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

exact pole assignment using direct or dynamic output feedback this note addresses the problem of the assignability of the eigenvalues of the matrix a bpc by choice of the matrix p this mathematical problem corresponds to pole assignment in the direct output feedback control problem and by proper changes of variables it also represents the pole assignment problem with dynamic feedback controllers the key to our solution is the introduction of the new concept of local complete assignability which in loose terms is the arbitrary perturbability of the eigenvalues of a bpc by perturbations of p if n x is the order of the system we show that if a bp 0 c has distinct eigenvalues a necessary and sufficient condition for local complete assignability at p 0 is that the matrices c a bp 0 c i 1 b be linearly independent for 1 leq i leq n x in special cases this condition reduces to known criteria for controllability and observability although these latter properties are necessary conditions for assignability we also address the question of the assignability of uncontrollable or unobservable systems both by direct output feedback and dynamic compensation the main result of this note yields an algorithm that assigns the closed loop poles to arbitrarily chosen values in the direct and in the dynamic output feedback control problems

stochastic gradient based implementation of spatially preprocessed speech distortion weighted multichannel wiener filtering for noise reduction in hearing aids recently a generalized noise reduction scheme has been proposed called the spatially preprocessed speech distortion weighted multichannel wiener filter sp sdw mwf it encompasses the generalized sidelobe canceller gsc and a multichannel wiener filtering technique as extreme cases compared with the widely studied gsc with quadratic inequality constraint qic gsc the sp sdw mwf achieves a better noise reduction performance for a given maximum speech distortion level we develop a low cost stochastic gradient implementation of the sp sdw mwf to speed up convergence and reduce computational complexity the algorithm is implemented in the frequency domain experimental results with a behind the ear hearing aid show that the proposed frequency domain stochastic gradient algorithm preserves the benefit of the exact sp sdw mwf over the qic gsc while its computational cost is comparable to the least mean square based scaled projection algorithm for qic gsc

a fractionally spaced blind equalizer based on linear programming we formulate the blind fractionally spaced equalization fse problem as one that minimizes a piecewise linear convex function subject to some linear constraints on the equalizer parameters we show that this formulation achieves both the interference removal and the carrier phase recovery when the input signal possesses a certain quadrature amplitude modulation qam type symmetry a fast linear programming implementation is presented to solve the convex minimization problem computer simulation results indicate the new linear programming based fse is able to accurately equalize channels that are known to be not equalizable by t spaced or baud rate blind equalizers and yields superior performance to other blind fse methods

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

numerical algorithms for eigenvalue assignment by constant and dynamic output feedback algorithms are proposed for eigenvalue assignment eva by constant as well as dynamic output feedback the main algorithm is developed for single input multioutput systems and the results are then extended to multiinput multioutput systems in computing the feedback use is made of the fact that the closed loop eigenvalues can almost always be assigned arbitrarily close to the desired locations in the complex plane provided the system satisfies the condition m p n where m p and n are respectively the number of inputs outputs and states of the system the eva problem has been treated as a converse of the algebraic eigenvalue problem the proposed algorithms are based on the implicitly shifted qr algorithm for solving the algebraic eigenvalue problem the performance of the algorithms is illustrated by several numerical examples

fast and low complexity blind equalization via subgradient projections we propose a novel blind equalization method based on subgradient search over a convex cost surface this is an alternative to the existing iterative blind equalization approaches such as the constant modulus algorithm cma which often suffer from the convergence problems caused by their nonconvex cost functions the proposed method is an iterative algorithm called subgradient based blind algorithm sgba for both real and complex constellations with a very simple update rule it is based on the minimization of the l sub spl infin norm of the equalizer output under a linear constraint on the equalizer coefficients using subgradient iterations the algorithm has a nice convergence behavior attributed to the convex l sub spl infin cost surface as well as the step size selection rules associated with the subgradient search we illustrate the performance of the algorithm using examples with both complex and real constellations where we show that the proposed algorithm s convergence is less sensitive to initial point selection and a fast convergence behavior can be achieved with a judicious selection of step sizes furthermore the amount of data required for the training of the equalizer is significantly lower than most of the existing schemes

