on undershoot and nonminimum phase zeros in this note we derive a simple necessary and sufficient condition for a stable system to exhibit an undershooting step response specifically we show that undershoot occurs if and only if the plant has an odd number of real right half plane zeros

perfect and subperfect regulation in linear multivariable control systems this paper is concerned with the synthesis of a high gain feedback control called perfect regulation p r for linear multivariable systems with external signals the existence condition for p r is derived in which the minimum phase property plays an essential role the use of an observer is discussed for achieving p r under restricted state observation some asymptotically ideal feedback properties are demonstrated such as the complete desensitization the complete servo performance with decoupling and the complete disturbance rejection which formulate the loop tightness for multivariable systems a design method for applying p r to non minimum phase systems called subperfect regulation s p r is proposed based on the factorization of the plant transfer function matrix into the minimum phase part and the totally non minimum phase part it is a multivariable extension of a well known design technique for scalar systems to overcome the difficulty of phase non minimality computational procedures for p r and s p r are discussed an illustrative example is shown

conditional cumulant of exposure method in logistic missing covariate regression summary we consider estimation in logistic regression where some covariate variables may be missing at random satten and kupper 1993 journal of the american statistical association88 200 208 proposed estimating odds ratio parameters using methods based on the probability of exposure by approximating a partial likelihood we extend their idea and propose a method that estimates the cumulant generating function of the missing covariate given observed covariates and surrogates in the controls our proposed method first estimates some lower order cumulants of the conditional distribution of the unobserved data and then solves a resulting estimating equation for the logistic regression parameter a simple version of the proposed method is to replace a missing covariate by the summation of its conditional mean and conditional variance given observed data in the controls we note that one important property of the proposed method is that when the validation is only on controls a class of inverse selection probability weighted semiparametric estimators cannot be applied because selection probabilities on cases are zeros the proposed estimator performs well unless the relative risk parameters are large even though it is technically inconsistent small sample simulations are conducted we illustrate the method by an example of real data analysis

the inverse mean curvature flow and the riemannian penrose inequality let m be an asymptotically flat 3 manifold of nonnegative scalar curvature the riemannian penrose inequality states that the area of an outermost minimal surface n in m is bounded by the adm mass m according to the formula n 16 m 2 we develop a theory of weak solutions of the inverse mean curvature flow and employ it to prove this inequality for each connected component of n using geroch s monotonicity formula for the adm mass our method also proves positivity of bartnik s gravitational capacity by computing a positive lower bound for the mass purely in terms of local geometry

optimal h sup infinity norm computation for multivariable systems with multiple zeros b c chang and j b peason s see ibid vol ac 29 p 880 7 oct 1984 computation of the optimal h sup infinity norm is generalized to the case with multiple right half plane zeros d sarason s 1967 interpolation theory is used to reduce the problem to a simple eigenvalue or singular value computation

computation of transmission zeros for distributed parameter systems the transmission zeros for a class of distributed parameter systems are defined as the limit points of the spectrum as the feedback gain increases to infinity a simple criterion which characterizes the transmission zeros different from the system operators spectrum is found the case when the transmission zeros belong to the spectrum is also discussed the presented theory is clarified with an example

characterization of all controlled invariant subspaces for spectral systems for a class of spectral systems a complete characterization of all controlled invariant subspaces contained in a closed subspace will be given this characterization is given in terms of the invariant zeros of the transfer function as a consequence of this we derive necessary and sufficient conditions for the existence of v operatorname ker c the largest controlled invariant subspace in the kernel of c

a nonparametric method for dealing with mismeasured covariate data abstract mismeasurement of covariate data is a frequent problem in statistical data analysis however when true and mismeasured data are obtained for a subsample of the observations it is possible to estimate the parameters relating the outcome to the covariate of interest maximum likelihood methods that rely on parametric models for the mismeasurement have not met with much success realistic models for the mismeasurement process are difficult to construct the form of the likelihood is often intractable and more important such methods are not robust to model misspecification we propose an easily implemented method that is nonparametric with respect to the mismeasurement process and that is applicable when mismeasurement is due to the problem of missing data errors in variables or use of imperfect surrogate covariates specifically denote the outcome variable by y the covariate data subject to mismeasurement by x and the remaining covariates including perhaps surrogates or mismeasured values

