output feedback stabilization for uncertain systems constrained riccati approach in this paper the problem of output feedback stabilization of linear systems with mismatched uncertainties is investigated a new approach to the design of output feedback controller is proposed and the respective output feedback gains are obtained through the solution of a riccati equation with linear constraints solvability conditions for such a constrained riccati problem are derived and a systematic algorithm for obtaining an output feedback controller which guarantees the system state is globally exponentially stable is provided

technical communique design of static output feedback controller for uncertain systems this paper considers the problem of designing a single static output feedback stabilizing controller for a finite set of linear systems for this purpose a set of square equal number of inputs and outputs minimum phase systems is considered using the notions of quadratic stabilizability the existence of output feedback controller is derived in terms of the solvability of a set of matrix inequalities then the existence of the solution of such inequalities are derived for special class of systems it is proved that a set of partially commutative or partially normal systems are stabilizable by a single static output feedback controller these classes of systems are shown to be different from the well known matched uncertain systems and considered to be new classes of systems an algorithm is also presented to compute the controller gain

characterization of robust controllers abstract this paper presents a procedure for designing a robust controller which is able to stabilize a multivariable system with interval uncertainties in the system parameters the uncertain parameters are assumed to lie within known intervals the fundamental idea behind the procedure is to characterize the set of robust controllers as a convex set by the new matrix inequalities result a suitable controller can then be chosen by means of an optimization algorithm the controller thus chosen will be able to ensure that the closed loop matrix lies within desired intervals for all the prescribed interval uncertainties in the system parameters

on discrete time output feedback min max controllers in this paper a constructive design procedure is presented that solves the problem of realizing stabilizing discrete time min max controllers via measured outputs for non square systems with matched uncertainties the conditions for the existence of such a controller will be given and a parameterization of the available design freedom will be proposed an explicit procedure explains how a lyapunov matrix which satisfies both the discrete riccati inequality and a structural constraint is obtained a numerical linear matrix inequality based method to optimally select the lyapunov matrix so that the computable upper bound on the allowable uncertainty is maximized is suggested the results of this paper will be illustrated by an aircraft example

theoretical and empirical estimates of mean variance portfolio sensitivity abstract this paper studies properties of an estimator of mean variance portfolio weights in a market model with multiple risky assets and a riskless asset theoretical formulas for the mean square error are derived in the case when asset excess returns are multivariate normally distributed and serially independent the sensitivity of the portfolio estimator to errors arising from the estimation of the covariance matrix and the mean vector is quantified it turns out that the relative contribution of the covariance matrix error depends mainly on the sharpe ratio of the market portfolio and the sampling frequency of historical data theoretical studies are complemented by an investigation of the distribution of portfolio estimator for empirical datasets an appropriately crafted bootstrapping method is employed to compute the empirical mean square error empirical and theoretical estimates are in good agreement with the empirical values being in general higher

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

boundaries of the risk aversion coefficient should we invest in the global minimum variance portfolio due to estimation risk the portfolios on the efficient frontier can be statistically indistinguishable from the global minimum variance portfolio we provide a methodology for determining a bound on the risk aversion coefficient which separates portfolios that are equivalent or significantly different from the global minimum variance gmv portfolio we conclude that investing in the gmv portfolio is statistically justified for investors with a very wide range of the risk aversion coefficients

the distribution of the sample minimum variance frontier in this paper we present a finite sample analysis of the sample minimum variance frontier under the assumption that the returns are independent and multivariate normally distributed we show that the sample minimum variance frontier is a highly biased estimator of the population frontier and we propose an improved estimator of the population frontier in addition we provide the exact distribution of the out of sample mean and variance of sample minimum variance portfolios this allows us to understand the impact of estimation error on the performance of in sample optimal portfolios

a sufficient condition of output feedback stabilization of uncertain systems a sufficient condition is derived for the existence of an output constant gain feedback controller which stabilizes a single input single output dynamical system with a linear nominal part and matched uncertainties the sufficient condition is significantly less restrictive than a recently derived one 1 if such a controller exists it may readily be computed

output feedback stabilization of uncertain dynamical systems given an uncertain dynamical system with a linear nominal part matched uncertainties and a measured output a sufficient condition is given for the existence of an output feedback stabilizing controller for the general multiinput multioutput case checking the sufficient condition involves the selection of a matrix f for the special class of single input single output systems f is a positive or negative scalar and it is shown that if the nominal system transfer function is strictly positive real then an output feedback stabilizing controller does indeed exist

