pole placement by parametric output feedback abstract this note presents a new analytical solution to the problem of pole placement via constant output feedback under the condition m p n where n m and p are the number of states inputs and outputs respectively the approach is based upon parametric eigenstructure assignment of linear time invariant multivariable systems in combination with a special explicit formulation of the pole assignment equations thus the resulting analytical solution explicitly offers all remaining m p n degrees of freedom beyond eigenvalue assignment which can be used for additional design goals such as response shaping minimizing the norm of the feedback matrix and robust control respectively

a general weighted median filter structure admitting negative weights weighted median smoothers which were introduced by edgemore in the context of least absolute regression over 100 years ago have received considerable attention in signal processing during the past two decades although weighted median smoothers offer advantages over traditional linear finite impulse response fir filters it is shown in this paper that they lack the flexibility to adequately address a number of signal processing problems in fact weighted median smoothers are analogous to normalized fir linear filters constrained to have only positive weights it is also shown that much like the mean is generalized to the rich class of linear fir filters the median can be generalized to a richer class of filters admitting positive and negative weights the generalization follows naturally and is surprisingly simple in order to analyze and design this class of filters a new threshold decomposition theory admitting real valued input signals is developed the new threshold decomposition framework is then used to develop fast adaptive algorithms to optimally design the real valued filter coefficients the new weighted median filter formulation leads to significantly more powerful estimators capable of effectively addressing a number of fundamental problems in signal processing that could not adequately be addressed by prior weighted median smoother structures

survey paper static output feedback a survey this paper reviews the static output feedback problem in the control of linear time invariant lti systems it includes analytical and computational methods and presents in a unified fashion the knowledge gained in the decades of research into this important open problem the paper shows that although many approaches and techniques exist to approach different versions of the problem no efficient algorithmic solutions are available

robustness of dynamic output feedback control for singular perturbation systems abstract the problem of the robustness of dynamic output feedback control for singular perturbation systems is investigated the solution to this problem is reduced to the simultaneous design of static output feedback controllers for the fast subsystem and the so called auxiliary system of the slow subsystem some conditions are proposed to ensure the robustness of the actual closed loop system the exact upper bound of the parasitic parameter for the controlled system is also determined finally an actual model which failed in dynamic output feedback control in 4 is reexamined successfully here

robust frequency selective filtering using weighted myriad filters admitting real valued weights weighted myriad smoothers have been proposed as a class of nonlinear filters for robust non gaussian signal processing in impulsive noise environments however weighted myriad smoothers are severely limited since their weights are restricted to be non negative this constraint makes them unusable in bandpass or highpass filtering applications that require negative filter weights further they are incapable of amplifying selected frequency components of an input signal in this paper we generalize the weighted myriad smoother to a richer structure a weighted myriad filter admitting real valued weights this involves assigning a pair of filter weights one positive and the other negative to each of the input samples equivalently the filter can be described as a weighted myriad smoother applied to a transformed set of samples that includes the original input samples as well as their negatives the weighted myriad filter is analogous to a normalized linear fir filter with real valued weights whose absolute values sum to unity by suitably scaling the output of the weighted myriad filter we extend it to yield the so called scaled weighted myriad filter which includes but is more powerful than the traditional unconstrained linear fir filter finally we derive stochastic gradient based nonlinear adaptive algorithms for the optimization of these novel myriad filters under the mean square error criterion

a new interpretation of the fault detection filter part 1 closed form algorithm a novel interpretation is presented of the detection filter in the context of an eigenstructure assignment problem the detection filter is shown to be equivalent to the combination of two decoupled observers with the advantage that theories already developed for conventional observers can be utilized as design aids detection space and detection order are re defined accordingly and it is shown that of the two observers that constitute a detection filter the one associated with the detection space is a single output system this fact is important since it explains important properties of the fault detection filter in a very uncomplicated fashion leading to a clear interpretation of the freedom available in designing the filter in particular it is proven that the detection filter gains are unique given the eigenvalues of the detection space further the formulation leads to a closed form expression for the detection filter and is therefore well suited to the development of simple design algorithms

functional calculus for the ornstein uhlenbeck operator let be the gauss measure on rd and l the ornstein uhlenbeck operator which is self adjoint in l2 for every p in 1 p 2 set p arc sin 2 p 1 and consider the sector s p z c arg z p the main result of this paper is that if m is a bounded holomorphic function on s p whose boundary values on s p satisfy suitable hormander type conditions then the spectral operator m l extends to a bounded operator on lp and hence on lq for all q such that 1 q 1 2 1 p 1 2 the result is sharp in the sense that l does not admit a bounded holomorphic functional calculus in a sector smaller than s p

systems of coupled generalized sylvester matrix equations this paper studies some systems of coupled generalized sylvester matrix equations we present some necessary and sufficient conditions for the solvability to these systems we give the expressions of the general solutions to the systems when their solvability conditions are satisfied

eigenvalue generalized eigenvector assignment by output feedback this note generalizes the previous results of the closed loop eigenstructure assignment via output feedback in linear multivariable systems necessary and sufficient conditions for the closed loop eigenstructure assignment by output feedback are presented some known results on entire eigenstructure assignment are deduced from this result

