reachability indices of periodic positive systems via positive shift similarity the problem of the paper is the formulation of the concept of reachability indices of periodic linear positive systems a positive system is one in which the positive orthant is an invariant subset with respect to positive input signals the concept of shift similarity for periodic positive systems is defined and the associated cyclically augmented system is considered the results are the relation of the positive similarity of both representations the formulation of the reachability indices and a detailed example

a faffa mlfma algorithm for electromagnetic scattering based on the multilevel fast multipole algorithm mlfma an efficient method is proposed to accelerate the solution of the combined field integral equation in electromagnetic scattering and radiation where the fast far field approximation faffa is combined with mlfma the translation between groups in mlfma is expensive because spherical hankel functions and legendre polynomials are involved and the translator is defined on an eward sphere with many k spl circ directions when two groups are in the far field region however the translation can be greatly simplified by faffa where only a single k spl circ direction is involved in the translator the condition for using faffa and the way to efficiently incorporate faffa with mlfma are discussed complexity analysis illustrates that the computational cost in faffa mlfma can be asymptotically cut by half compared to the conventional mlfma numerical results are given to verify the efficiency of the algorithm

multilevel plane wave based near field far field transformation for electrically large antennas in free space or above material halfspace a recently presented fully probe corrected near field far field transformation employing plane wave expansion and diagonal translation operators enables near field far field transformation for arbitrary measurement contours and arbitrary antennas a multilevel extension inspired by the multilevel fast multipole method is presented that is suitable for the efficient transformation of electrically large antennas with a size of tens or even hundreds of wavelengths the measurement points are grouped in a multilevel fashion and translations are carried out to the box centers on the highest level only the plane waves are processed through the different levels to the measurement points using a disaggregation and anterpolation procedure resulting in a reduced overall complexity in the second part of this paper the influence of perfectly conducting ground planes and dielectric halfspaces as an approximation for ground effects in a real measurement setup is investigated as such ground reflected waves are assumed which propagate from the investigated antenna to the field probe and add to the direct wave contributions the far field conditions required for these assumptions are achieved by a source box grouping scheme by this extension ground effects are directly considered within the near field far field transformation transformation results using simulated and measured near field data are shown

eigenvalue assignment by minimal state feedback gain in lti multivariable systems in this article an improved method for eigenvalue assignment via state feedback in the linear time invariant multivariable systems is proposed this method is based on elementary similarity operations and involves mainly utilisation of vector companion forms and thus is very simple and easy to implement on a digital computer in addition to the controllable systems the proposed method can be applied for the stabilisable ones and also systems with linearly dependent inputs moreover two types of state feedback gain matrices can be achieved by this method 1 the numerical one which is unique and 2 the parametric one in which its parameters are determined in order to achieve a gain matrix with minimum frobenius norm the numerical examples are presented to demonstrate the advantages of the proposed method

numerical analysis of quasioptical multireflector antennas in 2 d with the method of discrete singularities e wave case numerical method for modeling the e polarized wave scattering by electrically large quasioptical two dimensional 2 d reflectors is presented reflectors are assumed zero thickness and perfectly electrically conducting efficient numerical solution is obtained from the coupled singular integral equations discretized using new quadrature formulas of interpolation type it has controlled accuracy and deals with small size matrices to simulate a small horn feeding the incident field is taken as a beam generated by a complex source point csp current presented numerical results validate empirical rule of 10 db edge illumination needed to provide the best electromagnetic performance of reflector

controllability observability and duality in singular systems the concepts of controllability and observability for systems of the form e dot x ax bu y cx e singular are considered a theory is presented which unifies the three main approaches to this topic already existing in the literature the development includes a generalization of the duality theorem from state space theory

a domain decomposition method for electromagnetic radiation and scattering analysis of multi target problems a domain decomposition method is presented for analyzing electromagnetic problems involving multiple separable scatterers the method first decomposes the original problem into several disjoint subregions in each subregion the domain decomposition method is further applied by decomposing the region into smaller possibly repeated subdomains the domain decomposition method is general enough for arbitrary geometries but is also capable of exploiting repetitions this renders geometrically complicated and electrically large subregion problems tractable the subregions communicate through the near field green s function to overcome the vast computational costs required in exchanging information between electrically large subregions the adaptive cross approximation algorithm is adopted to expedite the process the method is applied to study radiation characteristics of a reflector antenna system and an antenna array in the presence of a frequency selective surface to demonstrate the utility of the present approach

