially symmetric receiving characteristic with this formulation the time functions which characterize the source are found using only the signal at the output of the probe both formulations are such that they are not specific to the scan surface radius furthermore they are entirely in the time domain requiring no inverse fourier transformations left to be performed

mappings of the finite and the infinite zero structures and invertibility structures of general linear multivariable systems under the bilinear transformation this paper presents a comprehensive picture of the mapping of structural properties associated with general linear multivariable systems under bilinear transformation while the mapping of poles of linear multivariable systems under such a transformation is well known the question of how the structural invariant properties of a given system are mapped remains unanswered this paper addresses this question more specifically we investigate how the finite and infinite zero structures as well as invertibility structures of a general continuous time discrete time linear time invariant multivariable system are mapped to those of its discrete time continuous time counterpart under the bilinear inverse bilinear transformation we demonstrate that the structural invariant indices lists i2 and i3 of morse remain invariant under the bilinear transformation while the structural invariant indices lists i1 and i4 of morse are in general changed

squaring down by static and dynamic compensators given a system which is not necessarily invertible and which has an unequal number of inputs a method of squaring down that is a method of designing pre compensators and postcompensators such that the resulting system has an equal number of inputs and outputs and is invertible is presented the compensators are in general dynamic and have the property that the additional finite zeros induced by them are assignable to the open left half complex plan furthermore the compensators are asymptotically stable and hence do not deteriorate the robustness and performance of an eventual feedback design also the compensator design preserves the stabilizability detectability and minimum phase properties and the infinite zero structure of the original system thus a method of designing nonsquare systems by converting them to square invertible systems is introduced two applications of such a design philosophy 1 diagonal decoupling with state feedback and 2 almost disturbance decoupling with output feedback are pointed out

brief solutions to disturbance decoupling problem with constant measurement feedback for linear systems we study in this paper the problem of disturbance decoupling with constant i e static measurement feedback ddpcm for linear systems for a class of systems which have a left invertible transfer function from the control input to the controlled output or a right invertible transfer function from the disturbance input to the measurement output we obtain a complete characterization of all solutions to the ddpcm for a system that does not satisfy the above invertibility condition we use the special co ordinate basis to obtain a reduced order system then a complete characterization of all possible solutions to the ddpcm for the given system can be explicitly obtained if the obtained reduced order system itself satisfies the invertibility condition the main advantage of these solutions is that the solutions are given in a set of linear equations this resolves the well known difficulty in solving non linear equations associated with the ddpcm

short note a fast and stable method for rotating spherical harmonic expansions in this paper we present a simple and efficient method for rotating a spherical harmonic expansion this is a well studied problem arising in classical scattering theory quantum mechanics and numerical analysis usually addressed through the explicit construction of the wigner rotation matrices we show that rotation can be carried out easily and stably through pseudospectral projection without ever constructing the matrix entries themselves existing fast algorithms based on recurrence relations are subject to a variety of instabilities limiting the effectiveness of the approach for expansions of high degree

smith mcmillan factorizations at infinity of rational matrix functions and their control interpretation in this paper the smith mcmillan factorizations at infinity of a transfer function are studied the non uniqueness of these factorizations is characterized via a multiplicative group of bicausal isomorphisms control interpretations are given in terms of system equivalence under some groups of transformations a characterization of the stabilizer of morse group at a b c is given for irreducible systems

the almost disturbance decoupling problem with internal stability for linear systems subject to input saturation state feedback case abstract we consider the almost disturbance decoupling problem addp and or almost d bounded disturbance decoupling problem addp d with internal stability for linear systems subject to input saturation and input additive disturbance via linear static state feedback we show that the almost d bounded disturbance decoupling problem with local asymptotic stability addp las d is always solvable via linear static state feedback as long as the system in the absence of input saturation is stabilizable no matter where the poles of the open loop system are and the locations of these poles play a role only in the solution of addp gas d addp sgas d or addp gas where semi global or global asymptotic stability is required

a pole zero representation for the admittance matrix of elastic beam and plate systems the behavior of coupled elastic systems is often analyzed in terms of the admittances or impedances of the component systems in many applications the admittances are approximated by a small number of simple oscillators i e a low order truncation of the normal mode expansion such an approach is reasonable in the neighborhood of system resonances but is much less convenient and accurate in the neighborhood of antiresonances pole zero product expansions of the sort employed in circuit analysis offer a potential means of improving the accuracy of low order approximations the validity of such representations of the admittance matrix is explored here and it is noted that in general the off diagonal components cannot be written in this fashion nevertheless it is shown below that the entire admittance matrix of beam and plate strip systems can always be represented in the pole zero product form further the representation is shown to be valid even when the beam or plate is coupled to an arbitrary conservative elastic structure

global stabilization of partially linear composite systems a linear stabilizable nonlinear asymptotically stable cascade system is globally stabilizable by smooth dynamic state feedback if a the linear subsystem is right invertible and weakly minimum phase and b the only linear variables entering the nonlinear subsystem are the output and the zero dynamics corresponding to this output both of these conditions are coordinate free and there is freedom of choice for the linear output variable this result generalizes several earlier sufficient conditions for stabilizability moreover the weak minimum phase condition for the linear subsystem cannot be relaxed unless a growth restriction is imposed on the nonlinear subsystem