adaptive weighted myriad filter algorithms for robust signal processing in spl alpha stable noise environments stochastic gradient based adaptive algorithms are developed for the optimization of weighted myriad filters wmyfs wmyfs form a class of nonlinear filters motivated by the properties of spl alpha stable distributions that have been proposed for robust non gaussian signal processing in impulsive noise environments the weighted myriad for an n long data window is described by a set of nonnegative weights w sub i sub i l sup n and the so called linearity parameter k 0 in the limit as k spl rarr spl infin the filter reduces to the familiar weighted mean filter which is a constrained linear fir filter necessary conditions are obtained for optimality of the filter weights under the mean absolute error criterion an implicit formulation of the filter output is used to find an expression for the gradient of the cost function using instantaneous gradient estimates an adaptive steepest descent algorithm is then derived to optimize the weights this algorithm involves a very simple update term that is computationally comparable to the update in the classical lms algorithm the robust performance of this adaptive algorithm is demonstrated through a computer simulation example involving lowpass filtering of a one dimensional chirp type signal in impulsive noise

the boundedness of riesz transforms for hermite expansions on the hardy spaces abstract let l x 2 be a hermite operator where is the laplacian on r d in this paper we first characterize the hardy spaces h l 1 r d associated with l by a new version of area integral then we use it to prove the boundedness of riesz transforms r j l j 1 2 for l on h l 1 r d moreover we characterize the hardy space h l 1 r d by r j l this gives a negative answer to a question asked by thangavelu

eigenstructure assignment for descriptor systems by output feedback compensation abstract a method for output feedback compensator design that assigns the eigenstructure of a descriptor system is presented the adopted approach is based on transforming the problem into that of eigenstructure assignment for a linear state space system using output feedback

optimal weighted median filtering under structural constraints a new expression for the output moments of weighted median filtered data is derived the noise attenuation capability of a weighted median filter can now be assessed using the l vector and m vector parameters in the new expression the second major contribution of the paper is the development of a new optimality theory for weighted median filters this theory is based on the new expression for the output moments and combines the noise attenuation and some structural constraints on the filter s behavior in certain special cases the optimal weighted median filter can be obtained by merely solving a set of linear inequalities this leads in some cases to closed form solutions for optimal weighted median filters some applications of the theory developed in this paper in 1 d signal processing and image processing are discussed throughout the analysis some striking similarities are pointed out between linear fir filters and weighted median filters

γ radonifying operators and umd valued littlewood paley stein functions in the hermite setting on bmo and hardy spaces abstract in this paper we study littlewood paley stein functions associated with the poisson semigroup for the hermite operator on functions with values in a umd banach space b if we denote by h the hilbert space l 2 0 d t t h b represents the space of radonifying operators from h into b we prove that the hermite square function defines bounded operators from bmo l r n b respectively h l 1 r n b into bmo l r n h b respectively h l 1 r n h b where bmo l and h l 1 denote bmo and hardy spaces in the hermite setting also we obtain equivalent norms in bmo l r n b and h l 1 r n b by using littlewood paley stein functions as a consequence of our results we establish new characterizations of the umd banach spaces

parametric compensator design a parametrization of dynamical output feedback compensators that will assign a complete set of distinct eigenvalues to a given state space system is presented the main result is a compact parametric expression for the gain matrices of an output feedback compensator of dynamical order i n m r explicitly characterized by two sets of free parameters the set of n l closed loop system eigenvalues and a set of n mr n m r 1 effective free parameters for n state r input m output systems these latter n effective free parameters are determined by a sequential design procedure the principal benefits of the explicit characterization of a parametric class of dynamical output feedback compensators lie in the ability to directly accommodate various different design criteria

an addendum to output feedback eigenstructure assignment retro assignment this addendum paper presents additional material on an output feedback eigenstructure assignment approach derived in clarke et al 2003 there a two stage process is followed in which a subset of the desired eigenvectors is assigned in the first stage followed by a dual set in the second stage depending upon the number of available degrees of freedom and the manner in which they are distributed between the stages it is possible that not all are used a technique to recover these unused degrees of freedom in a final and independent stage is presented here the technique known as retro assignment is illustrated using an extension to the original numerical example

closed form solutions to the nonhomogeneous yakubovich transpose matrix equation abstract the nonhomogeneous yakubovich transpose matrix equation x a x t b c y r which contains the well known kalman yakubovich transpose matrix equation and general discrete lyapunov transpose matrix equation as special cases has many important applications in control system theory this study presents two methods to obtain the closed form solutions of the nonhomogeneous yakubovich transpose matrix equation moreover the equivalent forms of the solutions are provided and one of the solutions is established with the controllability matrix the observability matrix and symmetric operator matrix

parametric eigenstructure assignment by output feedback control the case of multiple eigenvalues this paper deals with closed loop eigenstructure assignment by output feedback control in linear multivariable systems for the general case of multiple eigenvalues the approach is algebraic in nature and operates directly on the closed loop characteristic equation using fundamental properties of determinants and their derivatives a compact form for the controller gain matrix is derived and expressed in terms of a set of parameter vectors that specify the non uniqueness of the solution of the eigenvalue assignment problem some of these parameter vectors assume restricted forms while others are free a computational scheme is given in which the free parameter vectors are determined in such a way as to assign the corresponding eigenvectors and generalized eigenvectors in a weighted least square error sense an illustrative numerical example is included