output feedback control of uncertain coupled systems the stabilization of uncertain dynamical systems on n that admit a decomposition into two coupled subsystems of dimension nc and nr respectively is studied we refer to the nc dimensional sybsystem as the reduced order system and to the nr dimensional subsystem as the residual system the overall n dimensional system is termed the full system the prototype for which is a mechanical model arising in the study of the active control of structures each subsystem is modelled by a differential equation with a linear nominal part and a nonlinear perturbation of a specified class the output available for feedback purposes is an nc valued linear combination of the state components of the full system and is subject to bounded measurement noise with known bound an output feedback strategy is described and sufficient conditions are obtained for the existence of a calculable global uniform compact attractor containing the state origin for controlled systems of this class

robust decentralized stabilization of a class of linear discrete time systems with non linear interactions this paper deals with robust stabilization of a class of linear discrete time systems under non linear perturbations via output feedback a bound on the non linear perturbations is maximized in the design it is shown that degree of freedoms by the introduction of instrumental variables employed in this paper lead to much flexibility in obtaining both a robust output feedback controller and a maximal allowable bound of the non linear perturbations an improved method involving linear matrix inequalities are suggested to solve the matrix inequalities characterizing a solution of the robust stabilization problem consequently the proposed method can yield a much less conservative result than that of earlier methods of major interest is an extension to a class of interconnected systems composed of linear subsystems with non linear interactions a robust decentralized controller is presented such that the closed loop systems are maximally tolerant to interconnected non linear couplings numerical examples i

dominating estimators for minimum variance portfolios abstract in this paper we derive two shrinkage estimators for minimum variance portfolios that dominate the traditional estimator with respect to the out of sample variance of the portfolio return the presented results hold for any number of assets d 4 and number of observations n d 2 the small sample properties of the shrinkage estimators as well as their large sample properties for fixed d but n and n d but n d q are investigated furthermore we present a small sample test for the question of whether it is better to completely ignore time series information in favor of naive diversification

an extended stochastic finite element method for solving stochastic partial differential equations on random domains abstract recently a new strategy was proposed to solve stochastic partial differential equations on random domains it is based on the extension to the stochastic framework of the extended finite element method x fem this method leads by a direct calculus to an explicit solution in terms of the variables describing the randomness on the geometry it relies on two major points the implicit representation of complex geometries using random level set functions and the use of a galerkin approximation at both stochastic and deterministic levels in this article we detail the basis of this technique from theoretical and technical points of view several numerical examples illustrate the efficiency of this method and compare it to other approaches

estimation of the global minimum variance portfolio in high dimensions abstract we estimate the global minimum variance gmv portfolio in the high dimensional case using results from random matrix theory this approach leads to a shrinkage type estimator which is distribution free and optimal in the sense of minimizing the out of sample variance its asymptotic properties are investigated assuming that the number of assets p depends on the sample size n such that p n c 0 as n tends to infinity the results are obtained under weak assumptions imposed on the distribution of the asset returns only the existence of the fourth moments is required furthermore we make no assumption on the upper bound of the spectrum of the covariance matrix as a result the theoretical findings are also valid if the dependencies between the asset returns are described by a factor model which appears to be very popular in the financial literature nowadays this is also documented in a numerical study where the small and large sample behavior of the derived estimator is compared with existing estimators of the gmv portfolio the resulting estimator shows significant improvements and it turns out to be robust if the assumption of normality is violated

a new class of stabilizing controllers for uncertain dynamical systems this paper is concerned with the problem of designing a stabilizing controller for a class of uncertain dynamical systems the vector of uncertain parameters q cdot is time varying and its values q t lie within a prespecified bounding set q in r p furthermore no statistical description of q cdot is assumed and the controller is shown to render the closed loop system practically stable in a so called guaranteed sense that is the desired stability properties are assured no matter what admissible uncertainty q cdot is realized within the perspective of previous research in this area this paper contains one salient feature the class of stabilizing controllers which we characterize is shown to include linear controllers when the nominal system happens to be linear and time invariant in contrast in much of the previous literature see for example 1 2 7 and 9 a linear system is stabilized via nonlinear control another feature of this paper is the fact that the

distributional properties of portfolio weights in this paper we prove several distributional properties for optimal portfolio weights the weights are estimated by replacing the parameters with the sample counterparts all results for finite samples are made assuming normally distributed returns we calculate the exact covariances for the weights obtained by the expected quadratic utility additionally we derive the multivariate density function of the global minimum variance portfolio and the univariate density of the tangency portfolio we obtain the conditional density for the sharpe ratio optimal weights and show that the expectations of the sharpe ratio optimal weights do not exist moreover we determine the asymptotic distributions of the estimated weights assuming that the returns follow a multivariate stationary gaussian process

a sufficient condition for output feedback stabilization of uncertain dynamical systems a different proof than the one given by e zeheb ibid vol ac 31 p 1055 7 nov 1986 is given for the existence of an output feedback controller which stabilizes an uncertain single input single output dynamical system with a linear nominal part and matched uncertainties however there is no need to assume that the nominal system is stable a simple expression is obtained for the feedback gain which is necessary for the closed loop nominal system to become strictly positive real