convergence of the sign algorithm for adaptive filtering with correlated data convergence of a decreasing gain sign algorithm sa for adaptive filtering is analyzed the presence of the hard limiter in the algorithm makes a rigorous analysis difficult therefore there are few results available such results normally include restrictive assumptions such as the assumptions that successive observation vectors are independent and the new error signal of the adaptive filter has a time invariant probability density function the former assumption is not valid in the context of adaptive filtering since two successive observation vectors share most of their components while the latter assumption is a restriction on the adaptive weights whose evolution is a priori unknown in lieu of using these assumptions an almost sure convergence of the sa is proved under the assumption that the sequence of observation vectors is m dependent this assumption allows strong correlation between successive observations

on a special case of model matching a special case of model matching a generalized version of the feedback simulation problem is considered and a necessary condition of its solvability is established this condition is also a new necessary and sufficient condition of solvability for the feedback simulation problem

feedback invariants of matrices with prescribed rows abstract let a f n n b f n m where f is an arbitrary field in this paper we solve the problem of the existence of the matrix a b when its feedback invariants and some rows are prescribed

reduced complexity hmm filtering with stochastic dominance bounds a convex optimization approach this paper uses stochastic dominance principles to construct upper and lower sample path bounds for hidden markov model hmm filters we consider an hmm consisting of an x state markov chain with transition matrix p by using convex optimization methods for nuclear norm minimization with copositive constraints we construct low rank stochastic matrices underline p and bar p so that the optimal filters using underline p bar p provably lower and upper bound with respect to a partially ordered set the true filtered distribution at each time instant since underline p and bar p are low rank say r the computational cost of evaluating the filtering bounds is o x r instead of o x 2 a monte carlo importance sampling filter is presented that exploits these upper and lower bounds to estimate the optimal posterior finally explicit bounds are given on the variational norm between the true posterior and the upper and lower bounds in terms of the dobrushin coefficient

on line blind multichannel equalization based on mutually referenced filters this paper presents a novel approach to the blind linear equalization of possibly nonminimum phase and time varying communication channels in the context of channel diversity we introduce the concept of mutually referenced equalizers mres in which several filters are considered the outputs of which act as training signals for each other a corresponding constrained multidimensional mean square error mse cost function is derived the minimization of which is shown to be a necessary and sufficient condition for equalization the links with a standard linear prediction problem are demonstrated the proposed technique exhibits properties of important practical concern 1 the proposed algorithm is globally convergent 2 simple closed form solutions exist for the mres but the mres also lend themselves readily to adaptive implementation in particular the recursive least squares rls algorithm can be used to offer optimal convergence rate 3 the mre method provides a solution for all equalization delays which results in robustness properties with respect to snr and ill defined channel lengths

assignment of complete structural properties of linear systems via sensor selection for x ax bu the problem of structural assignment via sensor selection is to find an output equation y cx du such that the resulting system a b c d has the pre specified structural properties such as the finite and infinite zero structures as well as the invertibility properties in this paper we establish a set of necessary and sufficient conditions under which a complete set of system structural properties can be assigned and an explicit algorithm for constructing the required matrix pair c d

feedback invariants of a pair of matrices with prescribed columns abstract this paper studies the possible feedback equivalence classes of a pair of matrices with some prescribed columns and related problems

convergence analysis of self adaptive equalizers a theoretical analysis of self adaptive equalization for data transmission is carried out starting from known convergence results for the corresponding trained adaptive filter the development relies on a suitable ergodicity model for the sequence of observations at the output of the transmission channel thanks to the boundedness of the decision function used for data recovery it can be proved that the algorithm is bounded strong convergence results can be reached when a perfect noiseless equalizer exists the algorithm will converge to it if the eye pattern is initially open otherwise convergence may take place towards certain other stationary points of the algorithm for which domains of attraction have been defined some of them will result in a poor error rate the case of a noisy channel exhibits limit points for the algorithm that differ from those of the classical trained algorithm the stronger the noise the greater the difference is one of the principal results of this study is the proof of the stability of the usual decision feedback algorithms once the learning period is over