fractional square functions and potential spaces abstract carlos segovia and richard wheeden defined fractional square functions involving fractional derivatives they obtained characterizations of potential spaces via square functions our aim in this paper is to reconsider the ideas of segovia and wheeden under the light of the semigroups of operators we develop a quite general theory of fractional square functions associated to certain classes of operators we present some examples of differential operators where our theory applies we recover in a more compact way the results of segovia and wheeden and we obtain new characterizations of the potential spaces associated to the harmonic oscillator and ornstein uhlenbeck operators

hardy sobolev spaces associated with hermite expansions and interpolation abstract let a x 2 be a hermite operator where is the laplacian on r d in this paper we first define the hardy sobolev spaces associated with hermite expansions then we give the atomic decomposition and the real interpolation with sobolev spaces as an application we consider the endpoint version of the div curl theorem for the hermite operator

bmo spaces related to schrodinger operators with potentials satisfying a reverse holder inequality we identify the dual space of the hardy type space related to the time independent schrodinger operator v with v a potential satisfying a reverse holder inequality as a bmo type space we prove the boundedness in this space of the versions of some classical operators associated to hardy littlewood semigroup and poisson maximal functions square function fractional integral operator we also get a characterization of in terms of carlesson measures

an iterative algorithm for the least frobenius norm least squares solution of a class of generalized coupled sylvester transpose linear matrix equations abstract the iterative algorithm of a class of generalized coupled sylvester transpose matrix equations is presented we prove that if the system is consistent a solution can be obtained within finite iterative steps in the absence of round off errors for any initial matrices if the system is inconsistent the least squares solution can be obtained within finite iterative steps in the absence of round off errors furthermore we provide a method for choosing the initial matrices to obtain the least frobenius norm least squares solution of the problem finally numerical examples are presented to demonstrate that the algorithm is efficient

chaotic behavior of the riesz transforms for hermite expansions we prove a characterization for hypercyclic and chaotic unbounded unilateral weighted shifts of order p as applications we obtain that the natural derivatives associated to hermite expansions are chaotic on the other hand the corresponding riesz transforms are not hypercyclic and even more they are a kind of border line operator which separates the chaotic behavior

pole placement and compensator design of generalized systems abstract the system considered is a generalized system e ax bu y cx with matrix e singular when the impulsive modes of the system are both controllable and observable it is shown in this paper that these modes can be eliminated by almost any constant output feedback for a strongly controllable and observable generalized system after its impulsive modes are eliminated the poles of the system can be assigned arbitrarily by state feedback even if the states are not available the paper adopts an efficient method to design a compensator for the system

eigenstructure assignment by decentralized output feedback a complete parametric approach the problem of eigenstructure assignment in multivariable linear systems by decentralized output feedback is considered by using a complete parametric solution of a generalized sylvester matrix equation parametric representations of both the left and right closed loop eigenvectors and generalized eigenvectors as well as the feedback gains with respect to the closed loop eigenvalues and two series of partially free parameter vectors are established the obtained result does not require any conditions on the closed loop eigenvalues and generalizes some previous results in this area an example shows the effect of the proposed approach

on characterization of poisson integrals of schrodinger operators with bmo traces abstract let l be a schrodinger operator of the form l v acting on l 2 r n where the nonnegative potential v belongs to the reverse holder class b q for some q n let bmo l r n denote the bmo space on r n associated to the schrodinger operator l in this article we will show that a function f bmo l r n is the trace of the solution of l u u t t l u 0 u x 0 f x where u satisfies a carleson condition sup x b r b r b n 0 r b b x b r b t u x t 2 d x d t c conversely this carleson condition characterizes all the l harmonic functions whose traces belong to the space bmo l r n this result extends the analogous characterization founded by fabes johnson and neri in 13 for the classical bmo space of john and nirenberg

transmission zero assignment using semistate descriptions the problem of finite infinite transmission zero assignment is examined by squaring a system from the outputs to the inputs in particular this problem is studied in two cases state accessible systems and partially state accessible systems it is shown that the problem of transmission zero assignment for state accessible state variable systems is equivalent to a pole placement problem with state feedback for a generalized system which always has a solution in the case of partially state accessible systems it is shown that the transmission zero assignment problem is equivalent to a pole placement problem with output feedback for a generalized system in both cases the block hessenberg form of the system and the extended lower triangular hessenberg form are exploited to formulate the problem

a simultaneous decomposition for seven matrices with applications abstract let h m n be the set of all m n matrices over the quaternion algebra h in this paper we construct a simultaneous decomposition for seven matrices with compatible sizes a h m n b h m p 1 c h m p 2 d h m p 3 e h q 1 n f h q 2 n and g h q 3 n as applications of the simultaneous matrix decomposition we give some solvability conditions general solutions as well as the range of ranks of the general solutions to the following two generalized sylvester matrix equations b x e c y f d z g a and b x w e c y f d z g a where a b c d e f and g are given quaternion matrices moreover we provide some numerical examples to illustrate the results of this paper