a fast linear programming algorithm for blind equalization a fast implementation of a special non mse cost function for blind equalization is presented here this baud rate equalization algorithm is based on a convex cost function coupled with a simple linear constraint on the equalizer parameters for a generic class of channels with persistently exciting quadrature amplitude modulation input signals this new algorithm allows the convergence of equalizer parameters to a unique global minimum achieving intersymbol interference suppression and carrier phase recovery

bounds on the minimax rate for estimating a prior over a vc class from independent learning tasks abstract we study the optimal rates of convergence for estimating a prior distribution over a vc class from a sequence of independent data sets respectively labeled by independent target functions sampled from the prior we specifically derive upper and lower bounds on the optimal rates under a smoothness condition on the correct prior with the number of samples per data set equal the vc dimension these results have implications for the improvements achievable via transfer learning we additionally extend this setting to real valued function where we establish consistency of an estimator for the prior and discuss an additional application to a preference elicitation problem in algorithmic economics

a quadratic programming approach to blind equalization and signal separation blind equalization and signal separation are two well established signal processing problems in this paper we present a quadratic programming algorithm for fast blind equalization and signal separation by introducing a special non mean square error mse objective function we reformulate fractionally spaced blind equalization into an equivalent quadratic programming problem based on a clear geometric interpretation and a formal proof we show that a perfect equalization solution is obtained at every local optimum of the quadratic program because blind source separation is by nature and mathematically a closely related problem we also generalize the algorithm for blind signal separation we show that by enforcing source orthogonalization through successive processing the quadratic programming approach can be applied effectively moreover the quadratic program is easily extendible to incorporate additional practical conditions such as jamming suppression constraints we also provide evidence of good performance through computer simulations

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

on eigenstructure assignment by gain output feedback in this paper the eigenstructure assignment of linear multivariable control systems is studied from a geometric point of view for the class of systems in which the number of outputs plus the number of inputs exceeds the number of states genericity properties relative to this problem are derived it is shown without any assumption on the genericity of the system that the pole assignment can be carried out by choosing some closed loop eigenvectors almost freely the crucial point is that all the expected degrees of freedom in pole assignment are so described without redundancy which fully justifies the practical interest of such techniques despite the technicality required for the derivation of intermediate results the main result which is an eigenstructure assignment algorithm is very easy to implement because it is only based on the computation of certain sums and intersections of characteristic subspaces furthermore it is shown how the basic tools developed here can be used to tackle the prob

pole assignment of strictly proper and proper linear systems by constant output feedback a new unifying approach for the study of pole assignment by constant output feedback cpap for strictly proper and proper linear systems is presented the multilinear nature of cpap is reduced to a linear problem and to the standard multilinear problem of decomposability of multivectors the solvability of cpap thus becomes a problem of finding real intersections of a linear variety with the grassmann variety of a projective space an alternative proof to the ml n m i n are the numbers of outputs inputs states necessary and sufficient condition for generic pole assignability of strictly proper systems by complex output feedback is given the above result is extended to the ml n 1 condition for the case of proper systems stronger necessary conditions for generic pole assignment by a real output feedback are obtained by using the recently introduced invariant the plucker matrix pn such conditions are that pn must have full rank and ml n strictly proper case or ml n 1 proper case it is sh

paper low order control design for lmi problems using alternating projection methods computational techniques based on alternating projections are proposed to solve control design problems described by linear matrix inequalities lmis in particular we concentrate on the stabilization and the suboptimal h output feedback control design problems these problems can be described by a pair of lmis and an additional coupling condition this coupling condition is convex for the full order control design problem but convexity is lost for the control problem of order strictly less than the plant order we formulate these problems as feasibility problems with matrix constraint sets of simple geometry and we utilize this geometry to obtain analytical expressions for the orthogonal projection operators onto these sets full order and low order controllers are designed using alternating projection methods for the full order controller case global convergence of the alternating projection methods to a feasible solution is guaranteed however for the low order control case only local convergence is guaranteed an example is provided to illustrate the use of these methods for the full order and the low order controller design