a characterization of feedback equivalence this paper provides a new characterization of feedback equivalence that can be applied to controllable and noncontrollable matrix pairs a b this result is based on a generalization of a theorem of rosenbrock describing the closed loop invariant polynomials that are attainable by applying state feedback to a given system dot x ax bu

impulse controllability and observability of rectangular descriptor systems the presence of impulsive responses in descriptor systems and how it relates to impulse controllability and impulse observability is considered it is shown that the equivalence between impulse controllability observability and the existence of an impulse eliminating semistate feedback output injection gain although true for square descriptor systems does not hold for rectangular descriptor systems in general hence necessary and sufficient conditions for the existence of an impulse eliminating semistate feedback output injection gain are presented

controllability and hermite indices of matrix pairs given a pair of matrices a b we can associate to each nice basis of the controllability subspace of a b a set of integers to be called the indices of the basis each set provides partial information about the similarity class of a the relationship between several sets of indices as well as the constraints that they impose on the invariant factors of a are investigated special attention is paid to the controllability and hermite indices of a given pair a b

classification of pairs of linear mappings between two vector spaces and between their quotient space and subspace we classify pairs of linear mappings u v u u v in which u v are finite dimensional vector spaces over a field if and u are their subspaces c 2016 elsevier inc all rights re

efficient analysis of aperture antennas on generally shaped convex multilayered surfaces using a hybrid sd utd method a novel hybrid method is described for analyzing convex multilayered conformal array antennas the hybrid method is based on the spectral domain approach in combination with the ray based uniform theory of diffraction utd method the analysis is divided in two parts first the spectral domain approach is accelerated by using an asymptotic extraction technique where the extracted term of the green s function is calculated using utd it is shown that this new approach results in significant acceleration of the existing spectral domain algorithm without losing accuracy the modified spectral domain method is then used in the second part where generally shaped convex multilayered surfaces are analyzed by using sets of canonically shaped surfaces spheres and or circular cylinders their radii are obtained using the utd formulation which contains important information such as distance and curvature of the generally shaped surface along each geodesic the results obtained using the new algorithm are compared to the available results calculated and measured for different conformal antennas showing very good agreement

blind adaptive multiuser detection the decorrelating detector and the linear minimum mean square error mmse detector are known to be effective strategies to counter the presence of multiuser interference in code division multiple access channels in particular those multiuser detectors provide optimum near far resistance when training data sequences are available the mmse multiuser detector can be implemented adaptively without knowledge of signature waveforms or received amplitudes this paper introduces an adaptive multiuser detector which converges for any initialization to the mmse detector without requiring training sequences this blind multiuser detector requires no more knowledge than does the conventional single user receiver the desired user s signature waveform and its timing the proposed blind multiuser detector is made robust with respect to imprecise knowledge of the received signature waveform of the user of interest

constant solutions of polynomial equations abstract a necessary and sufficient condition is given for the equation ax by c in polynomial matrices to have a constant solution pair x y and also for x to be non singular a sufficient condition is then established under which the equation with a and b fixed has a constant solution for each c from a given class applications to the construction of static state feedback or static output injection in linear systems are discussed

bidirectional analytic ray tracing for fast computation of composite scattering from electric large target over a randomly rough surface the bidirectional analytic ray tracing bart method is developed to rapidly calculate composite scattering from three dimensional 3d electrically large complex targets above a randomly rough surface ray tracing is carried out both along the incident forward direction and converse direction of scattering backward recording different orders of ray illumination on each facet or edge of the target and surface once a pair of forward and backward rays meet on a facet edge a scattering term is constructed using the diffused scattering diffraction of this facet edge and all reflections occurred on the tracing paths the rough surface is modeled with ldquorough facetsrdquo including coherent scattering and diffused incoherent scattering which can be directly calculated according to the iem integral equation method of a randomly rough surface analytic tracing of polygon ray tubes is developed to precisely calculate the illumination and shadowing of facets which exempt large patches of the target from any finer meshing it significantly reduces the complexity relevant to the target electric size higher orders of scattering and in particular interactions between the target and rough surface are then taken into account the accuracy and performance of bart is validated and evaluated by comparing with exact computational electromagnetic methods for electrically small targets numerical examples of angularly composite scattering from a three dimensional electrically large e g a ship like target over a randomly rough surface are presented and discussed