a sharp weighted transplantation theorem for laguerre function expansions abstract we find the sharp range of boundedness for transplantation operators associated with laguerre function expansions in l p spaces with power weights namely the operators interchanging l k and l k are bounded in l p y p if and only if 2 1 p 1 1 p 2 where min this improves a previous partial result by stempak and trebels which was only sharp for 0 our approach is based on new multiplier estimates for hermite expansions weighted inequalities for local singular integrals and a careful analysis of kanjin s original proof of the unweighted case as a consequence we obtain new results on multipliers riesz transforms and g functions for laguerre expansions in l p y p

bounded influence propagation tau estimation a new robust method for arma model estimation a new robust and statistically efficient estimator for arma models called the bounded influence propagation estimator is proposed the estimator incorporates an auxiliary model which prevents the propagation of outliers strong consistency and asymptotic normality of the estimator for arma models that are driven by independently and identically distributed iid innovations with symmetric distributions are established to analyze the infinitesimal effect of outliers on the estimator the influence function is derived and computed explicitly for an ar 1 model with additive outliers to obtain estimates for the ar p model a robust durbin levinson type and a forward backward algorithm are proposed an iterative algorithm to robustly obtain arma p q parameter estimates is also presented the problem of finding a robust initialization is addressed which for orders p q 2 is a nontrivial matter numerical experiments are conducted to compare the finite sample performance of the proposed estimator to existing robust methodologies for different types of outliers both in terms of average and of worst case performance as measured by the maximum bias curve to illustrate the practical applicability of the proposed estimator a real data example of outlier cleaning for r r interval plots derived from electrocardiographic data is considered the proposed estimator is not limited to biomedical applications but is also useful in any real world problem whose observations can be modeled as an arma process disturbed by outliers or impulsive noise

on the robustness of the class of stack filters a widely held view in the nonlinear signal processing community is that the class of stack filters is robust although this is supported by extensive experimental evidence no systematic theoretical justification exists despite the availability of analytical tools for studying robustness of individual stack filters we focus on rank selection probabilities rsps as measures of robustness as it is well known that other statistical characterizations of stack filters such as output distributions breakdown probabilities and output distributional influence functions can be represented in terms of rsps we show in a very general sense that the class of stack filters is highly robust it is also shown that almost all stack filters have very similar output distributions for independent and identically distributed i i d input signals and thus very similar statistical behavior

a new solution to the generalized sylvester matrix equation av evf bw abstract this note deals with the problem of solving the generalized sylvester matrix equation av evf bw with f being an arbitrary matrix and provides complete general parametric expressions for the matrices v and w satisfying this equation the primary feature of this solution is that the matrix f does not need to be in any canonical form and may be even unknown a priori the results provide great convenience to the computation and analysis of the solutions to this class of equations and can perform important functions in many analysis and design problems in control systems theory

controllability of descriptor systems different concepts of controllability for descriptor systems ex ax bu have been proposed and investigated in this paper their relationship their interpretation in terms of the kronecker canonical form of e a and the implications in terms of pole assignment regularity and robustness of the closed loop system are discussed

on eigenstructure assignment in linear multivariable systems the eigenvalue assignment approach of brogan 1 2 is generalized and extended to the assignment of the entire closed loop eigenstructure of linear multivariable systems the set of assignable eigenvectors and generalized eigenvectors emerges naturally in the solution and is given moreover in an explicit parametric form two numerical examples are worked out to demonstrate the application of the procedure

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

parametric output feedback control with response insensitivity a recent parameterization of the class of linear output feedback controllers that assign a set of desired self conjugate eigenvalues to the closed loop system is used to formulate and solve a fundamental response insensitivity problem it is established to what extent output feedback control can be used to render the closed loop system response insensitive to possibly many not necessarily small parameter variations in the open loop state space model a non conservative sequential design procedure is developed for making as many of the closed loop system eigenmodes as possible totally insensitive while retaining arbitrary assignment of the maximum number of closed loop eigenvalues the main result is a class of desensitizing fixed gain output feedback controllers explicitly specified by a set of free parameters which may be chosen to satisfy additional design requirements conditions are given for total modal decoupling insensitivity to possibly many not necessarily small parameter variations in the open l

conical square functions associated with bessel laguerre and schrodinger operators in umd banach spaces abstract in this paper we consider conical square functions in the bessel laguerre and schrodinger settings where the functions take values in umd banach spaces following a recent paper of hytonen van neerven and portal 36 in order to define our conical square functions we use radonifying operators we obtain new equivalent norms in the lebesgue bochner spaces l p 0 b and l p r n b 1 p in terms of our square functions provided that b is a umd banach space our results can be seen as banach valued versions of known scalar results for square functions

closed form solutions to sylvester conjugate matrix equations some explicit closed form solutions of homogeneous and nonhomogeneous sylvester conjugate matrix equations are provided in this paper one of the solutions is expressed in terms of controllability matrices and observability matrices the proposed approach does not require all the coefficient matrices to be in any canonical forms and the solutions provide a significant degree of freedom which is represented by an arbitrarily chosen parameter matrix by specifying the solutions of the homogeneous sylvester conjugate equation some new expressions of the solutions of the normal sylvester normal sylvester conjugate and sylvester equations are given this fact reveals that the sylveter conjugate matrix equations are a more general class of some previously investigated matrix equations

