wavelets and filter banks theory and design the wavelet transform is compared with the more classical short time fourier transform approach to signal analysis then the relations between wavelets filter banks and multiresolution signal processing are explored a brief review is given of perfect reconstruction filter banks which can be used both for computing the discrete wavelet transform and for deriving continuous wavelet bases provided that the filters meet a constraint known as regularity given a low pass filter necessary and sufficient conditions for the existence of a complementary high pass filter that will permit perfect reconstruction are derived the perfect reconstruction condition is posed as a bezout identity and it is shown how it is possible to find all higher degree complementary filters based on an analogy with the theory of diophantine equations an alternative approach based on the theory of continued fractions is also given these results are used to design highly regular filter banks which generate biorthogonal continuous wavelet bases with symmetries

pole assignment by output feedback using cylindrical algebraic decomposition recently a new polynomial method for pole assignment by static output feedback has been developed in this paper we show how this method can be generalized to partial pole clustering some poles are exactly assigned the others being clustered in a specified region of the complex plane a constructive and systematic algorithm for the numerical resolution of both problems the collins cylindrical algebraic decomposition algorithm is presented and applied to an illustrative example

robust pole assignment in singular control systems abstract necessary conditions are given for the problem of pole assignment by state feedback in singular linear systems descriptor systems to have a solution which is regular and nondefective for a robust solution such that the assigned closed loop poles are insensitive to perturbations in the system data the same conditions must hold it can be shown that these conditions are also sufficient for the existence of a feedback which assigns the maximum possible number of finite poles with regularity these results provide the basis of a procedure for constructing closed loop semistate systems with given poles guaranteed regularity and maximum robustness

algebraic characterization of controllability subspaces in the current base and its practical computation from the concepts of input chain and controllability chain introduced by heymann and in view of the generalized eigenvector assignment a new algebraic characterization of controllability subspaces css is developed compared with the previous ones based on matrix pencil theory it presents both the advantages of being stated in the current base and of being derived without resorting to use of canonical forms a practical algebraic algorithm is provided in order to compute the controllable structure of a given pair a b this approach is then applied to characterize css contained in a given subspace and span css via eigenvector assignment

sparsity and conditioning of impedance matrices obtained with semi orthogonal and bi orthogonal wavelet bases wavelet and wavelet packet transforms are often used to sparsify dense matrices arising in the discretization of cem integral equations this paper compares orthogonal semi orthogonal and bi orthogonal wavelet and wavelet packet transforms with respect to the condition numbers matrix sparsity and number of iterations for the transformed systems the best overall results are obtained with the orthogonal wavelet packet transforms that produce highly sparse matrices requiring fewest iterations among wavelet transforms the semi orthogonal wavelet transforms lead to the sparsest matrices but require too many iterations due to high condition numbers the bi orthogonal wavelets produce very poor sparsity and require many iterations and should not be used in these applications

nonexistence of asymptotically free solutions for a nonlinear schrodinger equation let u be a nontrivial smooth solution to iut u u p 1u if n 1 and 2 p 3 then there does not exist any finite energy free solution v such that u t v t 2 0 as t this extends a theorem of strauss in which the same result was proved for 1 p 2

a closed form solution to the discrete time kalman filter and its applications abstract this paper presents a closed form solution to the discrete time kalman filter and its applications we first represent the kalman filter in terms of model parameters without using the riccati equation and requiring any artificial conditions such as invertibility of a system matrix and no system noises replacing the initial time with the fixed lag time to achieve the finite memory with respect to inputs and outputs and choosing the proper initial covariances on the recent finite horizon we easily obtain the minimum variance finite memory filter and then propose its iterative computation algorithm as another application a closed form solution to the difference riccati equation on the finite horizon is utilized to obtain a stabilizing gain matrix of a luenberger type filter as in ackermann s formula