fundamental theorem of state feedback for singular systems abstract the limits of state feedback in altering the dynamics of singular systems are studied a necessary and sufficient condition is given for a list of polynomials to be invariant polynomials of a proper system obtained by state feedback from the singular system the condition consists of inequalities which involve the controllability indices of the singular system and the degrees of the invariant polynomials the development is based on the properties of polynomial matrices a procedure is given for the calculation of a feedback gain which achieves the desired dynamics

linear systems with prescribed similarity structural invariants the problem of the existence of linear systems dot x t ax t bu t with prescribed structural invariants for system similarity is studied namely we solve the problem of the existence of such a system with prescribed controllability indices hermite indices and invariant factors when the invariant factors of a which are also invariants under system similarity are given

generalized hermite matrices and complete invariants of strict system equivalence a complete list of invariants for reachable system matrices sigma s left begin array 20 c p s q s v s w s end array right with respect to strict system equivalence s s e is determined by polynomial methods the polynomial input output pairs u y for which there exists a polynomial vector z such that pz qu and y vz wu form a k s module mu sigma it is shown that the unique basis matrix of mu sigma in hermite form yields a complete set of discrete hermite indices resp continuous invariants of s s e the hermite invariants are characterized in state space terms and a realization of sigma s in hermite canonical form is presented nice orders and generalized hermite forms are introduced in order to develop a framework that encompasses hermite invariants and kronecker invariants hermite s theorem is generalized to these matrices finally nice orders are used to single out unique representatives among all minimal bas

a hybrid febi mlfmm utd method for numerical solutions of electromagnetic problems including arbitrarily shaped and electrically large objects numerical solutions of electromagnetic scattering and radiation problems including arbitrarily shaped objects are obtained by solving integral equations with the method of moments mom fast and efficient solution of the integral equation with low computation and memory complexity is provided by the multilevel fast multipole method mlfmm the presence of electrically large conducting objects leads to hybrid mom techniques with high frequency methods for ray based high frequency methods no discretization of the electrically large objects is needed resulting into a more efficient numerical treatment of the problem however in order to retain low computation and memory complexity the high frequency fields must be taken into account in the matrix vector product computations in the various levels of the mlfmm in this contribution a ray based hybridization of the mlfmm with the uniform geometrical theory of diffraction utd is proposed within a hybrid finite element boundary integral febi technique using the combined field integral equation cfie resulting into a hybrid febi mlfmm utd method the hybridization is performed at the translation procedure on the various levels of the mlfmm using a far field approximation of the appropriate translation operator to obtain the high frequency incident fields at the critical points of the utd the formulation of this new hybrid technique is presented and numerical results are shown

analysis of mean square error and transient speed of the lms adaptive algorithm for the least mean square lms algorithm we analyze the correlation matrix of the filter coefficient estimation error and the signal estimation error in the transient phase as well as in steady state we establish the convergence of the second order statistics as the number of iterations increases and we derive the exact asymptotic expressions for the mean square errors in particular the result for the excess signal estimation error gives conditions under which the lms algorithm outperforms the wiener filter with the same number of taps we also analyze a new measure of transient speed we do not assume a linear regression model the desired signal and the data process are allowed to be nonlinearly related the data is assumed to be an instantaneous transformation of a stationary markov process satisfying certain ergodic conditions

on pole structure assignment in linear systems the problem of pole structure assignment psa by state feedback in implicit linear and uncontrollable systems is discussed in the article it is shown that the problem is solvable if the system is regularisable then necessary and sufficient conditions for characteristic polynomial assignment are established in the case of psa invariant polynomials assignment just necessary conditions have been obtained but it turns out that these conditions are also sufficient in some special cases this happens for example when the system does not possess any non proper controllability indexes a possible application of the achieved results to modelling a constrained movement of a robot arm is outlined too

interlacing inequalities and control theory abstract given a p by p matrix a we solve the problem of the existence of a p by q matrix b such that a b has prescribed controllability indices and i p a b has prescribed invariant polynomials the solution of this problem together with an earlier theorem of the author s is used to provide a new proof of the sa thompson interlacing inequalities for invariant polynomials

interlacing inequalities for regular pencils abstract we solve the problem of finding a necessary and sufficient condition for the existence of a regular pencil when its invariant homogeneous factors and a subpencil are prescribed the solution obtained is an extension of the well known sa thompson interlacing inequalities for invariant factors of characteristic matrices