linear quadratic suboptimal control with static output feedback abstract this paper considers the design of a stabilizing static output feedback gain which keeps linear quadratic lq performance index less than a specified number we call this an lq suboptimal controller existence of such a controller is shown to be equivalent to the existence of a positive definite matrix p such that p satisfies two linear matrix inequalities lmis while p 1 satisfies another lmi all lq suboptimal controllers are explicitly parametrized by the freedom in the choice of the positive definite matrix p satisfying the lmis and an arbitrary positive scalar and an arbitrary matrix of fixed dimension with a norm bound a modified version of the min max algorithm is given to find a positive definite solution p to the lmis

some results on the genericity of the pole placement problem abstract in this note the pole placement problem for a linear mimo systems with p outputs and m inputs is studied from the algebraic point of view a formulation is proposed that allows to analyze both theoretical and numerical aspects of the case min m p 2 with more sharpness moreover here it is shown that arbitrary pole placement by static output feedback of unitary rank is generically not possible even if m p n holds true

covariance controllers a new parametrization of the class of all stabilizing controllers abstract the class of all stabilizing controllers is parametrized in terms of a system matrix called the one at a time covariance and an arbitrary skew hermitian matrix the new parametrization is in closed form for any specified controller order and provides a deterministic version of the stochastic problem of covariance assignment

stationary points of the constant modulus algorithm for real gaussian signals an analysis of the stationary points for four versions of the constant modulus algorithm cma when the received signal is a zero mean real gaussian process is presented with this type of signal it is well known that cma generally cannot equalize a communication channel the analysis of the cma performance function demonstrates how this occurs it is shown that in each case the stationary points are determined by a condition on the variance of the equalizer output and they depend only on the modulus factor r and the received signal correlation matrix r as a result there can be an infinity of weight vector solutions each corresponding to a stationary point of the cma performance function

output feedback and generic stabilizability we consider questions of pole placement and stabilization for generic linear systems with prescribed state input and output dimensions where the controller must be implemented by linear memoryless output feedback we present a criterion in terms of a special pole placement property for generic stabilizability and apply this to describe constraints on the dimensions which are consistent with generic stabilizability we also discuss the rationality and solvability by radicals of stabilizing or pole positioning gains and we describe how decision algebra can theoretically handle existence questions for generic systems

a geometric framework for pole assignment algorithms the problem of pole assignment by gain output feedback or by low order dynamical compensator is considered from a geometric point of view this makes it possible to unify in a general framework most of the existing pole assignment methods formulated in a state space context such as the minimal order observers the brasch pearson compensator and the methods proposed by h kimura and to simplify their presentation moreover new pole assignment algorithms may be derived from this general formulation

applications of convex optimization in signal processing and digital communication in the last two decades the mathematical programming community has witnessed some spectacular advances in interior point methods and robust optimization these advances have recently started to significantly impact various fields of applied sciences and engineering where computational efficiency is essential this paper focuses on two such fields digital signal processing and communication in the past the widely used optimization methods in both fields had been the gradient descent or least squares methods both of which are known to suffer from the usual headaches of stepsize selection algorithm initialization and local minima with the recent advances in conic and robust optimization the opportunity is ripe to use the newly developed interior point optimization techniques and highly efficient software tools to help advance the fields of signal processing and digital communication this paper surveys recent successes of applying interior point and robust optimization to solve some core problems in these two fields the successful applications considered in this paper include adaptive filtering robust beamforming design and analysis of multi user communication system channel equalization decoding and detection throughout our emphasis is on how to exploit the hidden convexity convex reformulation of semi infinite constraints analysis of convergence complexity and performance as well as efficient practical implementation

stabilization of a linear plant via a stable compensator having no real unstable zeros abstract this paper studies the following problem under what conditions can a linear plant be stabilized by a stable compensator having no real zeros in the closed right half plane solving this problem is an important step towards to solving the problems of stabilization of linear systems via stable minimum phase compensation and simultaneous stabilization of n n 2 plants in the paper necessary and sufficient conditions are derived these conditions are completely general and therefore encompass unstable nonminimum phase plants as well it is shown that the stabilizability solely depends on the locations of real zeros and real poles of a given plant for a plant satisfying the stabilizability conditions a computational design procedure for constructing a desired compensator is also provided and illustrated via an example