an algorithm for pole assignment in high order multivariable systems an efficient computational method is presented for solving the problem of pole assignment by state feedback in linear multivariable systems with large dimensions a given multiinput system is first transformed to an upper block hessenberg form by means of orthogonal state coordinate transformations the state feedback problem is then reformulated in terms of the sylvester equation the transformed system matrices along with certain assumed block forms for unknown matrices enable the sylvester equation to be decomposed and solved effectively a distinct point of the proposed algorithm is that the solution procedure can be tailored to parallel implementation and is therefore fast computational aspects of the algorithm are discussed and numerical examples are provided

improved impedance matrix localization method em problems moment method calculations have the well known limitations of requiring excessive storage and execution times for even modestly large electromagnetics problems the impedance matrix localization iml method was introduced as a modification to standard moment method calculations to ease these limitations it utilizes a matrix transformation which effectively changes the basis testing functions into ones resembling traveling waves an improved method that uses an orthogonal transformation to generate standing wave like basis functions is presented here remarkable improvements are achieved in the numerical stability of the method and in its compatibility with iterative solvers furthermore the correspondence of the large elements in this matrix to geometrical theory of diffraction gtd terms is strengthened as is the possibility of further increasing the speed of iterative solutions by constructing preconditioners based on the pattern of nonzero matrix elements

eigenvalue assignment in a single input linear system a procedure for eigenvalue assignment in a single input linear system in hessenberg form is described the procedure uses real arithmetic throughout and includes a facility for estimating the robustness of the assigned eigenvalues the assigned eigenvalues may be real or complex simple or multiple

entropy based algorithms for best basis selection adapted waveform analysis uses a library of orthonormal bases and an efficiency functional to match a basis to a given signal or family of signals it permits efficient compression of a variety of signals such as sound and images the predefined libraries of modulated waveforms include orthogonal wavelet packets and localized trigonometric functions and have reasonably well controlled time frequency localization properties the idea is to build out of the library functions an orthonormal basis relative to which the given signal or collection of signals has the lowest information cost the method relies heavily on the remarkable orthogonality properties of the new libraries all expansions in a given library conserve energy and are thus comparable several cost functionals are useful one of the most attractive is shannon entropy which has a geometric interpretation in this context

on the use of spatio temporal multiresolution analysis in method of moments solutions of transient electromagnetic scattering a novel method of moments approach to the solution of time domain integral equation formulation of electromagnetic scattering problems is presented the method is based on a spatio temporal multiresolution analysis this analysis facilitates a basis from which a small number of expansion functions is selected via an iterative procedure and utilized to model the unknown current distribution in contrast to marching on in time sequential procedures the proposed method models the unknown current simultaneously at all the time steps within the time frame of interest this new method is applied to a one dimensional 1 d problem of electromagnetic plane wave interaction with a dielectric slab a comparison of the computed results with results based on the analytic solution demonstrates that the method is capable of attaining accurate results while achieving substantial reduction in computation time and resources

cauchy problem of nonlinear schrodinger equation with initial data in sobolev space w s p for p 2 in this paper we consider in r n the cauchy problem for the nonlinear schrodinger equation with initial data in the sobolev space w s p for p n 1 1 p moreover we show that in one space dimension the problem is locally well posed in l p for any 1 p 2

output deadbeat control discrete time multivariate systems an algorithm is presented to compute output deadbeat controls for linear multivariable systems the algorithm based on quadratic optimization with no cost on control cheap control is numerically stable and covers the most general cases the resulting controls are internally stable and are shown to drive the outputs of the system to zero in minimum time using state feedback the central part of the algorithm is the construction of the nonunique state cost matrix two alternatives are presented having different complexities and resulting in solutions having different properties

low regularity solutions for a 2d quadratic nonlinear schrodinger equation we establish that the initial value problem for the quadratic nonlinear schrodinger equation iu t u u 2 where u r 2 x r c is locally well posed in h s r 2 when s 1 the critical exponent for this problem is s c 1 and previous work by colliander delort kenig and staffilani 2001 established local well posedness for s 3 4