optimality of the myriad filter in practical impulsive noise environments linear filtering theory has been largely motivated by the characteristics of gaussian signals in the same manner the proposed myriad filtering methods are motivated by the need for a flexible filter class with high statistical efficiency in non gaussian impulsive environments that can appear in practice we introduce several important properties of the myriad filter and prove its optimality in the family of spl alpha stable distributions

adaptive l_p norm spectrum sensing for cognitive radio networks in cognitive radio cr systems reliable spectrum sensing techniques are required in order to avoid interference to the primary users of the spectrum whereas most of the existing literature on spectrum sensing considers impairment by additive white gaussian noise awgn only in practice crs also have to cope with various types of non gaussian noise such as man made impulsive noise co channel interference and ultra wideband interference in this paper we propose an adaptive lp norm detector which does not require any a priori knowledge about the primary user signal and performs well for a wide range of circularly symmetric non gaussian noises with finite moments we analyze the probabilities of false alarm and missed detection of the proposed detector in rayleigh fading in the low signal to noise ratio regime and investigate its asymptotic performance if the number of samples available for spectrum sensing is large furthermore we consider the deflection coefficient for optimization of the lp norm parameters and discuss its connection to the probabilities of false alarm and missed detection based on the deflection coefficient an adaptive algorithm for online optimization of the lp norm parameters is developed analytical and simulation results show that the proposed lp norm detector yields significant performance gains compared to conventional energy detection in non gaussian noise and approaches the performance of the locally optimal detector which requires knowledge of the noise distribution

riesz transforms for the dunkl harmonic oscillator we propose an approach to the theory of riesz transforms in a framework emerging from certain reflection symmetries in euclidean spaces relying on rosler s construction of multivariable generalized hermite functions associated with a finite reflection group on mathbb r d we define and investigate a system of riesz transforms related to the dunkl harmonic oscillator in the case isomorphic with the group mathbb z d 2 it is proved that the riesz transforms are calderon zygmund operators in the sense of the associated space of homogeneous type thus their mapping properties follow from the general theory

two sided coupled generalized sylvester matrix equations solving using a simultaneous decomposition for fifteen matrices abstract in this paper we investigate and analyze in detail the structure and properties of a simultaneous decomposition for fifteen matrices a i c p i t i b i c s i q i c i c p i t i 1 d i c s i 1 q i and e i c p i q i i 1 2 3 we show that from this simultaneous decomposition we can derive some necessary and sufficient conditions for the existence of a solution to the system of two sided coupled generalized sylvester matrix equations with four unknowns a i x i b i c i x i 1 d i e i i 1 2 3 apart from proving an expression for the general solutions to this system we derive the range of ranks of these solutions using the ranks of the given matrices a i b i c i d i and e i we provide some numerical examples to illustrate our results moreover we present a similar approach to consider the simultaneous decomposition for 5k matrices and the system of k two sided coupled generalized sylvester matrix equations with k 1 unknowns a i x i b i c i x i 1 d i e i i 1 k k 4 the main results are also valid over the real number field and the real quaternion algebra

meridian filtering for robust signal processing a broad range of statistical processes is characterized by the generalized gaussian statistics for instance the gaussian and laplacian probability density functions are special cases of generalized gaussian statistics moreover the linear and median filtering structures are statistically related to the maximum likelihood estimates of location under gaussian and laplacian statistics respectively in this paper we investigate the well established statistical relationship between gaussian and cauchy distributions showing that the random variable formed as the ratio of two independent gaussian distributed random variables is cauchy distributed we also note that the cauchy distribution is a member of the generalized cauchy distribution family recently proposed myriad filtering is based on the maximum likelihood estimate of location under cauchy statistics an analogous relationship is formed here for the laplacian statistics as the ratio of laplacian statistics yields the distribution referred here to as the meridian interestingly the meridian distribution is also a member of the generalized cauchy family the maximum likelihood estimate under the obtained statistics is analyzed motivated by the maximum likelihood estimate under meridian statistics meridian filtering is proposed the analysis presented here indicates that the proposed filtering structure exhibits characteristics more robust than that of median and myriad filtering structures the statistical and deterministic properties essential to signal processing applications of the meridian filter are given the meridian filtering structure is extended to admit real valued weights utilizing the sign coupling approach finally simulations are performed to evaluate and compare the proposed meridian filtering structure performance to those of linear median and myriad filtering

alpha stable signals and adaptive filtering let d sub k x sub k be jointly stationary symmetric spl alpha stable processes with index 1 spl alpha 2 we first consider the problem of optimal fir linear and regression filters we then consider the signed error and sign sign adaptive filtering algorithms for the estimation of the desired signal d sub j on the basis of the input vector x sub j various convergence results are established for the signal and tap weights estimation errors

eigenstructure assignment by output feedback this paper looks at the problem of eigenstructure assignment using the system outputs the algorithm developed is a single pass solution based on the singular value decomposition used to assess rank deficiency the technique uses metrics to assess the time response actuator movement and output decoupling of the eigenstructure problem the paper then applies the algorithm to a multi input system and demonstrates the use of the decoupling and actuator metrics