stabilizability conditions of multivariable uncertain systems via output feedback control a stabilizability condition is established for stabilizing multivariable uncertain dynamical systems with matched uncertainties by linear static output feedback control it is shown that under the assumptions of minimum phase and nonsingular high frequency gain for the nominal plant stabilization with linear static output feedback control is achievable a necessary and sufficient condition is also obtained for the existence of constant output feedback which makes the closed loop system strictly positive real

learnability and the vapnik chervonenkis dimension valiant s learnability model is extended to learning classes of concepts defined by regions in euclidean space e n the methods in this paper lead to a unified treatment of some of valiant s results along with previous results on distribution free convergence of certain pattern recognition algorithms it is shown that the essential condition for distribution free learnability is finiteness of the vapnik chervonenkis dimension a simple combinatorial parameter of the class of concepts to be learned using this parameter the complexity and closure properties of learnable classes are analyzed and the necessary and sufficient conditions are provided for feasible learnability

np hardness of some linear control design problems we show that some basic linear control design problems are np hard implying that unless p np they cannot be solved by polynomial time algorithms the problems that we consider include simultaneous stabilization by output feedback stabilization by state or output feedback in the presence of bounds on the elements of the gain matrix and decentralized control these results are obtained by first showing that checking the existence of a stable matrix in an interval family of matrices is np hard

a globally convergent algorithm for the optimal constant output feedback problem a dual version of the levine athans algorithm for solving the optimal constant output feedback gain for continuous time systems is studied global convergence of the procedure to a stationary point of the loss function is proved a global convergence property of the levine athans algorithm is also obtained

rates of convergence of minimum distance estimators and kolmogorov s entropy on construit des estimateurs robustes et on montre que le taux de convergence resultant depend naturellement d une fonction entropie

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

blind fractionally spaced equalization of noisy fir channels direct and adaptive solutions blind fractionally spaced equalizers reduce intersymbol interference using second order statistics without the need for training sequences methods for finding fir zero forcing blind equalizers directly from the observations are described and adaptive versions are developed in contrast most current methods require channel estimation as a first step to estimating the equalizer the direct methods can be zero forcing minimum mean square error or even minimum mean square error mmse within the class of zero forcing equalizers performance of the proposed methods and comparisons with existing approaches are shown for a variety of channels including an empirically measured digital microwave channel

all controllers for the general h control problem lmi existence conditions and state space formulas this paper presents all controllers for the general h control problem with no assumptions on the plant matrices necessary and sufficient conditions for the existence of an h controller of any order are given in terms of three linear matrix inequalities lmis our existence conditions are equivalent to scherer s results but with a more elementary derivation furthermore we provide the set of all h controllers explicitly parametrized in the state space using the positive definite solutions to the lmis even under standard assumptions full rank etc our controller parametrization has an advantage over the q parametrization the freedom q a real rational stable transfer matrix with the h norm bounded above by a specified number is replaced by a constant matrix l of fixed dimension with a norm bound and the solutions x y to the lmis the inequality formulation converts the existence conditions to a convex feasibility problem and also the free matrix l and the pair x y define a finite dimensional design space as opposed to the infinite dimensional space associated with the q parametrization

stabilization via static output feedback necessary and sufficient conditions for the existence of a stabilizing static output feedback gain matrix are presented it is shown that any such gain matrix is the solution of some linear quadratic control problem where the cost functional has a suitable cross term

on convergence analysis of fractionally spaced adaptive blind equalizers in this paper we study the convergence analysis of fractionally spaced adaptive blind equalizers we show that based on the trivial and nontrivial nullspaces of a channel convolution matrix all equilibria can be classified as channel dependent equilibria cde or algorithm dependent equilibria ade because oversampling provides channel diversity the nullspace of the channel convolution matrix is affected we show that fractionally spaced equalizers fses do not possess any cde if a length zero condition is satisfied the convergence behavior of these fse are clearly determined by the specific choice of cost function alone we characterize the global convergence ability of several popular algorithms simply based on their ade we also present an fse implementation of the super exponential algorithm we show that the fse implementation does not introduce any nonideal approximation simulation results are also presented to illustrate the robustness and the improved performance of fse under the super exponential algorithm