fast algorithms for discrete and continuous wavelet transforms several algorithms are reviewed for computing various types of wavelet transforms the mallat algorithm 1989 the a trous algorithm and their generalizations by shensa the goal of this work is to develop guidelines for implementing discrete and continuous wavelet transforms efficiently and to compare the various algorithms obtained and give an idea of possible gains by providing operation counts most wavelet transform algorithms compute sampled coefficients of the continuous wavelet transform using the filter bank structure of the discrete wavelet transform although this general method is already efficient it is shown that noticeable computational savings can be obtained by applying known fast convolution techniques such as the fft fast fourier transform in a suitable manner the modified algorithms are termed fast because of their ability to reduce the computational complexity per computed coefficient from l to log l within a small constant factor for large filter lengths l for short filters smaller gains are obtained fast running fir finite impulse response filtering techniques allow one to achieve typically 30 savings in computations

impedance matrix compression imc using iteratively selected wavelet basis we present a novel approach for the incorporation of wavelets into the solution of frequency domain integral equations arising in scattering problems in this approach we utilize the fact that when the basis functions used are wavelet type functions only a few terms in a series expansion are needed to represent the unknown quantity to determine these dominant expansion functions an iterative procedure is devised the new approach combined with the iterative procedure yields a new algorithm that has many advantages over the presently used methods for incorporating wavelets numerical results which illustrate the approach are presented for three scattering problems

approximate pole assignment a novel approach and some new algorithms for the pole assignment problem of a controllable time invariant linear multivariable system with linear state or output feedback are presented the main theme of the approach and the algorithms is to satisfy some constraints in the problem approximately various rank 1 update algorithms can then be derived depending on different extents to which the constraints are approximated functionals have to be minimized when eigenvectors of the closed loop system are chosen a perturbation analysis on the effect of the approximation and several numerical examples will be presented

sharp well posedness and ill posedness results for a quadratic non linear schrodinger equation abstract we establish that the quadratic non linear schrodinger equation iu t u xx u 2 where u r r c is locally well posed in h s r when s 1 and ill posed when s 1 previous work in c kenig g ponce l vega quadratic forms for the 1 d semilinear schrodinger equation trans amer math soc 346 1996 3323 3353 had established local well posedness for s 3 4 the local well posedness is achieved by an iteration using a modification of the standard x s b spaces the ill posedness uses an abstract and general argument relying on the high to low frequency cascade present in the non linearity and a computation of the first non linear iterate

boundary control of the linearized ginzburg landau model of vortex shedding in this paper we continue the development of state feedback boundary control laws based on the backstepping methodology for the stabilization of unstable parabolic partial differential equations we consider the linearized ginzburg landau equation which models for instance vortex shedding in bluff body flows asymptotic stabilization is achieved by means of boundary control via state feedback in the form of an integral operator the kernel of the operator is shown to be twice continuously differentiable and a series approximation for its solution is given under certain conditions on the parameters of the ginzburg landau equation compatible with vortex shedding modelling on a semi infinite domain the kernel is shown to have compact support resulting in partial state feedback simulations are provided in order to demonstrate the performance of the controller in summary the paper extends previous work in two ways 1 it deals with two coupled partial differential equations and 2 under certain circumstances handles equations defined on a semi infinite domain

on a class of predefined wavelet packet bases for efficient representation of electromagnetic integral equations a general wavelet packet tree is proposed to design predefined wavelet packet pwp bases for the efficient representation of electrodynamic integral equations the wavelet packet decomposition tree is constructed by zooming in along the spectral oscillatory frequency of the free space green s function numerical results show that for typical two dimensional 2 d scatterers the number of above threshold elements in the pwp based moment matrix is on the order of o n sup 1 3 and tends to grow at a rate of o n spl middot log n for large scale problems therefore the complexity of solving the moment equations can be reduced accordingly furthermore it is shown that the elements of the moment matrix based on the pwp bases can be computed directly at approximately the same complexity as the fast wavelet transform approach consequently with on the fly thresholding of the matrix elements the o n sup 2 memory bottleneck in the formation of the pwp based moment matrix can be circumvented