eigenstructure assignment in linear multivariable systems a parametric solution this paper generalizes a recently reported method 1 of closed loop eigenstructure assignment via state feedback in a linear multivariable system with n states and r control inputs by introducing a lemma on the differentiation of determinants the class of assignable eigenvectors and generalized eigenvectors associated with the assigned eigenvalues is explicitly described by a complete set of n r dimensional free parameter vectors this parametric characterization conveniently organizes the nonuniqueness of the solution of the eigenvalue assignment problem and thereby provides an efficient means of further modifying the system dynamic response a numerical example is worked out to demonstrate the feasibility of the method

output feedback eigenstructure assignment using a new reduced orthogonality condition this paper presents a new method of output feedback eigenstructure assignment a new reduced orthogonality condition is derived which is less restrictive on the design degrees of freedom than others in the literature from this a novel general formulation for the gain matrix is admitted which utilizes a two stage design process in the first stage a subset of desired eigenvectors is assigned either left or right in the second stage a dual set is assigned which adheres to the necessary and sufficient conditions for output feedback eigenstructure assignment proved earlier in the paper a numerical example is presented to illustrate the whole procedure

matched median filtering a class of median type filters called matched median filters is defined for the estimation of the information which is carried by the amplitude of a noisy signal these filters form the natural counterpart of linear matched filters in the class of median type filters and are maximum likelihood estimators if the noise is biexponential matched median filters are defined both for baseband and passband systems their statistical properties are analyzed and simulation results presented

solutions to a family of matrix equations by using the kronecker matrix polynomials closed form solutions to a family of generalized sylvester matrix equation in form of i 0 fa ixf email protected i 0 jb kyf email protected j 0 fe jrf j are given by using the so called kronecker matrix polynomials it is found that the structure of the solutions is independent of the orders f j and f this type of uniform closed form solutions includes our early results as special cases the results provide great convenience to the computation and analysis of the solutions to this class of equations and can perform important functions in many analysis and design problems in linear systems

poisson integrals and riesz transforms for hermite function expansions with weights we consider expansions with respect to the multi dimensional hermite functions which are eigenfunctions of the harmonic oscillator l x 2 for the heat diffusion and poisson semigroups corresponding to a self adjoint extension l of l we investigate their boundary behaviour and mapping properties all this is done for functions from lp w 1 p w ap then riesz transforms and conjugate poisson integrals are considered the riesz transforms occur to be calderon zygmund operators hence their mapping properties follow by using results from a general theory

riesz transforms and conjugacy for laguerre function expansions of hermite type riesz transforms and conjugate poisson integrals for multi dimensional laguerre function expansions of hermite type with index are defined and investigated it is proved that for any multi index 1 d such that i 1 2 i 1 2 1 2 the appropriately defined riesz transforms rj j 1 2 d are calderon zygmund operators hence their mapping properties follow from a general theory similar mapping results are obtained in one dimension without excluding 1 2 1 2 by means of a local calderon zygmund theory and weighted hardy s inequalities the conjugate poisson integrals are shown to satisfy a system of cauchy riemann type equations and to recover the riesz laguerre transforms on the boundary the two specific values of 1 2 1 2 and 1 2 1 2 are distinguished since then a connection with riesz transforms for multi dimensional hermite function expansions is established

multistage parametric eigenstructure assignment by output feedback control this paper develops an efficient multistage parametric approach for eigenstructure assignment in linear multivariable systems by output feedback control the sets of closed loop eigenvalues and associated eigenvectors are suitably divided into subsets and the entire eigenstructure is constructed by parts in two or more consecutive stages this allows the subsets of right and left eigenvectors to be assigned in separate stages and thus the computational algorithm is relaxed from the orthogonality conditions the number of effective free parameters beyond eigenvalue assignment is determined and the notion of redistributing these parameters among the assignable right and left eigenvectors is introduced numerical examples are included to demonstrate the design procedure

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

eigenvector assignment using output feedback the application of constant gain output feedback to arbitrarily assign eigenvectors for a system with a given set of eigenvalues is investigated necessary and sufficient conditions for the existence of an output feedback gain matrix for a given eigen structure are developed the allowable eigenspaces are thus characterized and the design procedure is illustrated through numerical examples

eigenstructure assignment via linear state feedback control in fahmy and o reilly 1982 a b a parametric solution for the linear state feedback eigenstructure assignment problem is developed this approach is here modified in such a way as to accommodate the case where the set of closed loop eigenvalues and the set of open loop eigenvalues have elements in common it is particularly shown that each common eigenvalue introduces a number of partially free design parameter vectors in addition to the original free ones the paper concludes with illustrative numerical examples

optimal pivot selection in fast weighted median search weighted median filters are increasingly being used in signal processing applications and thus fast implementations are of importance this paper introduces a fast algorithm to compute the weighted median wm of n samples which has linear time and space complexity as opposed to o n log n which is the time complexity of traditional sorting algorithms a popular selection algorithm often used to find the wm in large data sets is quickselect whose performance is highly dependent on how the pivots are chosen we introduce an optimization based pivot selection strategy which results in significantly improved performance as well as a more consistent runtime compared to traditional approaches the selected pivots are order statistics of subsets in order to find the optimal order statistics as well as the optimal subset sizes a set of cost functions are derived which when minimized lead to optimal design parameters we compare the complexity to floyd and rivest s algorithm select which to date has been the fastest median finding algorithm and we show that the proposed algorithm compared with select requires close to 30 fewer comparisons it is also shown that the proposed selection algorithm is asymptotically optimal for large n