statistical data analysis and inference prologue c radhakrishna rao s contributions to statistics y dodge nonlinear estimation in linear models f hampel on the maximum number of factors in two construction methods for orthogonal arrays a s hedayat j stufken some geometrical aspects of data analysis and statistics j m oller inferences and test of hypotheses on bayes and empirical bayes two stage allocation procedures for selection problems s s gupta t c liang multi sample functional statistical data analysis e parzen discussing truth or falsity by computing a q value w schaafsma j tolboom b van der meulen linear pivotals and the bayes non bayes compromise g a barnard bayes modified minimax experimental design r v canfield a simple class of tests locally better than the score test t k chandra comparison of tests in the presence of a nuisance parameter r mukerjee tests for redundancy of some variables in multivariate analysis y fujikoshi model choice in the context of simultaneous inference t havranek o soudsky first zeros of empirical characteristic functions and extreme values of gaussian processes j husler parameter and variance estimation comparison of experiments with weighted distributions m j bayarri m h de groot optimal estimation for weighted distributions semi parametric models v p godambe m b rajarshi on efficiency for quasi likelihood and composite quasi likelihood methods c c heyde improved estimators of dispersion of an inverse gaussian distribution n pal b k sinha applications of edgeworth expansions to bootstrap a review g j babu dual poincare type inequalities via the cramer rao and the cauchy schwarz inequalities and related characterizations th cacoullos some optimality results on stein s two stage sampling j k ghosh r mukerjee the cramer frechet rao inequality for sequential estimation in non regular case z govindarajulu i vincze whither delete k jackknifing for smooth statistical functionals p k sen distributions weighted distributions and characterization three useful expressions for expectations involving a wishart matrix and its inverse g p h styan characterizations of distributions via moments of order statistics a survey and comparison of methods g d lin constancy of regression of a polynomial of sample average of positive random variables on their ratios characterizes gamma distribution a kagan probing encountered data meta analysis and weighted distribution methods g p patil c taillie further results on identification when the parameters are partially unknown s el khattabi f streit linear models and matrices weighted least squares estimation in the general gauss markov model j k baksalary s puntanen evaluating pre test predictors of success in linear regression models a cohen h b sackrowitz optimum invariant tests in mixed linear models with two variance components th mathew

a stochastic collocation method for elliptic partial differential equations with random input data in this paper we propose and analyze a stochastic collocation method to solve elliptic partial differential equations with random coefficients and forcing terms input data of the model the input data are assumed to depend on a finite number of random variables the method consists in a galerkin approximation in space and a collocation in the zeros of suitable tensor product orthogonal polynomials gauss points in the probability space and naturally leads to the solution of uncoupled deterministic problems as in the monte carlo approach it can be seen as a generalization of the stochastic galerkin method proposed in i babuscka r tempone and g e zouraris siam j numer anal 42 2004 pp 800 825 and allows one to treat easily a wider range of situations such as input data that depend nonlinearly on the random variables diffusivity coefficients with unbounded second moments and random variables that are correlated or even unbounded we provide a rigorous convergence analysis and demonstrate exponential convergence of the probability error with respect to the number of gauss points in each direction in the probability space under some regularity assumptions on the random input data numerical examples show the effectiveness of the method

extended stochastic finite element method for the numerical simulation of heterogeneous materials with random material interfaces an extended stochastic finite element method has been recently proposed for the numerical solution of partial differential equations defined on random domains this method is based on a marriage between the extended finite element method and spectral stochastic methods in this article we propose an extension of this method for the numerical simulation of random multi phased materials the random geometry of material interfaces is described implicitly by using random level set functions a fixed deterministic finite element mesh which is not conforming to the random interfaces is then introduced in order to approximate the geometry and the solution classical spectral stochastic finite element approximation spaces are not able to capture the irregularities of the solution field with respect to spatial and stochastic variables which leads to a deterioration of the accuracy and convergence properties of the approximate solution in order to recover optimal convergence properties of the approximation we propose an extension of the partition of unity method to the spectral stochastic framework this technique allows the enrichment of approximation spaces with suitable functions based on an a priori knowledge of the irregularities in the solution numerical examples illustrate the efficiency of the proposed method and demonstrate the relevance of the enrichment procedure copyright 2010 john wiley sons ltd

modified output error identification elimination of the spr condition in this note we present a modified adaptive output error algorithm for identification we refer to both the continuous time and the discrete time cases in the standard algorithm stability requires that a certain transfer function should be strictly positive real spr however in the present algorithm the spr condition which is difficult to satisfy is eliminated this is achieved by adding a fixed feedback gain when there exists an a priori partial knowledge about the parameters of the plant we provide a simple procedure to design that gain an illustrative example comparing the modified algorithm to the standard one is provided