robust control with pole shifting via performance index modification robust controllers that ensure closed loop eigenvalue placement are designed for linear systems with parametric uncertainties by using an appropriate state weighting matrix choice and a relative stability degree an lmi based algorithm is proposed to provide guaranteed cost controllers that ensure i the closed loop nominal eigenvalues shifting by a pre specified amount ii a prescribed degree of stability for all system uncertainties of a given class a certain level of closed loop performance is also ensured by minimizing the associated guaranteed cost

fast solution of electromagnetic integral equations using adaptive wavelet packet transform the adaptive wavelet packet transform is applied to sparsify the moment matrices for the fast solution of electromagnetic integral equations in the algorithm a cost function is employed to adaptively select the optimal wavelet packet expansion testing functions to achieve the maximum sparsity possible in the resulting transformed system the search for the best wavelet packet basis and the moment matrix transformation are implemented by repeated two channel filtering of the original moment matrix with a pair of quadrature filters it is found that the sparsified matrix has above threshold elements that grow only as o n sup 1 4 for typical scatterers consequently the operations to solve the transformed moment equation using the conjugate gradient method scales as o n sup 1 4 the additional computational cost for carrying out the adaptive wavelet packet transform is evaluated and discussed

global feedback control for pattern forming systems global feedback control of pattern formation in a wide class of systems described by the swift hohenberg sh equation is investigated theoretically by means of stability analysis and numerical simulations two cases are considered i feedback control of the competition between hexagon and roll patterns described by a supercritical sh equation and ii the use of feedback control to suppress the blowup in a system described by a subcritical sh equation in case i it is shown that feedback control can change the hexagon and roll stability regions in the parameter space as well as cause a transition from up to down hexagons and stabilize a skewed mixed mode hexagonal pattern in case ii it is demonstrated that feedback control can suppress blowup and lead to the formation of spatially localized patterns in the weakly nonlinear regime the effects of a delayed feedback are also investigated for both cases and it is shown that delay can induce temporal oscillations as well as blowup

wavelet packets for fast solution of electromagnetic integral equations this paper considers the problem of wavelet sparsification of matrices arising in the numerical solution of electromagnetic integral equations by the method of moments scattering of plane waves from two dimensional 2 d cylinders is computed numerically using a constant number of test functions per wavelength discrete wavelet packet dwp similarity transformations and thresholding are applied to system matrices to obtain sparsity if thresholds are selected to keep the relative residual error constant the matrix sparsity is of order o n sup p with p 2 this stands in contrast with o n sup 2 sparsities obtained with standard wavelet transformations numerical tests also show that the dwp method yields faster matrix vector multiplication than some fast multipole algorithms

on the use of wavelet expansions in the method of moments em scattering an approach which incorporates the theory of wavelet transforms in method of moments solutions for electromagnetic wave interaction problems is presented the unknown field or response is expressed as a twofold summation of shifted and dilated forms of a properly chosen basis function which is often referred to as the mother wavelet the wavelet expansion can adaptively fit itself to the various length scales associated with the scatterer by distributing the localized functions near the discontinuities and the more spatially diffused ones over the smooth expanses of the scatterer the approach is thus best suited for the analysis of scatterers which contain a broad spectrum of length scales ranging from a subwavelength to several wavelengths using a galerkin method and subsequently applying a threshold procedure the moment method matrix is rendered sparsely populated the structure of the matrix reveals the localized scale fitting distribution long before the matrix equation is solved the performance of the proposed discretization scheme is illustrated by a numerical study of electromagnetic coupling through a double slot aperture

brief augmented gradient flows for on line robust pole assignment via state and output feedback this paper is concerned with robust pole assignment in synthesis of linear control systems via state and output feedbacks first both the pole assignment and robustness requirements are appropriately formulated as two optimization problems then gradient flow models are developed for the on line computation of feedback gain matrices that result in robust pole assignment by solving these two optimization problems a technique is introduced to facilitate the real time matrix inverse involved for realizing the gradient flow models the resulting augmented gradient flows have desired convergence properties simulation results are included to show the effectiveness of the proposed approach