polynomial weighted median filtering this paper extends weighted median wm filters to the class of polynomial weighted median pwm filters traditional polynomial filtering theory based on linear combinations of polynomial terms is able to approximate important classes of nonlinear systems the linear combination of polynomial terms however yields poor performance in environments characterized by heavy tailed distributions weighted median filters in contrast are well known for their outlier suppression and detail preservation properties the weighted median sample selection methodology is naturally extended to the polynomial sample case yielding a filter structure that exploits the higher order statistics of the observed samples while simultaneously being robust to outliers moreover the pwm filter class is well motivated by an analysis of cross and square term statistics a presented probability density function analysis shows that these terms have heavier tails than the observed samples indicating that robust combination methods should be utilized to avoid undue influence of outliers further analysis shows weighted median processing of polynomial terms is justified from a maximum likelihood perspective the established pwm filter class is statistically analyzed through the determination of the filter output distribution and breakdown probability filter parameter optimization procedures are also presented finally the effectiveness of pwm filters is demonstrated through simulations that include temporal spectrum and bispectrum analysis

on the performance of single threshold detectors for binary communications in the presence of gaussian mixture noise in this paper probability of error performance of single threshold detectors is studied for binary communications systems in the presence of gaussian mixture noise first sufficient conditions are proposed to specify when the sign detector is not an optimal detector among all the single threshold detectors then a monotonicity property of the error probability is derived for the optimal single threshold detector in addition a theoretical limit is obtained on the maximum ratio between the average probabilities of error for the sign detector and the optimal single threshold detector finally numerical examples are presented to investigate the theoretical results

riesz transforms for multi dimensional laguerre function expansions abstract riesz transforms and conjugate poisson integrals for multi dimensional laguerre function expansions of type are defined and investigated it is proved that for any multi index 1 d such that i 1 2 the appropriately defined riesz laguerre transforms r j j 1 2 d are calderon zygmund operators in the sense of the associated space of homogeneous type hence their mapping properties follow from the general theory similar results are obtained for all higher order riesz laguerre transforms the conjugate poisson integrals are shown to satisfy a system of equations of cauchy riemann type and to recover the riesz laguerre transforms on the boundary

eigenvalue placement for generalized linear systems this paper deals with some aspects of eigenvalue placement by state feedback for generalized linear systems described by e ax bu where e is a singular map it is shown that controllability of the infinite eigenvalues of the pencil se a is equivalent to the existence of a state feedback map which assigns those eigenvalues to pre specified complex numbers a procedure for the assignment of all eigenvalues to distinct complex numbers is also discussed

a geometric approach to eigenstructure assignment for singular systems moore s well known result on the feedback assignment of eigenstructure in linear state space systems 5 was generalized to descriptor systems in 9 in this note we make some useful extensions to fill out the theory to begin with we do not assume controllability of the plant it is shown that the maximum number of finite closed loop eigenvalues is equal to dim el where l is the supremal a e r b invariant subspace in order to relate the possible closed loop structure to the open loop plant structure we define a set of indexes for descriptor systems which are in many respects similar to the controllability indexes of state space systems in terms of these controllability indexes we give a systematic approach to selecting the closed loop eigenvectors a major contribution of this note is the fact that it is geometric in nature and hence avoids any decomposition of the system matrices into a special form e g weierstrass form 1 the geometric setting introduced here should constitute a basis for further research in generalizing the well known results in geometric system theory disturbance decoupling input output decoupling etc to singular systems

solutions to matrix equations x axb cy r and x axb cy r abstract the present work proposed an alternative approach to find the closed form solutions of the nonhomogeneous yakubovich matrix equation x a x b c y r based on the derived closed form solution to the nonhomogeneous yakubovich matrix equation the solutions to the nonhomogeneous yakubovich quaternion j conjugate matrix equation x a x b c y r are obtained by the use of the real representation of a quaternion matrix the existing complex representation method requires the coefficient matrix a to be a block diagonal matrix over complex field in contrast in this publication we allow a quaternion matrix of any dimension as an application eigenstructure assignment problem for descriptor linear systems is considered

a new approach to eigenstructure assignment by output feedback the eigenstructure assignment problem for a linear time invariant multi input multi output system using output feedback is considered a new approach is developed which identifies the eigenspaces for the desired set of all the closed loop eigenvalues for the assignment of this desired set necessary and sufficient conditions are established these conditions contain two coupled sylvester matrix equations one of which is proven to be a reduced order square sylvester matrix equation this results in an efficient analytical procedure numerically superior to known techniques for the determination of the output feedback gain matrix

transference between laguerre and hermite settings in this paper we present a new method in order to transfer boundedness results for operators associated with hermite functions to boundedness results for operators associated with laguerre functions the technique relies on an exact point wise identity relating the heat kernels of both systems the method that we present here has the novelty that can be used backwards that is boundedness results for laguerre systems can be also transfered to boundedness results for hermite systems we apply our method in order to get new properties of some operators in the laguerre setting among others we mention the description of riesz transforms as principal value operators as an application of the reversibility of the method we characterize the class of banach spaces b for which the riesz transforms in the laguerre setting are bounded from lbp into itself it is shown that this class coincides with the umd class