ghosts in modular representation theory a ghost over a finite p group g is a map between modular representations of g which is invisible in tate cohomology motivated by the failure of the generating hypothesis the statement that ghosts between finite dimensional g representations factor through a projective we define the ghost number of kg to be the smallest integer l such that the composite of any l ghosts between finite dimensional g representations factors through a projective in this paper we study ghosts and the ghost numbers of p groups we begin by showing that a weaker version of the generating hypothesis where the target of the ghost is fixed to be the trivial representation k holds for all p groups we then compute the ghost numbers of all cyclic p groups and all abelian 2 groups with c2 as a summand we obtain bounds on the ghost numbers for abelian p groups and for all 2 groups which have a cyclic subgroup of index 2 using these bounds we determine the finite abelian groups which have ghost number at most 2 our methods involve techniques from group theory representation theory triangulated category theory and constructions motivated from homotopy theory

on the structure of strongly controllable systems an important problem in the structure theory of linear systems is the construction of a canonical form for strongly controllable systems i e surjective systems without finite zeros the problem has been solved in principle morse 1973 kronecker 1890 but without a clear identification of the system theoretic meaning of the construction steps this paper proposes the concept of a train basis in order to give this interpretation the second main idea of the paper is the system associated with a sub space through which concept it is possible to translate problems concerning a b invariance etc of subspaces in terms of input output systems in this way we make contact with results of willems 1980 on almost invariance

squaring down of general mimo systems to invertible uniform rank systems via pre and or post compensators abstract pre and or post compensators are designed to square down a general mimo system to a uniform rank system the structure of which is almost similar to a siso system the method of squaring down either does not change the finite zero structure of the given mimo system or simply adds additional finite zeros in the left half s plane the significance of such a squaring down lies in the simplicity of the structure of a uniform rank system lending itself for easy analysis and control design

linear time domain model of the acoustic potential field a new time domain formulation of the acoustic wave is developed to avoid approximating assumptions of the linearized scalar wave equation that limit its validity to low mach particle velocity modeling or to a smooth potential field in a stationary medium the proposed model offers precision of the moving frame while retaining the form of the widely used linearized scalar wave equation although with respect to modified coordinates it is applicable to field calculations involving transient waves with unlimited particle velocity propagating in inhomogenous fluids or in those with time varying density the model is based on the exact flux continuity equation and the equation of motion both using the moving reference frame the resulting closed form free space scalar wave equation employing total derivatives is converted back to the partial differential form by using modified independent variables the modified variables are related to the common coordinates of space and time following integral expressions involving transient particle velocity representing wave radiated by each point of a stationary source consequently transient field produced by complex surface velocity sources can be calculated following existing surface integrals of the radiation theory although using modified coordinates the use of the proposed model is presented in a numerical simulation of a transient velocity source vibrating at selected magnitudes leading to the determination of the propagating pressure and velocity wave at any point

on structural decomposition and stabilization of large scale control systems graph theoretic concepts are used to decompose a large control system into a block triangular interconnection of input reachable subsystems stabilization of the system is thereby reduced to stabilization of a number of smaller subsystems the special structural properties of the obtained subsystems can be exploited to further simplify the stabilization problem

computation of nonlinear ultrasound fields using a linearized contrast source method nonlinear ultrasound is important in medical diagnostics because imaging of the higher harmonics improves resolution and reduces scattering artifacts second harmonic imaging is currently standard and higher harmonic imaging is under investigation the efficient development of novel imaging modalities and equipment requires accurate simulations of nonlinear wave fields in large volumes of realistic lossy inhomogeneous media the iterative nonlinear contrast source incs method has been developed to deal with spatiotemporal domains measuring hundreds of wavelengths and periods this full wave method considers the nonlinear term of the westervelt equation as a nonlinear contrast source and solves the equivalent integral equation via the neumann iterative solution recently the method has been extended with a contrast source that accounts for spatially varying attenuation the current paper addresses the problem that the neumann iterative solution converges badly for strong contrast sources the remedy is linearization of the nonlinear contrast source combined with application of more advanced methods for solving the resulting integral equation numerical results show that linearization in combination with a bi conjugate gradient stabilized method allows the incs method to deal with fairly strong inhomogeneous attenuation while the error due to the linearization can be eliminated by restarting the iterative scheme

an advanced time approach for acoustic analogy predictions abstract this paper deals with a new interpretation of the retarded time approach that is widely used in the prediction of acoustic fields from moving sources a hierarchical inversion between the emission time and the reception time leads to advanced time approach this consists in projecting the current status of a source in the observer time domain where the received signal is progressively built the practical relevance of this methodology lies on two statements no retarded time equations must be solved an aerodynamic noise prediction can be processed parallelly to the aerodynamic computation theoretically the advanced time approach differs from the retarded time approach only in one aspect a signal emitted at a given instant by a point source moving at subsonic as well as supersonic velocity is received only one time by an observer moving at subsonic velocity consequently only one value of the advanced time corresponds to a value of the emission time the advanced time approach is herein applied to a retarded time solution of the ffowcs williams and hawkings equation proposed by farassat the noise radiated by elementary acoustic sources in complex motion is then computed and checked against analytical solutions

path following for nonlinear systems with unstable zero dynamics in the path following problem formulated in this note it is required that the error between the system output and the desired geometric path eventually be less than any prespecified constant if in a nonlinear multiple input multiple output mimo system the output derivatives do not enter into its zero dynamics a condition relating path geometry and stabilizability of the zero dynamics is given under which a solution to this problem exists the solution is obtained by combining input to state stability and hybrid system methodologies

solvability conditions for disturbance decoupling problems with static measurement feedback two well known disturbance decoupling problems are considered a checkable necessary and sufficient condition is derived under which the disturbance decoupling problem with static measurement feedback ddpkm is solvable for a class of multi input and multi output linear time invariant systems which have a left invertible transfer matrix function from the control input to the controlled output the set of all solutions that solve the ddpkm is constructed and parametrized explicitly this set is then used to solve the disturbance decoupling problem with static measurement feedback and with internal stability ddpkms