new approach to robust observer design this paper shows that based on the recent development of observer design solution an observer pole selection method can be formulated to minimize the observer gain to the system input it is proved that this method is a deterministic approach to the recovery of the loop transfer function and robustness of direct state feedback systems

the generalized eigenstructure problem in linear system theory the algebraic theory of linear time invariant systems has been studied in large detail during the past few decades and numerous computational algorithms have been developed to solve problems arising in this context in this paper the numerical aspects of a certain class of such algorithms dealing with what the author calls generalized eigenstructure problems are discussed some new and or modified algorithms are presented both the nmnerical stability of the algorithms and the conditioning of the problems they solve are analyzed using numerical criteria

a new design approach to unknown input observers this paper proposes a fundamentally new unknown input observer uio which has uniquely r decoupled modes provides r linearly independent combinations of plant system states and has zero gain to all p unknown inputs the parameter r is adjustable if the plant system satisfies the conditions of the existing uio then r n plant system order and there is no difference between our uio and the existing regular uio however if the plant system satisfies either of the following two significantly more general conditions m p m is the number of plant output measurements and at least one stable transmission zero then 1 n and our uio can still generate some constrained state feedback control signals hence this new uio can completely unify the regular uio r n and the static output feedback r m the two basic feedback structures of modern control theory far from being unified before

optimal grouping of basis functions when using the method of moments to solve scattering problems a crucial factor is the appropriate choice of basis functions a judicious choice of the basis functions can lead to a sparse impedance matrix or to a sparse solution vector both of which will reduce the computational burden however pulse basis functions are usually used both due to their simple description and because there are already many software tools written for this aim therefore some efforts have been invested in transforming a formulation that is the result of using pulse basis functions to one using preferred basis functions this transform produces grouping of the pulse functions into a new more appropriate set of basis functions this paper discusses the search for an optimal grouping where optimality is measured in terms of the sparseness of the resulting solution vector various options are demonstrated and discussed and numerical examples are given it is important to note that the optimal grouping suggested herein is expected to be optimal on the average when tried on many sample problems adjusting the optimization to a more specific set of problems and scenarios will lead to even better performances and is a viable option in practical cases

some necessary and sufficient conditions for eigenstructure assignment abstract some necessary and sufficient conditions for closed loop eigenstructure assignment by output feedback in time invariant linear multivariable control systems are presented a simple condition on a square matrix necessary and sufficient for it to be the closed loop plant matrix of a given system with some output feedback is the basis of the paper some known results on entire eigenstructure assignment are deduced from this the concept of an inner inverse of a matrix is employed to obtain a condition concerning the assignment of an eigenstructure consisting of the eigenvalues and a mixture of left and right eigenvectors

a new approach for computing the state feedback gains of multivariable systems this note presents some new results in linear systems first the relationship between the polynomial matrix description and the state space representation of multivariable systems is clarified then we show that once such a relationship is determined the coprime matrix fraction description can be easily computed and we can further develop a closed form formula to solve the pole assignment problem of multivariable systems such formula can be thought of as an extension of the ackermann s formula for mimo systems thus this note potentially gives us a clearer insight into linear systems from the theoretical viewpoint

critical nonlinear schrodinger equations with data in homogeneous weighted l2 spaces abstract we consider the initial value problem for nonlinear schrodinger equations with the critical nonlinearities 1 u 2 n u where im 1 0 when the space dimension n 1 2 we prove the global existence of small solutions in homogeneous weighted l 2 r n spaces it is shown that the small solutions decay uniformly like t n 2 for t 1 if im 1 0 the higher uniform time decay rates t n 2 log t n 2 for t 1 are obtained if im 1 0