logistic regression with incompletely observed categorical covariates a comparison of three approaches summary a logistic regression analysis based on the complete cases neglects the information due to subjects with missing values in at least one but not in all covariates three different approaches allowing the use of this information are compared maximum likelihood estimation pseudo maximum likelihood estimation and probability imputation the first two yield consistent estimates of the regression coefficients and asymptotic normality allows the construction of asymptotically valid confidence intervals the only necessary assumption is that the probability for the occurrence of missing values does not depend on the true value of the hidden covariates whereas there may be a dependence on completely observed covariates and on the outcome variable their relative efficiency and the gain relative to a complete case analysis is investigated comparison with imputation methods shows that imputation of conditional probabilities can be regarded as a close approximation to the pseudo maximum likelihood estimation whereas imputation of unconditional probabilities is associated with serious bias

choice of sampling to ensure minimum phase behaviour sufficient conditions for ensuring that a continuous stable proper minimum phase plant remains minimum phase when sampled have been derived as a corollary the critical sampling frequency the fastest sampling frequency ensuring minimum phase behaviour is shown to satisfy a simple equation an engineering method to obtain the critical sampling by use of a relay is proposed this method requires no prior knowledge of the plant

deformations of the hemisphere that increase scalar curvature consider a compact riemannian manifold m of dimension n whose boundary m is totally geodesic and is isometric to the standard sphere s n 1 a natural conjecture of min oo asserts that if the scalar curvature of m is at least n n 1 then m is isometric to the hemisphere s n equipped with its standard metric this conjecture is inspired by the positive mass theorem in general relativity and has been verified in many special cases in this paper we construct counterexamples to min oo s conjecture in dimension n 3

special coordinate basis for multivariable linear systems finite and infinite zero structure squaring down and decoupling abstract a special coordinate basis for multivariable linear systems is introduced here several fundamental properties of linear systems regarding controllability stabiliza bility observability detectability invariant zeros decoupling zeros infinite zero structure effect of feedback on zero structure squaring down diagonal and triangular decoupling etc can be directly displayed in terms of the special coordinate basis moreover connections between the special coordinate basis and the important invariant subspaces of the geometric theory of linear systems are established

on the riemannian penrose inequality in dimensions less than eight the positive mass theorem states that a complete asymptotically flat manifold of nonnegative scalar curvature has nonnegative mass and that equality is achieved only for the euclidean metric the riemannian penrose inequality provides a sharp lower bound for the mass when black holes are present more precisely this lower bound is given in terms of the area of an outermost minimal hypersurface and equality is achieved only for schwarzschild metrics the riemannian penrose inequality was first proved in three dimensions in 1997 by g huisken and t ilmanen for the case of a single black hole see hi in 1999 bray extended this result to the general case of multiple black holes using a different technique see br in this article we extend the technique of br to dimensions less than eight part of the argument is contained in a companion article by lee l the equality case of the theorem requires the added assumption that the manifold be spin

multivariate logistic models for incomplete binary responses abstract in this article we describe a likelihood based regression model appropriate for analyzing incomplete multivariate binary responses we focus on marginal models that is models where the marginal mean or expectation of the binary response is related to a set of covariates the association between the binary responses is modeled in terms of conditional log odds ratios when the nonresponse mechanism is ignorable it is not necessary to specify a nonresponse model and valid inferences can be obtained provided that the likelihood for the responses has been correctly specified but when the nonresponse mechanism is nonignorable valid inferences can only be obtained by incorporating a model for nonresponse an unresolved issue with nonignorable models concerns the identifiability of the parameters so far no general and practically useful necessary and sufficient conditions for identifiability are available here we suggest some simple procedures for examining the identifiability status of nonign

determination of invariant zeros and zero directions of the system s a b c e mita 1977 presented a simple method for the invariant zeros of a linear multivariable system by constructing its maximal unobservable subspace mus however the results of this method have been restricted to a class of controllable and right invertible systems satisfying the diagonal decoupling condition and described by the triple a b c here a general method based on the theory of decoupling extends mita s results for all classes of systems described by the 4 tuples a b c e with no special requirements the mus of all classes of such systems is simply constructed and its order is given in terms of the system order n and the infinite zeros or the minimal observability indices of the system in addition the invariant zeros and zero directions are found from the eigenvalues and eigenvectors of a reduced order matrix having the dimension of the mus obtained directly from the state space parameters algorithms are presented for the invariant zeros and zero directions of invertible decouplable o

