a condition for robust stabilizability a family of linear time invariant finite dimensional plants is called robustly stabilizable if there exists a single controller that stabilizes each plant in the family a condition for robust stabilizability is given that requires the plant transmission zeros to remain in the left half complex plane and moreover imposes a restriction on the high frequency behavior of the plant transfer matrix

an iterative design procedure for simultaneous stabilization of mimo systems this paper considers the problem of finding one compensator which simultaneously stabilizes a family of mimo plants the family of plants bdp s q q q represented by their transfer function matrices may be uncountable thus allowing for the possibility of a continuum of variations in plant parameters a hermite invariant factorization of the plant is introduced and shown to be quite useful as far as stabilization is concerned to obtain the desired results a number of assumptions describing the set of allowable plants are imposed these assumptions include some regularity conditions on the plant and mimo versions of minimum phase and one sign high frequency gain requirements the satisfaction of these assumptions guarantees the existence of a strictly proper stable compensator c s guaranteeing simultaneous stabilization the algorithm used for controller design has one most attractive feature namely it is recursive in nature and allows the designer to select one compensator coefficient at a time

quadratic stability and stabilization of uncertain linear discrete time systems with state delay abstract this paper deals with the problem of quadratic stability analysis and quadratic stabilization for uncertain linear discrete time systems with state delay the system under consideration involves state time delay and time varying norm bounded parameter uncertainties appearing in all the matrices of the state space model necessary and sufficient conditions for quadratic stability and quadratic stabilization are presented in terms of certain matrix inequalities respectively a robustly stabilizing state feedback controller can be constructed by using the corresponding feasible solution of the matrix inequalities two examples are presented to demonstrate the effectiveness of the proposed approach

algebraic design techniques for reliable stabilization in this paper we study two problems in feedback stabilization the first is the simultaneous stabilization problem which can be stated as follows given plants g 0 g 1 g l does there exist a single compensator c that stabilizes all of them the second is that of stabilization by a stable compensator or more generally a least unstable compensator given a plant g we would like to know whether or not there exists a stable compensator c that stabilizes g if not what is the smallest number of right half place poles counted according to their mcmillan degree that any stabilizing compensator must have we show that the two problems are equivalent in the following sense the problem of simultaneously stabilizing l 1 plants can be reduced to the problem of simultaneously stabilizing l plants using a stable compensator which in turn can be stated as the following purely algebraic problem given 2l matrices a 1 a l b 1 b l where a i b i are right coprime for all i does there exist a matrix m such that a i mb i is unimodular for all i conversely the problem of simultaneously stabilizing l plants using a stable compensator can be formulated as one of simultaneously stabilizing l 1 plants the problem of determining whether or not there exists an m such that a bm is unimodular given a right coprime pair a b turns out to be a special case of a question concerning a matrix division algorithm in a proper euclidean domain we give an answer to this question and we believe this result might be of some independent interest we show that given two n times m plants g 0 and g 1 we can generically stabilize them simultaneously provided either n or m is greater than one in contrast simultaneous stabilizability of two single input single output plants g 0 and g 1 is not generic

variable bandwidth kernel estimators of regression curves on montre qu en termes de l erreur en moyenne quadratique integree asymptotique les estimateurs du noyau avec un certain choix de largeur de bande local sont superieurs aux estimateurs ordinaires du noyau avec un choix de largeur de bande global si on utilise des largeurs de bandes optimales

generalized density clustering we study generalized density based clustering in which sharply defined clusters such as clusters on lower dimensional manifolds are allowed we show that accurate clustering is possible even in high dimensions we propose two data based methods for choosing the bandwidth and we study the stability properties of density clusters we show that a simple graph based algorithm successfully approximates the high density clusters

h sub infinity control and quadratic stabilization of systems with parameter uncertainty via output feedback the article concerns linear systems which are subject to both time varying norm bounded parameter uncertainty and exogenous disturbance it addresses the robust h sub infinity control problem of designing a linear dynamic output feedback controller such that the closed loop system is quadratically stable and achieves a prescribed level of disturbance attenuation for all admissible parameter uncertainties it is shown that such a problem is equivalent to a scaled h sub infinity control problem

robust output tracking control of siso plants with multiple operating points and with parametric and unstructured uncertainties the robust output tracking control problem is considered for single input single output plants with multiple operating points and with both parametric and unstructured uncertainties i e interval parameter uncertainties and norm bounded unmodelled dynamics the parametric uncertainties can involve parameter perturbations as well as degree variations the plant with uncertainties is assumed to be of minimum phase but is not required to have a fixed number of unstable poles a new method is presented by which a linear time invariant robust controller is designed in two steps first a nominal controller is designed to get exact output tracking for the nominal plant then a robust compensator is added to achieve robust properties it is shown that robust stability robust static state property robust transient property and robust tracking property can be achieved simultaneously a computationally tractable design procedure is presented a salient feature of our results shown in the present paper is th

optimal disturbance reduction in linear multivariable systems this paper presents a computational solution to an important optimization problem arising in optimal sensitivity theory the approach is to treat the multivariable problem exactly as the scalar problem in that stability constraints are handled via interpolation the resulting computations are easily implemented using existing methods

partial identification and inference in censored quantile regression abstract in this paper we study partial identification and inference in a linear quantile regression where the dependent variable is subject to possibly unknown dependent censoring characterized by an archimedean copula an outer set of the identified set for the regression coefficient is characterized via inequality constraints for one parameter ordered families of archimedean copulas we construct a simple confidence set by inverting an asymptotically pivotal statistic a bootstrap confidence set is also constructed sensitivity of the identified set to possible misspecification of the true copula and the finite sample performance of the boostrap confidence set are investigated numerically