robust eigenvalue assignment for generalized systems abstract in this paper we examine the problem of robust pole placement using state feedback in generalized systems we develop a robustness theory for the finite generalized spectrum of the system as a partial problem and for the infinite pole placement problem as a second partial problem where perfect conditioning is always achievable we also give bounds between the complete closed loop robust eigenvalue problem and the two partial ones the basic tool that is exploited in the presented theory is the concept of chordal metric in this paper we take advantage of this notion and present a compact theory for the robust eigenvalue assignment problem in generalized systems the proposed theory is easy to implement retrieves the results for the state variable case as a special case and takes advantage of well known computational results

impedance matrix compression using adaptively constructed basis functions wavelet expansions have been employed recently in numerical solutions of commonly used frequency domain integral equations in this paper we propose a novel method for integrating wavelet based transforms into existing numerical solvers the newly proposed method differs from the presently used ones in two ways first the transformation is affected by means of a digital filtering approach this approach renders the transform algorithm adaptive and facilitates the derivation of a basis which best suits the problem at hand second the conventional thresholding procedure applied to the impedance matrix is substituted for by a compression process in which only the significant terms in the expansion of the yet unknown current are retained and subsequently derived numerical results for a few tm scattering problems are included to demonstrate the advantages of the proposed method over the presently used ones

nonlinear schrodinger systems in 2d with nondecaying final data abstract we consider nonlinear schrodinger systems with quadratic nonlinearities in two space dimensions we prove the existence of modified wave operators and uniform time decay of solutions when the fourier transform of the final data does not necessarily decay at spatial infinity and is small in uniform norm

robust pole assignment in linear state feedback numerical methods are described for determining robust or well conditioned solutions to the problem of pole assignment by state feedback the solutions obtained are such that the sensitivity of the assigned poles to perturbations in the system and gain matrices is minimized it is shown that for these solutions upper bounds on the norm of the feedback matrix and on the transient response are also minimized and a lower bound on the stability margin is maximized a measure is derived which indicates the optimal conditioning that may be expected for a particular system with a given set of closed loop poles and hence the suitability of the given poles for assignment

an algorithm for computing state feedback in multiinput linear systems a new algorithm is proposed in this note to compute the state feedback for arbitrary pole placement in multiinput linear systems the algorithm has good numerical behavior it also allows the user to adjust the eigenstructure of the resulting feedback system and therefore improve the condition of the problem and computation

the decay of stabilizability with reynolds number in a linear model of spatially developing flows this article characterizes the gradual decay of stabilizability with reynolds number in the linear complex ginzburg landau model of spatially developing ow systems when a single spatially localized actuator is used to apply the control forcing it is shown that technically the system considered is linearly stabilizable for all actuator locations at any reynolds number however as the reynolds number is increased and an increasing number of modes of the open loop system become unstable the control authority on some of these open loop unstable modes is found to be exponentially small using nite precision arithmetic and any given numerical method for computing the feedback gains an e ective upper bound on the reynolds number is reached above which it is not possible to compute a linearly stabilizing control

asymptotics for large time of solutions to the nonlinear schrodinger and hartree equations we study the asymptotic behavior in time of solutions to the cauchy problems for the nonlinear schrodinger equation with a critical power nonlinearity and the hartree equation we prove the existence of modified scattering states and the sharp time decay estimate in the uniform norm of solutions to the cauchy problem with small initial data this estimate is very important for the proof of the existence of modified scattering states to the nonlinear schrodinger equations with a critical nonlinearity and the hartree equation in order to derive the desired estimates we introduce a certain phase function since the previous methods based solely on a priori estimates of the operator x it acting on the solution without specifying any phase function do not work for the critical case under consideration the well known nonexistence of the usual l 2 scattering states shows that our result is sharp

effects of using observers on stabilization of uncertain linear systems the effects of observers on robust linear feedback controllers are studied sufficient conditions are obtained that guarantee full recovery of the allowable uncertainty bounds attainable by full state feedback the effects of the resulting high gain observers on the disturbance rejection bounds are also studied it is shown that full recovery of the uncertainty bound leads to possible large degradation in disturbance rejection however if there is only additive plant disturbance and no measurement disturbance this degradation can be prevented