the transmission zeros of systems with delays in this paper we study the properties of the zeros of a system with general delays in the input state and control variables the main result of this paper shows that the zeros of the transfer function are always zeros of the system matrix with of at least the same multiplicity moreover when the system is canonical the zeros of the system matrix are zeros of the transfer function with the same multiplicity

sampling infinite zeros and decoupling of linear systems abstract in order to understand more fully some of the trade offs involved in using a sampled data representation of a continuous time system the effects of time sampling on the ability to achieve disturbance decoupling and input output decoupling for linear systems are investigated it is shown that disturbance decouplability is lost through sampling whereas row by row dynamic input output decouplability is preserved in a very strong way these results are obtained by analyzing the structure at infinity of a sampled data system

a treatment of jw axis model matching transformation zeros in the optimal h sup 2 and h sup infinity control designs a model matching transformation mmt zero is defined as a rank deficiency condition which prevents an h sup 2 or h sup infinity optimal control problem from being transformed into an equivalent model matching problem by imposing saturation constraints and accounting for additive instrument noise in the sensor and actuator signals all mmt zeros can be eliminated

on the generalized nyquist stability criterion the purpose of this paper is to provide a self contained proof of the generalized nyquist stability criterion the frequency dependent eigenvalues of a square transfer function matrix g 8 are defined directly from a matrix fraction decomposition of g 8 and a discussion of the fixed modes and fixed gains is given the theory of algebraic functions and riemann surfaces is employed in the proof and a detailed consideration is given to these theoretical ideas from the point of view of the stability result the question of the relationship between the poles and zeros of an algebraic function in the complex variable sense and the poles and zeros in the smith mcmillan sense is carefully examined and a proof of the argument principle for a regular region on a riemann surface is given

the mass of an asymptotically flat manifold we show that the mass of an asymptotically flat n manifold is a geometric invariant the proof is based on harmonic coordinates and to develop a suitable existence theory results about elliptic operators with rough coefficients on weighted sobolev spaces are summarised some relations between the mass scalar curvature and harmonic maps are described and the positive mass theorem for n dimensional spin manifolds is proved

paper self tuning control of nonminimum phase systems the instability that arises from the pole zero cancellation of elementary self tuners and most mrac algorithms has given rise to a misapprehension that nonminimum phase systems can pose insoluble problems with the application of adaptive control since most practical processes exhibit some form of nonminimum phase behaviour particularly when controlled digitally this appeared to restrict the usefulness of self tuning methods however during the last few years new algorithms have been suggested which partly overcome these difficulties and have been shown to be effective in industrial trials the paper describes the practical features that a self tuning controller must possess and discusses how plant dead time and excess continuous time poles can lead to discrete time nonminimum phase zeros the source of instability of elementary self tuners is analysed and various suggested approaches for overcoming this problem are reviewed these include the use of a generalized minimum variance cost function incorporating control weighting factorization methods which avoid cancellation of the offending zeros adaptive control based on state space linear quadratic gaussian lqg theory and explicit pole placement via solution of a diophantine or bezoutian equation gawthrop s hybrid controller which avoids those nonminimum phase zeros due to continuous time pole excess is briefly discussed a series of simulations in which a nonminimum phase plant is subjected to a pattern of set point changes is presented to show some of the features of the algorithms in applications the order of the process is unlikely to be known or indeed be finite the pole placement algorithm which is particularly effective in the known order case is shown to lack robustness to underspecified order the use of a large control weighting however restores stability to the generalized minimum variance controller the conclusions are that with appropriate design and engineering judgement adaptive control is viable even for nonminimum phase processes