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

some open problems in matrix theory arising in linear systems and control control theory has long provided a rich source of motivation for developments in matrix theory accordingly we discuss some open problems in matrix theory arising from theoretical and practical issues in linear systems theory and feedback control the problems discussed include robust stability matrix exponent induced norms stabilizability and pole assignability and nonstandard matrix equations a substantial number of references are included to acquaint matrix theorists with problems and trends in this application area feedback control theory has long provided a rich source of motivation for developments in matrix theory the purpose of this paper is to discuss several open problems in matrix theory that arise from theoretical and practical issues in feedback control theory and the associated area of linear systems theory many of these problems are remarkably simple to state are of intense interest in control theory and applications and yet remain unsolved besides leading to the resolution of these problems it is hoped that this paper will help to stimulate increased interaction between matrix and control theorists accord

global asymptotic linearisation of the pole placement map a closed form solution for the constant output feedback problem abstract the problem of pole assignment by constant output feedback controllers is studied for minimal systems described by a proper transfer function matrix g s r m p s with mcmillan degree n a new method is presented based on asymptotic linearisation around a degenerate point of the pole placement map related to the problem the essence of the present approach is to reduce the multilinear nature of the problem to one of solving a linear set of equations and this is achieved without losing any of the degrees of freedom in the controller the solution is given in closed form in terms of a one parameter family of static feedback compensators for which the closed loop poles approach the required ones as 0 conditions for the generic as well as exact solvability of the arbitrary pole placement problem are given in terms of the numbers m p n and the rank of a new system invariant the d restricted plucker matrix it is shown that the method works generically when mp n which along with the boundary case mp n is the best possible condition as far as the number of states of the open loop system is concerned for achieving arbitrary pole placement via constant output feedback

static output feedback pole placement via a trust region approach this technical note presents two closely related algorithms for the problem of pole placement via static output feedback the algorithms are based on two different trust region methods and utilize the derivatives of the closed loop poles extensive numerical experiments show the effectiveness of the algorithms in practice though convergence to a solution is not guaranteed for either algorithm while desired poles must be distinct strategies for dealing with repeated poles are also presented

a necessary and sufficient condition for output feedback stabilizability a necessary and sufficient condition for a linear system to be stabilizable via static output feedback is presented it makes an appeal to the linear quadratic regulator theory

exact pole assignment by output feedback part 1 abstract we shall prove that exact assignment of distinct poles using output feedback is possible in any controllable and observable linear time invariant multivariable system in which the number of inputs plus the number of outputs exceeds the number of states except in clearly identified circumstances furthermore we give a construction for the entire class of pathological cases the main part of our argument is concerned with the assigning of complex conjugate eigenvalues by means of a real feedback matrix indeed we begin by giving a simple algorithm which is effective over any field although this problem has been discussed by numerous authors in the past they have usually presented only generic results we examine the complete class of systems satisfying the hypotheses mentioned

geometric methods for the classification of linear feedback systems abstract the precise determination of the nature and form of system invariants under output feedback is of fundamental interest in classical and modern control theory an algebraic solution of this problem would entail for example a description of the generators and relations of the ring of output feedback invariants geometrically we seek to describe the basic properties of the quotient space whose points consist of feedback equivalence classes of the system recovering the algebraic theory in terms of the function theory on this space naturally any description should be made in system theoretic terms in this paper we construct and study in the scalar case the quotient manifold for linear systems modulo the full output feedback group using classical algebraic geometry as a corollary we obtain explicit generators for the associated ring of invariants which we then interpret in terms of classical control theory e g in terms of root locus plots turning to the question of the existence of continuous canonical forms we show that these exist globally only when the system order is odd in the even case the obstruction to the existence of globally defined continuous forms is described in terms of the values of the system cauchy index this is illustrated for low order examples and certain questions concerning relations among the generators is treated using methods of the schubert calculus the complete set of invariants for the full output feedback group is obtained and our results concerning the existence and nonexistence of canonical forms is also compared to related results contained in the literature