adaptive multiscale moment method ammm for analysis of scattering from three dimensional perfectly conducting structures the adaptive multiscale moment method ammm is presented for the analysis of scattering from three dimensional 3d perfectly conducting bodies this algorithm employs the conventional moment method mm using the subsectional triangular patch basis functions and a special matrix transformation which is derived from solving the fredholm equation of the first kind by the multiscale technique this methodology is more suitable for problems where the matrix solution time is much greater than the matrix fill time the widely used triangular patch vector basis functions developed by rao et al 1982 are used for expansion and testing functions in the conventional mm the objective here is to compress the unknowns in existing mm codes which solves for the currents crossing the edges of the triangular patch basis functions by use of a matrix transformation the currents source terms and impedance matrix can be arranged in the form of different scales from one scale to another scale the initial guess for the solution can be predicted according to the properties of the multiscale technique ammm can reduce automatically the size of the linear equations so as to improve the efficiency of the conventional mm the basic difference between this methodology and the other wavelet based techniques that have been presented so far is that we apply the compression not to the impedance matrix but to the solution itself directly in an iterative fashion even though it is an unknown two numerical results are presented which demonstrate that the ammm is a useful method for analysis of electromagnetic scattering from arbitrary shaped 3d perfectly conducting bodies

robust pole assignment for synthesizing feedback control systems using recurrent neural networks this paper presents a neurodynamic optimization approach to robust pole assignment for synthesizing linear control systems via state and output feedback the problem is formulated as a pseudoconvex optimization problem with robustness measure i e the spectral condition number as the objective function and linear matrix equality constraints for exact pole assignment two coupled recurrent neural networks are applied for solving the formulated problem in real time in contrast to existing approaches the exponential convergence of the proposed neurodynamics to global optimal solutions can be guaranteed even with lower model complexity in terms of the number of variables simulation results of the proposed neurodynamic approach for 11 benchmark problems are reported to demonstrate its superiority

numerically robust pole assignment for second order systems we propose two new methods for solution of the eigenvalue assignment problem associated with the second order control system global hsize 30pc specifically the methods construct feedback matrices f 1 and f 2 such that the closed loop quadratic pencil has a desired set of eigenvalues and the associated eigenvectors are well conditioned method 1 is a modification of the singular value decomposition based method proposed by juang and maghami which is a second order adaptation of the well known robust eigenvalue assignment method by kautsky et al for first order systems method 2 is an extension of the recent non modal approach of datta and rincon for feedback stabilization of second order systems robustness to numerical round off errors is achieved by minimizing the condition numbers of the eigenvectors of the closed loop second order pencil control robustness to large plant uncertainty will not be explicitly considered in this paper numerical results for both the two methods are favourable a compara

analysis of truncated periodic array using two stage wavelet packet transformations for impedance matrix compression a novel method of moments procedure is applied to the problem of scattering by metallic truncated periodic arrays in such problems the induced current shows localized behavior within the unit cell and at the same time exhibits cell to cell periodicity in order to select a set of expansion functions that may account for such behavior a two stage basis transformation of which the first stage is an ordinary wavelet transformation performed independently on each unit cell has been applied to a pulse basis the resultant basis functions at the first stage are regrouped and retransformed to reveal the periodicity of their coefficients expansion functions are then iteratively selected from this newly constructed basis to form a compressed impedance matrix the compression ratios obtained in this manner are higher than the compression ratio achieved using a basis constructed via an ordinary single stage wavelet transformation where compression is the ratio between the number of nonzero elements in the matrix used to solve the problem and the number of elements in the original matrix an even higher compression is attained by considering in addition functions that reveal array end related features and iteratively selecting the expansion from an overcomplete dictionary

a schur method for pole assignment in this paper a new numerical algorithm for pole assignment of linear time invariant systems is presented the proposed algorithm uses reliable numerical techniques based on the schur form of the state matrix and on the use of orthogonal transformations only the bad eigenvalues of the system are modified by a sequential pole shifting procedure and the resulted gains in the feedback matrix are minimized