on pole placement via eigenstructure assignment approach this note comes back to the hard problem of pole placement by static output feedback let a triplet of matrices a b c be given with n state variables m inputs and p ouputs find a matrix k such that the spectrum of a bkc equals a specified set when mp m p a simple noniterative technique based upon the notion of eigenstructure that in most cases assigns m p roots is proposed it therefore enables the designer to assign the whole of the desired spectrum when m p n mp

optimal discrete systems using time weighted performance index with prespecified closed loop eigenvalues a design problem of optimal regulators for discrete time linear multi input systems is investigated for the prespecified closed loop eigenvalues then the design freedom which remains after the prespecified closed loop eigenvalues are assigned is used to minimize a time weighted performance index necessary conditions for the optimality of the controller that satisfies the prespecified closed loop eigenvalues are derived and an algorithm for computing the optimal constant feedback gain is presented

solutions of the equation av bw vf and their application to eigenstructure assignment in linear systems two new simple complete analytical and restriction free solutions with complete and explicit freedom of the matrix equation av bw vf are proposed here ab is known and is controllable and f is in the jordan form with arbitrary given eigenvalues based on the proposed solutions of this matrix equation a complete parametric approach for eigenstructure assignment in linear systems via state feedback is proposed and two new algorithms are presented the proposed solutions of the matrix equation and the eigenstructure assignment result are generalizations of some previous results and are simpler and more effective

observers for discrete singular systems the author considers the design of observers for the discrete singular system ex k 1 ax k bu k y k cx k placing special emphasis on the problems of state reconstruction and minimal time state reconstruction it is shown that for a singular system finite poles can be moved to infinity by state feedback and the state can be reconstructed by causal observers

second order heavy tailed distributions and tail analysis this correspondence studies the second order distributions of heavy tail distributed random variables rvs two models for the heavy tailed distributions are considered power law and epsi contaminated distributions special cases of the models considered include 1 rvs formed by the product of two independent but not necessarily identically distributed heavy tailed rvs x and y such that z xy and 2 rvs formed through squaring a heavy tail distributed rv x such that w x2 tail analysis of the rvs their cross terms and square values shows the ordering of their tail heaviness the following results hold strictly for power law distributions and under mild conditions for epsi contaminated distributions the tail of f z x is heavier than that of fx x and the tail of fw x is heavier than that of fz x where f x denotes the probability density distribution of the corresponding random variable the heaviness of the tails indicates that robust methods of sample combination and output determination should be utilized to avoid undue influence of outliers and degradation in performance as examples the denoising and frequency selective filtering problems under the derived cross and square statistics for hyperbolic tailed and epsi contaminated models are considered simulation results indicate that the weighted myriad wmy filter outperforms the weighted median wm filter and the wm filter outperforms the weighted sum finite impulse response fir filter the results may be exploited in higher order applications of heavy tailed distributions in networking such as data traffic modeling and in nonlinear signal and image processing such as polynomial and volterra filtering

recursive weighted myriad based filters and their optimizations this paper proposes two new recursive filtering structures based on the nonlinear myriad operator first we develop the general class of recursive weighted myriad rwmy filters as a robust filtering structure against impulsive noise that includes as particular cases a normalized version of the linear infinite impulse response iir filter the recursive mode type filter and the non recursive weighted myriad filter secondly considering the fact that the additive noise that contaminates the previous filter s outputs is no longer impulsive we introduce a novel class of recursive hybrid myriad rhmy filters whose structure gathers the advantages of both the weighted myriad and the weighted mean in a single cost function to be minimized some properties of the rhmy filter are derived and a fast algorithm to compute the rhmy filter output is proposed furthermore adaptive algorithms for designing the proposed recursive structures under the equation error formulation framework are developed finally extensive numerical simulations are shown to evaluate both the iterative update of the adaptive algorithms and the performance of the proposed recursive filters against impulsive noise

a bilinear formulation for the output feedback problem in linear systems this note ties together a geometric theory and previous algebraic results for the closed loop eigenstructure assignment by output feedback in multivariable systems necessary and sufficient conditions for the closed loop stabilization eigenstructure assignment are presented in terms of a bilinear sylvester equation the solutions of which completely characterize the closed loop eigenstructure problem with output feedback some preliminary results for the solution of this bilinear equation are presented

robust eigenstructure assignment via dynamical compensators abstract based on a proposed complete parametric approach for eigenstructure assignment in multivariable linear systems via dynamical compensators insightful parametrizations of the closed loop eigenvalues sensitivities to the perturbed elements in the open loop system matrices are obtained and an effective algorithm for eigenvalue assignment with minimum sensitivity in multivariable linear systems via dynamical compensators is then proposed the algorithm does not contain going back procedures and allows the closed loop eigenvalues to be conveniently optimized within desired regions a numerical example demonstrates its effect simplicity and numerical property

a controllability condensed form and a state feedback pole assignment algorithm for descriptor systems a direct algorithm for the pole assignment problem of a time invariant linear multivariable descriptor system with linear state feedback is presented the system is assumed to be completely controllable for both finite and infinite poles the algorithm is based on the controllability condensed form which is derived