an exact characterization of linear systems with zeros everywhere in the complex plane in this note an exact characterization of autonomous linear multivariable systems with zeros everywhere in the complex plane is given in terms of the system matrices such systems are called degenerate an important consequence of this characterization is that nondegeneracy is equivalent to the concept of functional reproducibility introduced by brockett and mesarovic based on this equivalence a new test for nondegeneracy in terms of the functional reproducibility matrix is derived an example is included to show that controllability observability and output controllability are not sufficient to guarantee the nondegeneracy of a linear system

a parameter adaptive control structure for linear multivariable systems this paper presents an adaptive control structure which can be used to assign all poles and zeros of a continuous time linear multivariable system represented by an m times m strictly proper transfer matrix t s provided t s has no right half plane zeros the controller parameters can be directly estimated from input output data the paper also serves to point out the type of a priori information necessary for multivariable adaptive controller design this information is a natural extension of that required in the scalar case

optimal design of non minimum phase control systems with large plant uncertainty abstract a given linear time invariant controlled plant with non minimum phase and or unstable transfer function is considered that has significant plant parameter uncertainty but the ranges of the uncertain parameters are known it is desired that in response to a deterministic input over the entire range of parameter uncertainty the system output should lie with specified bounds a practical optimal design procedure that has been presented in the authors previous work is extended to deal with this problem furthermore the design philosophy is modified so that the two degree of freedom system configuration can be simplified

infinite structure and exact model matching problem a geometric approach we first generalize to a b c d quadruples the geometric characterization of the infinite zero structure we then give a new geometric proof for a solvability condition of the exact model matching problem expressed in terms of this concept and previously established in the polynomial context by morse verghese and pernebo this emphasizes the approach independent character of the infinite zero structure

the poles and zeros of a linear time varying system abstract for linear time varying discrete time and continuous time systems a notion of poles and zeros is developed in terms of factorizations of operator polynomials with time varying coefficients in the discrete time case it is shown that the poles can be computed by solving a nonlinear recursion with time varying coefficients in the continuous time case the poles can be calculated by solving a nonlinear differential equation with time varying coefficients the theory is applied to the study of the zero input response and asymptotic stability it is shown that if a time varying analogue of the vandermonde matrix is invertible the zero input response can be decomposed into a sum of modes associated with the poles stability is then studied in terms of the components of the modal decomposition

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

decentralized determinantal assignment problem fixed and almost fixed modes and zeros the decentralized determinantal assignment problem ddap is defined as the unifying description for the study of pole and zero assignment problems under decentralized output state feedback dof dsf and decentralized squaring down dsd respectively ddap is reduced to a linear problem of zero assignment of polynomial combinants and a multilinear problem of restricted decomposability of multivectors the decentralization characteristic dc and the decentralized polynomial grassmann representative d s gr of ddap are defined the fixed zero polynomial of ddap is then determined as the zero polynomial of d s gr the canonical d s gr cd r s gr and the decentralized plucker matrix dpm of ddap are introduced and necessary conditions for arbitrary assignment of the non fixed zeros are given in terms of the dpm the family of strongly zero non assignable sna systems is defined and for such systems the notion of the fixed zero is extended to that of the almost fixed zero afz an

scalar curvature deformation and a gluing construction for the einstein constraint equations on a compact manifold the scalar curvature map at generic metrics is a local surjection f m we show that this result may be localized to compact subdomains in an arbitrary riemannian manifold the method is extended to establish the existence of asymptotically flat scalar flat metrics on n n 3 which are spherically symmetric hence schwarzschild at infinity i e outside a compact set such metrics provide cauchy data for the einstein vacuum equations which evolve into nontrivial vacuum spacetimes which are identically schwarzschild near spatial infinity

inverse stable sampled low pass systems it is shown that for low pass systems the fractional order hold and the pulse amplitude modulation signal reconstruction methods produce an inverse stable sampled transfer function h z in some cases when zero order hold fails to do so therefore they may be desirable alternatives to the zero order hold reconstruction in certain control problems the problem of how well h z models the continuous g s is also discussed