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

output feedback eigenstructure assignment using two sylvester equations the eigenstructure assignment problem with output feedback is studied for systems satisfying the condition p m n the main tool used is the concept of c a b invariance and two coupled sylvester equations the solution of which leads to the computation of an output stabilizing feedback a computationally efficient algorithm for the solution of these two coupled equations which leads to the computation of a desired output feedback is presented

quadratic characterization and use of output stabilizable subspaces this note treats the problem of stabilization of linear systems by static output feedback using the concept of c a b invariant subspaces the work provides a new characterization of output stabilizable c a b invariant subspaces through two coupled quadratic stabilization conditions an equivalence is shown between the existence of a solution to this set of conditions and the possibility to stabilize the system by static output feedback an algorithm is provided and numerical examples are reported to illustrate the approach

multivariable nyquist criteria root loci and pole placement a geometric viewpoint classical control theory is concerned with the topics in our title in the context of single input single output systems there is now a large and growing literature on the extension of these ideas to the multiinput multioutput case this development has posed certain difficulties some due to the intrinsic nature of the problem and some we would argue due to an inadequate reflection on what the multivariable problem calls for in this paper we describe what seems to us to be the natural multivariable analogs of these concepts from classical control theory a rather satisfactory generalization of the nyquist criterion will be described and a clear analog of the asymptotic properties of the root locus will be obtained in the multiparameter case however an example is given which illustrates the quite surprising fact that the root locus map is not always continuous at infinite gains this calls for a new ingredient a compactification of the space of gains and perhaps the most interesting new feature in this circle of ideas comes in the area of pole placement this problem is difficult in the multivariable case but by establishing a correspondence with a classical set of problems in geometry we are able to understand its main aspects and to derive results on pole placement by output feedback over the real field

hermitian pencils and output feedback stabilization of scalar systems abstract necessary and sufficient semi algebraic conditions for a the stabilization of scalar transfer functions and b the assignability of real poles by static output feedback are given in terms of the weierstrass invariants of an associated hermitian matrix pencil an explicit graphical test for output feedback stabilizability is derived which is equivalent to the nyquist criterion

blind system identification using precise and quantized observations this paper studies the blind identification of multi channel fir systems using precise and quantized observations first a new deterministic blind identification dbi algorithm is presented for multi channel fir systems using precise observations in which the system parameters can be consistently estimated and the common source signal can be stably recovered when the observed samples are quantized by a static finite level quantizer an iterative deterministic blind identification idbi method is then provided the asymptotic characters of the proposed idbi method are discussed and the quantization effect on the identification performance is analyzed numerical simulations are given to support the developed dbi method and idbi method

properties of numerical algorithms related to computing controllability the numerical properties of some methods for computing controllability are used in an expository way to motivate a wider understanding of numerical computations in particular the numerical rank of a matrix the numerical stability of algorithms the sensitivity of problems and the scaling of problems are discussed a numerically stable algorithm is given for computing controllability but it is pointed out that a measure of the distance of the given system from the nearest uncontrollable system would be more useful and this appears to be an open computational problem

ill convergence of godard blind equalizers in data communication systems the existence of stable undesirable equilibria for the godard algorithm is demonstrated through a simple autoregressive ar channel model these undesirable equilibria correspond to local but nonglobal minima of the underlying mean cost function and thus permit the ill convergence of the godard algorithms which are stochastic gradient descent in nature simulation results confirm predicted misbehavior for channel input of constant modulus it is shown that attaining the global minimum of the mean cost necessarily implies correct equalization a criterion is also presented for allowing a decision at the equalizer as to whether a global or nonglobal minimum has been reached

eigenstructure assignment by output feedback and residue analysis this note deals with the use of feedback to approximate the closed loop eigenstructure of a system to a prescribed set of values a new method is proposed to reduce the controller complexity based on eigenvalue sensitivity concepts a flight control example is presented as an application

output feedback pole assignment procedure a new algorithm based on pole assignment considerations for linear time invariant m input p output systems by means of static output feedback is presented for the case in which the number of inputs m and the number of outputs p are less than the order of the system n this algorithm determines the output feedback matrix required to assign max p m 1 poles and simultaneously calculates the coefficients of the residual polynomial the roots of which are the remaining unassigned poles the root locus method is used to find an appropriate feedback gain to provide acceptable locations for the unassigned poles some numerical examples are provided to illustrate this method