a generalized state space for singular systems systems of the form e dot x ax bu y cx with e singular are studied of particular interest are the impulsive modes that may appear in the free response of such systems when arbitrary initial conditions are permitted modes that are associated with natural system frequencies at infinity a generalized definition of system order that incorporates these impulsive degrees of freedom is proposed and concepts of controllability and observability are defined for the impulsive modes allowable equivalence transformations of such singular systems are specified the present framework is shown to overcome several difficulties inherent in other treatments of singular systems and to extend in a natural and satisfying way many results previously known only for regular state space systems

eigenstructure assignment in linear descriptor systems given a linear controllable system ex spl dot fx gu we study the limits of linear proportional feedback u kx spl upsi in assigning a desired finite and infinite eigenstructure of the closed loop system ex spl dot f gk x g spl upsi the closed loop system is not restricted to be regular its rank makes part of the specifications necessary and sufficient conditions are established for the existence of a feedback gain k which assigns the desired eigenstructure and a procedure is outlined to calculate one such gain

a tutorial on the geometric analysis of linear time invariant implicit systems abstract a background of recent work in nonregular and regular implicit systems of the form e x ax bu is provided then the output nulling unknown input and composite subspaces are defined for singular systems with recursions given for their computation inner subspaces that is those in the domain of e and a are distinguished from outer subspaces those in the codomain of e and a the notions of composite preimage and composite image are introduced the result is a framework that unifies some of the recent work in the geometric theory of implicit systems system properties are discussed for both regular and nonregular systems and duality is investigated

feedback invariants via output injection abstract the feedback equivalence classes of matrix pairs a kc b kw obtained by output injection of matrix k on a system a b c w are completely characterized working on arbitrary fields some related problems are also solved

a polynomial approach to the invariant factors assignment problem via state feedback and output injection the characterization of the similarity classes of matrices a bf kc kwf obtained by state feedback and output injection on a system a b c w are revisited new more straighforward proofs are obtained the results hold working on arbitrary fields

structure and smith macmillan form of a rational matrix at infinity the use of special row and column operations in the reduction of a rational matrix to its smith macmillan form at infinity is investigated the connections between this reduction procedure and the valuation approach are established a graphical method for finding the smith macmillan form of a rational matrix at infinity from its bode magnitude array and some new results on realization theory for polynomial matrices are presented

interlacing and majorization in invariant factor assignment problems this paper shows some connections between pole assignment in control theory and assignment of invariant factors on matrices with some prescribed submatrices the majorization in the hardy littlewood polya sense and the interlacing inequalities for invariant factors play a fundamental role in the solution of some problems common to both theories

matrix pencils completion problems ii in this paper we give new simple and explicit necessary and sufficient conditions for the existence of a matrix pencil with prescribed kronecker invariants and a regular subpencil moreover we explicitly solve the problem of describing the possible kronecker invariants of a pencil with a prescribed subpencil in the case of the existence of an intermediate regular pencil all the results are obtained over algebraically closed fields

matrices with prescribed rows and invariant factors abstract in this paper we solve the problem of the existence of an n n matrix over an arbitrary field when its invariant polynomials and either some rows or columns are prescribed the solution is given in terms of invariant factor inequalities and of majorization inequalities involving controllability indices and the degrees of the invariant polynomials

equivalence of quadruples and feedback equivalence of related pairs in this paper we look for a generalization of a property of matrix pairs to quadruples of matrices it is known that it is possible to analyze the feedback equivalence of matrix pairs in terms of the similarity of the square matrices belonging to sets related to the pairs we will determine when it is possible to analyze the equivalence of matrix quadruples in terms of the feedback equivalence of matrix pairs

second order convergence analysis of stochastic adaptive linear filtering the convergence of an adaptive filtering vector is studied when it is governed by the mean square error gradient algorithm with constant step size we consider the mean square deviation between the optimal filter and the actual one during the steady state this quantity is known to be essentially proportional to the step size of the algorithm however previous analyses were either heuristic or based upon the assumption that successive observations were independent which is far from being realistic actually in most applications two successive observation vectors share a large number of components and thus they are strongly correlated in this work we deal with the case of correlated observations and prove that the mean square deviation is actually of the same order or less than the step size of the algorithm this result is proved without any boundedness or barrier assumption for the algorithm as it has been done previously in the literature to ensure the nondivergence our assumptions are reduced to the finite strong memory assumption and the finite moments assumption for the observation they are satisfied in a very wide class of practical applications