maximum likelihood estimation and model selection in contingency tables with missing data abstract in many studies the values of one or more variables are missing for subsets of the original sample this article focuses on the problem of obtaining maximum likelihood estimates mle for the parameters of log linear models under this type of incomplete data the appropriate systems of equations are presented and the expectation maximization em algorithm dempster laird and rubin 1977 is suggested as one of the possible methods for solving them the algorithm has certain advantages but other alternatives may be computationally more effective tests of fit for log linear models in the presence of incomplete data are considered the data from the protective services project for older persons blenkner bloom and nielsen 1971 blenkner bloom and weber 1974 are used to illustrate the procedures discussed in the article

maximum likelihood estimation for mixed continuous and categorical data with missing values summary maximum likelihood procedures for analysing mixed continuous and categorical data with missing values are presented the general location model of olkin tate 1961 and extensions introduced by krzanowski 1980 1982 form the basis for our methods maximum likelihood estimation with incomplete data is achieved by an application of the em algorithm dempster laird rubin 1977 special cases of the algorithm include orchard woodbury s 1972 algorithm for incomplete normal samples fuchs s 1982 algorithms for log linear modelling of partially classified contingency tables and day s 1969 algorithm for multivariate normal mixtures applications include a imputation of missing values b logistic regression and discriminant analysis with missing predictors and unclassified observations c linear regression with missing continuous and categorical predictors and d parametric cluster analysis with incomplete data methods are illustrated using data from the st louis risk research project some key word8 cluster analysis discriminant analysis em algorithm incomplete data linear regression logistic regression log linear model mixture model

covariate measurement error in generalized linear models summary the em algorithm is used to obtain estimators of regression coefficients for generalized linear models with canonical link when normally distributed covariates are masked by normally distributed measurement errors by casting the true covariates as missing data the em procedure suggests an iterative scheme in which each cycle consists of an e step requiring the computation of approximate first and second conditional moments of the true covariates given the observed data followed by an m step in which regression parameters are updated by iteratively reweighted least squares based on these approximations the proposed procedure is compared numerically with the exact maximum likelihood solution obtained by using gaussian quadrature instead of the approximations in the e step of the em algorithm and with alternative estimators for simple logistic regression with measurement error the results for the proposed procedure are encouraging a procedure is proposed in this paper for estimating regression coefficients in generalized linear models when one or more of the covariates is measured with error this work is related to the paper by carroll et al 1984 in which maximum likelihood estimates are considered for the structural logistic regression model these authors provide estimates for the computationally simpler probit regression model and suggest that the structural logistic regression can be done in principle this paper follows up on that suggestion but differs in detail from similar work by armstrong 1985 other procedures with related aims have been suggested by stefanski carroll 1985 wolter fuller 1982 and prentice 1982 for a quick introduction to the proposed method it is convenient to display the naive estimator which ignores measurement error in its standard computational form if yi is an observed response variable and xi is the observed covariate then for the model which equates the canonical parameter of the distribution of yi to xtf3 the maximum likelihood estimator of f3 can be obtained by iteratively reweighted least squares the estimate of f3 after s 1 cycles is given by

the equality case of the penrose inequality for asymptotically flat graphs we prove the equality case of the penrose inequality in all dimensions for asymptotically flat hypersurfaces it was re cently proven by g lam 19 that the penrose inequality holds for asymptotically flat graphical hypersurfaces in euclidean space with non negative scalar curvature and with a minimal boundary our main theorem states that if the equality holds then the hy persurface is a schwarzschild solution as part of our proof we show that asymptotically flat graphical hypersurfaces with a min imal boundary and non negative scalar curvature must be mean convex using the argument that we developed in 15 this en ables us to obtain the ellipticity for the linearized scalar curvature operator and to establish the strong maximum principles for the scalar curvature equation

vibrational feedback control zeros placement capabilities it is shown that in addition to closed loop pole placement vibrational feedback controllers lead in the sense specified below to a possibility of open loop zeros assignability on this basis the superior performance characteristics of continuous time periodic controllers discovered in 3 6 are explained

robustness with simultaneous pole and zero movement across the jω axis in this paper we present some new tests for assessing the robustness of the stability property of a feedback design the tests offer a wider scope of application than those previously described in the literature the main result is a robustness test which can be used to assess closed loop stability when the nominal plant model and perturbed plant model representing uncertainty have different numbers of poles and zeros in the right half plane this test also indicates over which frequencies good sensitivity and robust stability are compatible objectives and over which frequencies a compromise has to be made contrary to popular belief if there are no uncertain zeros which can move across the imaginary axis then good sensitivity and robust stability are compatible objectives over the same frequencies