perturbation theory of output feedback pole assignment perturbation theory for output feedback eigenstructure assignment is considered the analysis is based on general conditions for eigenstructure assignment together with the well known perturbation theory for the pseudo inverse of a matrix this enables us to present a variety of sensitivity analyses for this problem and to indicate some precautions when choosing eigenvectors in the pole assignment problem

liapunov and covariance controllers the early work of liapunov produced some of the most powerful tools for stability analysis that remain to this day to capture the class of all stabilizing controllers one would be well served by posing the problem in terms of the existence of a liapunov function since a liapunov function is known to exist for stable systems for linear systems this paper derives the set of all quadratic liapunov functions for output feedback control problems and in this way parametrizes the set of all stabilizing controllers of fixed order this is a unifying framework from which all other controllers can be produced by special choices of the free parameters in these controllers we will show how to choose the free parameters to produce all covariance controllers and all h controllers of fixed order these results also apply to robustness analysis and provide a closed form expression for the set of all stabilizing real structured perturbations due to the assignment of a matrix property to the system e g covaria

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

new criteria for blind deconvolution of nonminimum phase systems channels a necessary and sufficient condition for blind deconvolution without observing the input of nonminimum phase linear time invariant systems channels is derived based on this condition several optimization criteria are proposed and their solution is shown to correspond to the desired response these criteria involve the computation only of second and fourth order moments implying a simple tap update procedure the proposed methods are universal in the sense that they do not impose any restrictions on the probability distribution of the unobserved input sequence it is shown that in several important cases e g when the additive noise is gaussian the proposed criteria are essentially unaffected

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

analysis and synthesis of robust control systems via parameter dependent lyapunov functions in this paper the problem of robust stability of systems subject to parametric uncertainties is considered sufficient conditions for the existence of parameter dependent lyapunov functions are given in terms of a criterion which is reminiscent of but less conservative than popov s stability criterion an equivalent frequency domain criterion is demonstrated the relative sharpness of the proposed test and existing stability criteria is then discussed the use of parameter dependent lyapunov functions for robust controller synthesis is then considered it is shown that the search for robustly stabilizing controllers may be limited to controllers with the same order as the original plant a possible synthesis procedure and a numerical example are then discussed

on the existence of linear optimal control with output feedback a necessary and sufficient condition is established for the existence of an output feedback u ky that is lq optimal with respect to some nonsingular quadratic cost a fact that entails robustness in the closed loop systems it is shown that if the system with equal number of inputs and outputs is strict minimum phase and has nonsingular high frequency gain then there exists a linear static output feedback that minimizes a certain quadratic cost functional the minimization of h infty norm of the closed loop system with output feedback is also discussed

computational design techniques for reduced order compensators the authors propose two computational techniques for the pole placement problem using reduced order compensators computationally efficient algorithms are presented for the observer based compensator and the brasch pearson compensator the key tool for these algorithms is the concept of two coupled sylvester equations the solutions of which completely characterize the desired reduced order compensators

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

full diversity blind space time block codes in this paper the systematic design of a space time block code is considered for a wireless communication system with multiple transmitter receiver antennas and flat fading in which channel state information is completely unknown from the viewpoint of blind signal processing a necessary and sufficient condition is given for the unique identification of the multi input multi output flat fading channel and transmitted signal then some novel unique factorizations for a pair of coprime p ary and q ary phase shift keying psk constellations are established with this and currently available coherent space time block code designs a method is developed to systematically construct full diversity blind nonunitary space time block codes as well as unitary codes by just performing the qr decomposition of the nonunitary codes it is proved that under a noise free environment the code design proposed in this paper can guarantee that the transmitted signals and the channel coefficients are uniquely identified and that under a complex gaussian noise environment in which pth order and q th order statistics p and q are co prime of the received signals are available the channel coefficients can be still uniquely identified in addition a closed form solution to determine the channel coefficients is obtained

convergence of a numerical algorithm for calculating optimal output feedback gains a sequential numerical algorithm is described which obtains gains minimizing a broad class of performance indexes including the standard lq case the primary contribution is a proof that the algorithm converges to a local minimum under nonrestrictive assumptions numerical examples illustrate the theory the second example demonstrates an important lq design technique which permits the designer to prespecify the feedback structure subject to the requirement of output feedback stabilizability