feedback invariants of restrictions a polynomial approach the possible feedback invariants of a linear time invariant dynamical system represented by a pair of matrices a b are studied when the only information about the system is that it has an a b invariant subspace s whose restriction is an autonomous system and the quotient is controllable this problem is shown to be related to the problem of designing a control matrix b 1 for a series connected system to have prescribed feedback invariants

stochastic approximation with correlated data new almost sure convergence results for a special form of the multidimensional robbins monro stochastic approximation procedure are developed the results are applicable to cases where the training data is heavily correlated no conditional expectation properties or boundedness assumptions are required to apply the new results for example when the data sequence is normal and i m dependent ii autoregressive moving average or iii band limited the results can be used to establish the almost sure convergence of each algorithm treated the special form of the robbins monro procedure considered is motivated by a consideration of several algorithms that have been proposed for discrete time adaptive signal processing applications most of these algorithms can also be viewed as stochastic gradient following algorithm the ease with which the new results can be applied is illustrated

on the regularizability of singular systems the property of regularity of singular systems is not a feedback invariant to correct this deficiency a new property of regularizability is defined and geometric tests are given for it in terms of system matrices regularizability is shown to be the natural extension of regularity which is a condition on the homogeneous system to controlled singular systems definitions of controllability and reachability are modified depending on regularizability rather than regularity a brief comparison of proportional and proportional plus derivative feedback laws in the context of making the closed loop system regular regular and reachable and regular and controllable is also given dynamical interpretations of these properties are also presented

feedback invariants of matrix quadruple completions abstract given a matrix quadruple a 1 a 2 a 3 a 4 f n 1 n 1 f n 2 n 1 f n 1 n 3 f n 2 n 3 we completely characterize the feedback invariants of the matrix pair a 1 x a 2 y a 3 a 4 for all possible selections of matrices x f n 1 n 2 and y f n 2 n 2

singular systems state feedback problem in this paper the problem of kronecker invariants assignment by state feedback in singular linear systems is studied and resolved this result presents a generalization of the previous results of state feedback action on singular systems

embedding a regular subpencil into a general linear pencil abstract we study the possible strictly equivalence classes of a pencil when a regular subpencil is prescribed we also study the possible invariant polynomials and the possible characteristic polynomials of a by xc xdy when x and y vary

a multisolver scheme based on robin transmission conditions for electromagnetic modeling of highly complex objects a multisolver scheme based on robin transmission conditions rtcs is proposed for electromagnetic modeling of highly complex objects different from the traditional finite element boundary integral fe bi method that applies bi equations to truncate the fe domain the proposed multisolver scheme employs both fe and bi equations to model an object along with its background to be specific the entire computational domain consisting of the object and its background is first decomposed into multiple nonoverlapping subdomains with each modeled by either an fe or bi equation the equations in the subdomains are then coupled into a multisolver system by enforcing the rtc at the subdomain interfaces finally the combined system is solved iteratively with the application of an extended preconditioner based on an absorbing boundary condition and the multilevel fast multipole algorithm to obtain an accurate solution both the rao wilton glisson and the buffa christiansen functions are employed as the testing functions to discretize the bi equations this scheme is applied to a variety of benchmark problems and the scattering from an aircraft with a launched missile to demonstrate its accuracy versatility and capability the proposed scheme is compared with the multisolver scheme based on combined field integral equations to illustrate the differences between the two schemes

hermite indices and the action of the feedback group the controllability indices are a complete system of invariants for the feedback equivalence relation of controllable matrix pairs the hermite indices are invariant for the similarity of matrix pairs but they are not invariant by changing bases on the input space and performing state feedback the aim of this work is to partially characterize the hermite indices of a controllable matrix pair when transformations of the feedback group are performed on it

on feedback equivalence and completion problems abstract in 1987 i zaballa characterized the possible similarity classes of a square matrix with some prescribed rows in 1988 the same author characterized the possible feedback equivalence classes of a b where a is a fixed square matrix and b varies firstly in this paper we observe that these results are equivalent that is each one of them can be obtained as a corollary of the other then we apply similar arguments to other inverse problems in particular we study the possible invariant polynomials and the possible characteristic polynomials of a bx yc when x and y vary and we study the linear systems that can become completely observable with a suitable choice of linear state feedback control