low regularity bilinear estimates for a quadratic nonlinear schrodinger equation abstract in this article we establish the bilinear estimates corresponding to the 1d and 2d nls with a quadratic nonlinearity c 1 u 2 c 2 u 2 which imply the local well posedness of the cauchy problem in h s for s 1 in the 1d case and for s 1 in the 2d case this is a continuation of our study n kishimoto local well posedness for the cauchy problem of the quadratic schrodinger equation with nonlinearity u 2 commun pure appl anal 7 2008 1123 1143 on the 1d nls with nonlinearity c u 2 previous papers by kenig ponce and vega and colliander delort kenig and staffilani established local well posedness for s 3 4 in 1d and in 2d respectively and when the nonlinearity is restricted to c u 2 papers by bejenaru and tao and bejenaru and de silva improved these results to s 1 in 1d and s 1 in 2d the bilinear estimate for 2d also yields an improvement on the growth rate of sobolev norms of finite energy global in time solutions to the 2d cubic nls

projection free approximate balanced truncation of large unstable systems in this article we show that the projection free snapshot based balanced truncation method can be applied directly to unstable systems we prove that even for unstable systems the unmodified balanced proper orthogonal decomposition algorithm theoretically yields a converged transformation that balances the gramians including the unstable subspace we then apply the method to a spatially developing unstable system and show that it results in reduced order models of similar quality to the ones obtained with existing methods due to the unbounded growth of unstable modes a practical restriction on the final impulse response simulation time appears which can be adjusted depending on the desired order of the reduced order model recommendations are given to further reduce the cost of the method if the system is large and to improve the performance of the method if it does not yield acceptable results in its unmodified form finally the method is applied to the linearized flow around a cylinder at re 100 to show that it actually is able to accurately reproduce impulse responses for more realistic unstable large scale systems in practice the well established approximate balanced truncation numerical framework therefore can be safely applied to unstable systems without any modifications additionally balanced reduced order models can readily be obtained even for large systems where the computational cost of existing methods is prohibitive

existence of solutions for schrodinger evolution equations we study the existence uniqueness and regularity of the solution of the initial value problem for the time dependent schrodinger equationi u t 1 2 u v t x u u 0 u0 we provide sufficient conditions onv t x such that the equation generates a unique unitary propagatoru t s and such thatu t s u0ec1 l2 c0 h2 n foru0eh2 n the conditions are general enough to accommodate moving singularities of type x 2 n 4 or x n 2 n 3

a unified closed loop stability measure for finite precision digital controller realizations implemented in different representation schemes a computationally tractable unified finite word length closed loop stability measure is derived which is applicable to fixed point floating point and block floating point representation schemes both the dynamic range and precision of an arithmetic scheme are considered in this new unified measure for each arithmetic scheme the optimal controller realization problem is defined and a numerical optimization approach is adopted to solve it numerical examples are used to illustrate the design procedure and to compare the optimal controller realizations in different representation schemes

scattering for solutions of a dissipative nonlinear schrodinger equation abstract in this study we consider the cauchy problem for a dissipative nonlinear schrodinger equation in particular we show that for any data which belong to the weighted lebesgue space f h with some 0 min n 2 1 the solutions to a dissipative nonlinear schrodinger equation with the nonlinear exponent 1 4 n 2 p 1 4 n behave like the free solutions in f h at time positive infinity the lower bound for p is less than the strauss exponent for some 0 min n 2 1 and if the critical case n 2 the lower bound is equal to 1 2 n the main idea of proof is based on an a priori estimate for solutions in f h of fractional order

an algorithm for pole assignment of time invariant linear systems an algorithm is suggested for the computation of a linear state feedback for a single input system such that the resultant closed loop system has specified eigenvalues the algorithm is more efficient than many comparable techniques and has some desirable numerical properties it is closely related to the qr algorithm for the eigenproblem and extends to descriptor systems