disturbance decoupling problems via dynamic output feedback this paper considers the disturbance decoupling problems with or without internal stability and pole placement via dynamic output feedback using polynomial and rational matrix techniques we show that in all three problems considered the central solvability condition can be expressed as a two sided matching problem a bxc where a b and c are the polynomial system matrices of certain natural subsystems of the system model and x is to be determined over various subrings of the rational functions this matching problem can in turn be reduced to certain appropriate zero cancellation conditions on the polynomial system matrices a b and c

incomplete data in generalized linear models abstract this article examines incomplete data for the class of generalized linear models in which incompleteness is due to partially missing covariates on some observations under the assumption that the missing data are missing at random it is shown that the e step of the em algorithm for any generalized linear model can be expressed as a weighted complete data log likelihood when the unobserved covariates are assumed to come from a discrete distribution with finite range expressing the e step in this manner allows for a straightforward maximization in the m step thus leading to maximum likelihood estimates mle s for the parameters asymptotic variances of the mle s are also derived and results are illustrated with two examples

pseudo maximum likelihood estimation theory and applications abstract pseudo maximum likelihood estimation easily extends to k parameter models and is of interest in problems in which the likelihood surface is ill behaved in higher dimensions but well behaved in lower dimensions several signal plus noise or convolution models are examined which exhibit such behavior and satisfy the regularity conditions of the asymptotic theory for specific models a numerical comparison of asymptotic variances suggests that a psuedo maximum likelihood estimate of the signal parameter is uniformly more efficient than estimators that have been advanced by previous authors a number of other potential applications are noted

geometric invariance of mass like asymptotic invariants we study coordinate invariance of some asymptotic invariants such as the arnowitt deser misner mass or the chru ciel herzlich momentum given by an integral over a boundary at infinity when changing the coordinates at infinity some terms in the change of integrand do not decay fast enough to have a vanishing integral at infinity but they may be gathered in a divergence thus having vanishing integral over any closed hypersurface this fact could only be checked after direct calculation and was called a curious cancellation we give a conceptual explanation thereof

research on system zeros a survey this report provides a review of notable publications regarding the topic of zeros of multivariable systems in the period from 1970 into 1989 particular attention is paid to relationships between definitions of such zeros and their theoretical development transmission invariant system module infinite and finite zeros are addressed the latter subdivided into a hierarchical structure with respect to information considered in the definition process

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12

proof of the riemannian penrose inequality using the positive mass theorem we prove the riemannian penrose conjecture an important case of a con jecture 41 made by roger penrose in 1973 by defining a new flow of metrics this flow of metrics stays inside the class of asymptotically flat riemannian 3 manifolds with nonnegative scalar curvature which contain minimal spheres in particular if we consider a riemannian 3 manifold as a totally geodesic submanifold of a space time in the context of general relativity then outermost minimal spheres with total area a correspond to apparent horizons of black holes contributing a massa 16 scalar cur vature corresponds to local energy density at each point and the rate at which the metric becomes flat at infinity corresponds to total mass also called the adm mass the riemannian penrose conjecture then states that the total mass of an asymptotically flat 3 manifold with nonnegative scalar curvature is greater than or equal to the mass contributed by the black holes the flow of metrics we define continuously evolves the original 3 metric to a schwarzschild 3 metric which represents a spherically symmetric black hole in vacuum we define the flow such that the area of the minimal spheres which flow outward and hence the mass contributed by the black holes in each of the metrics in the flow is constant and then use the positive mass theorem to show that the total mass of the metrics is nonincreasing then since the total mass equals the mass of the black hole in a schwarzschild metric the riemannian penrose conjecture follows we also refer the reader to the beautiful work of huisken and ilmanen 30 who used inverse mean curvature flows of surfaces to prove that the total mass is at least the mass contributed by the largest black hole in sections 1 and 2 we motivate the problem discuss important quantities like total mass and horizons of black holes and state the positive mass theorem and the penrose conjecture for riemannian 3 manifolds in section 3 we give the proof of the riemannian penrose