fully coupled hybrid fem utd method using nurbs for the analysis of radiation problems a novel hybrid finite element method fem uniform theory of diffraction utd method for the analysis of radiating structures in the presence of electrically large objects is presented the hybridization is done in a fully coupled way taking into account mutual interactions between the fem and utd regions the utd objects are modeled using non uniform rational b spline nurbs surfaces ray acceleration techniques and simple clustering strategies are used to speed up the computation time numerical results are presented showing the validity of the method

convergence of an adaptive linear estimation algorithm in this work we prove the almost sure convergence of an adaptive linear estimator governed by a stochastic gradient algorithm with decreasing step size in the presence of correlated observations two complementary contributions are added to the famous 1977 ljung theorem first we drop the condition of nondivergence of the algorithm assumed by ljung while that condition can be ensured by adding a barrier the convergence of the suitably bounded algorithm itself is not established even on the basis of ljung theorem here the barrier problem is overcome by proving that it is not necessary for the convergence our second contribution is to generalize the model describing the correlated observations no state space model is used and no linear relationship between the observations and the signal to be estimated needs to be assumed instead we use a decreasing covariance model that agrees with a very wide class of practical applications

assignment of infinite structure to an open loop system abstract given a controllable pair of matrices a b rosenbrock s theorem on assignment of open loop zeros states that a matrix c may be chosen so that the transfer function matrix g s c sin a 1b has prescribed zeros that is prescribed numerator polynomials in its mcmillan form in the same way rosenbrock s theorem on assignment of closed loop poles states that a matrix c may be chosen so that the mcmillan form of the transfer function matrix of the closed loop system has prescribed denominator polynomials following rosenbrock s ideas we can prove that given any pair of matrices a b matrices c and d may be chosen so that the transfer function matrix of the system g s d c sin a 1b has prescribed infinite structure

invariant factor assignment under state feedback and output injection for a given system a b c necessary and sufficient conditions are given to assign invariant factors to the matrix of the system performing a state feedback and an output injection over an arbitrary field

analysis of adaptive step size sa algorithms for parameter tracking we present proofs and data for adaptive step size algorithms for tracking time varying parameters when recursive stochastic approximation type algorithms are used a classical problem in adaptive control and communication theory concerns the tracking of the best fit of a given form when the statistics or the parameters change slowly a major and yet unresolved problem has been the choice of the step sizes in the tracking algorithm an algorithm for adapting the step size using the same system measurements which are used for the tracking was suggested by benveniste and various examples worked out by brossier the numerical results were very encouraging but proofs were lacking these proofs are supplied here together with supporting numerical data the proofs are based on recent results in stochastic approximation the adaptive step size technique works very well indeed much supporting analysis is presented particularly concerning the interpretation of certain stationary processes as stationary pathwise derivatives finite difference forms are also treated these are mathematically simpler and can be applied to a wide variety of systems even when the system is not well modeled the data shows that they work well

some geometric considerations about the kronecker normal form abstract in the first part of this paper we develop general algorithms from the kronecker normal form of any matrix pencil and give some of their properties in the second part these results are applied to the so called restricted matrix pencil associated with a given c a b system and introduced by jaffe and karcanias 1981 this allows us to make a link with well known algorithms of the geometric approach particularly the a b invariant subspace algorithm and the almost a b controllability subspace algorithm finally relationships between morse s invariants morse 1973 and the invariants of the restricted matrix pencil are exhibited

hybrid sup 2 combining the three dimensional hybrid finite element boundary integral technique for planar multilayered media with the uniform geometrical theory of diffraction the fully three dimensional 3 d hybrid finite element fe boundary integral bi technique is extended by further hybridization with the uniform geometrical theory of diffraction utd resulting in a so called hybrid sup 2 fe bi utd approach the formulation is capable of modeling arbitrarily shaped strongly inhomogeneous objects together with electrically large obstacles of relatively simple shape within the common environment of a planar multilayered medium the arbitrarily shaped inhomogeneous objects are discretized by finite elements whereas the electrically large obstacles are described by the utd and both of these models are included into an integral equation derived from the equivalence principle for planar multilayered media thus full electromagnetic coupling is realized between all parts of the formulation the integral equation is implemented using mixed potentials with appropriate green s functions derived from sommerfeld integral representations for planar multilayered media the utd contributions are accounted for by corresponding modifications of the green s functions and the fe technique is coupled to the integral equation via introduction of equivalent surface current densities in the bounding surfaces of the discretized objects after presenting the formulation of this novel fully 3 d hybrid sup 2 technique the implemented computer code is validated against conventional hybrid fe bi computations and a wireless base station antenna is analyzed in several situations of complex real world microcell environments

weak convergence and asymptotic properties of adaptive filters with constant gains the basic adaptive filtering algorithm x n 1 epsilon x n epsilon epsilon y n y n x n epsilon psi n is analyzed using the theory of weak convergence apart from some very special cases the analysis is hard when done for each fixed epsilon 0 but the weak convergence techniques are set up to provide much information for small epsilon the relevant facts from the theory are given define x epsilon cdot by x epsilon t x n epsilon on n epsilon n epsilon epsilon then weak distributional convergence of x epsilon cdot and of x epsilon cdot t epsilon is proved under very weak assumptions where t epsilon rightarrow infty as epsilon rightarrow 0 the normalized errors x n epsilon theta sqrt epsilon are analyzed where theta is a stable point for the mean algorithm the asymptotic properties of a projection algorithm are developed where the x n epsilon are truncated at each iteration if they fall outside of a given set

performance analysis of general tracking algorithms a general family of tracking algorithms for linear regression models is studied it includes the familiar least mean square gradient approach recursive least squares and kalman filter based estimators the exact expressions for the quality of the obtained estimates are complicated approximate and easy to use expressions for the covariance matrix of the parameter tracking error are developed these are applicable over the whole time interval including the transient and the approximation error can be explicitly calculated

unified theorems on completions of matrix pencils abstract we generalize and unify some theorems concerned with the existence of a pencil with a prescribed subpencil and prescribed strict equivalence class

reachability and controllability indices for linear descriptor systems abstract it is now well understood that reachability and controllability are different properties of descriptor systems these properties can be studied through some lists of integers namely the reachability and controllability indices the aim of this note is to recall the geometric definition and to give two polynomial characterizations of these indices

continuous time tracking algorithms involving two time scale markov chains this work is concerned with least mean squares lms algorithms in continuous time for tracking a time varying parameter process a distinctive feature is that the true parameter process is changing at a fast pace driven by a finite state markov chain the states of the markov chain are divisible into a number of groups within each group the transitions take place rapidly among different groups the transitions are infrequent introducing a small parameter into the generator of the markov chain leads to a two time scale formulation the tracking objective is difficult to achieve nevertheless a limit result is derived yielding algorithms for limit systems moreover the rates of variation of the tracking error sequence are analyzed under simple conditions it is shown that a scaled sequence of the tracking errors converges weakly to a switching diffusion in addition a numerical example is provided and an adaptive step size algorithm developed

a diagonalized multilevel fast multipole method with spherical harmonics expansion of the k space integrals diagonalization of the fast multipole method fmm for the helmholtz equation is usually achieved by expanding the multipole representation in propagating plane waves the resulting k space integral over the ewald sphere is numerically evaluated storing the k space quadrature samples of the method of moments mom basis functions constitutes a large portion of the overall memory requirements of the resulting algorithm for solving the integral equations of scattering and radiation problems in this paper it is proposed to expand the k space representation of the basis functions by spherical harmonics in order to reduce the sampling redundancy introduced by numerical quadrature rules aggregations plane wave translations and disaggregations in the realized multilevel fast multipole method mlfmm are carried out using the k space samples of a numerical quadrature rule however the incoming plane waves on the finest mlfmm level are expanded in spherical harmonics again thus due to the orthonormality of spherical harmonics the testing integrals for the individual testing functions are simplified into series over products of spherical harmonics expansion coefficients overall the resulting mlfmm can save a considerable amount of memory without compromising accuracy and numerical speed

similarity and block similarity we present some equivalent characterizations of the block similarity of matrix pairs with an application to a characterization of the similarity of two square matrices also a survey of some generalizations of properties of the invariants of similarity to the invariants of block similarity is presented