feedback minimax sensitivity and optimal robustness in this paper we look for feedbacks that minimize the sensitivity function of a linear single variable feedback system represented by its frequency responses sensitivity to disturbances and robustness under plant perturbations are measured in a weighted h infty norm in an earlier paper zames proposed an approach to feedback design involving the measurement of sensitivity by multiplicative seminorms which have certain advantages over the widely used quadratic norm in problems where there is plant uncertainty or where signal power spectra are not fixed but belong to sets the problem was studied in a general setting and some h infty examples were solved here a detailed study of the single variable case is undertaken the results are extended to unstable plants and explicit formulas for the general situation of a finite number of right half plane rhp plant zeros or poles are provided the q or approximate inverse parametrization of feedbacks that maintain closed loop stability is extended to the ease of unstable plants the h infty and wiener hopf approaches are compared

a law of the logarithm for kernel density estimators in this paper we derive a law of the logarithm for the maximal deviation between a kernel density estimator and the true underlying density function extensions to higher derivatives are included the results are applied to get optimal window widths with respect to almost sure uniform convergence

a direct approach to inference in nonparametric and semiparametric quantile models we construct a generic confidence interval for a conditional quantile via the direct approach it avoids estimating the conditional density function of the dependent variable given the covariate and is asymptotically valid for any conditional quantile any conditional quantile estimator and any data structure provided that certain weak convergence of the conditional quantile process holds for the original quantile estimator we also construct a generic confidence band for the conditional quantile function across a range of covariate values by using yang stute estimator and two semiparametric quantile functions we demonstrate the flexibility and simplicity of the direct approach the advantages of our new confidence intervals are borne out in a simulation study

robust stabilizability for a class of transfer functions this paper is concerned with the robust stabilizability for single input single output plants robust stabilizability means that a fixed controller can stabilize simultaneously all the plants in a given class which is characterized by a frequency dependent uncertainty band function around the transfer function of a nominal model a necessary and sufficient condition for robust stabilizability is derived based on the well known nevanlinna pick theory in classical analysis it is shown that the values of the uncertainty band function should be restricted within a certain range at the unstable poles of the nominal model in order for the class to be robustly stabilizable a procedure of synthesizing a robust stabilizer is given and the parametrization of all the robust stabilizers is also shown

parametric uncertainty and unmodeled dynamics analysis via parameter space methods abstract a number of procedures exist for determining the stability of a linear system that is subject to parametric uncertainty provided the system order is constant over the range of parameter variations this paper extends these tests to systems with parametric uncertainties that induce order change the extended tests are also shown to apply to systems with nonparametric unstructured uncertainty through an equivalent parameterization of the nonparametric uncertainty class the results are applied to the stability analysis of a crane model with a flexible cable

perturbation bounds for robust stability in linear state space models abstract this paper addresses the aspect of stability robustness of linear systems in the time domain upper bounds on the linear perturbation of an asymptotically stable linear system are obtained to maintain stability both for structured as well as unstructured perturbations using the lyapunov approach for structured perturbation the resulting bound is such that it garners the structural information about the nominal as well as the perturbation matrix into a single unified expression in the case of unstructured perturbations special features of the nominally stable matrix are exploited resulting in simpler expressions for the bound without the need to solve the lyapunov equation improvement of the proposed measures is illustrated with the help of examples

robust controllers for uncertain linear multivariable systems abstract this paper is addressed to three distinct yet related topics in the design of controllers for imprecisely known linear multivariable systems in the first part it is supposed that the plant to be stabilized is subject to additive or multiplicative uncertainties and necessary and sufficient conditions are derived for the existence of a controller that stabilizes all plants within this band of uncertainty in the second part in contrast with the first part it is supposed that the number of unstable poles of the plant to be stabilized is not precisely known the type of plant uncertainty is the so called stable factor uncertainty and necessary and sufficient conditions are given for robust stabilization in the third part the model of uncertainty is a ball in the space of rational matrices metrized by the so called graph metric and sufficient conditions for robust stabilization are derived

robust stabilizability verification of polynomially uncertain lti systems this paper investigates the stabilizability of uncertain linear time invariant lti systems via structurally constrained controllers first an lti uncertain system is considered whose state space matrices depend polynomially on the uncertainty vector defined over some region it is shown that if the system is stabilizable by a structurally constrained controller in one point belonging to the region then it is stabilizable by a controller with the same structure in all points belonging to the region except for those located on an algebraic variety thus if a system is stabilizable via a constrained controller at the nominal point then it is almost always stabilizable at any operating point around the nominal model it is also shown how this algebraic variety or the dominant subvariety of it can be computed efficiently the results obtained in this paper encompass a broad range of the existing results in the literature on robust stability of the lti systems in addition to new ones

nonparametric density estimation the l 1 view differentiation of integrals consistency lower bounds for rates of convergence rates of convergence in l1 the automatic kernel estimate l1 and pointwise convergence estimates related to the kernel estimate and the histogram estimate simulation inequalities and random variate generation the transformed kernel estimate applications in discrimination operations on density estimates estimators based on orthogonal series index

uniform consistency of automatic and location adaptive delta sequence estimators the class of delta sequence estimators for a probability density includes the kernel histogram and orthogonal series types because each can be characterized as a collection of averages of some function that is indexed by a smoothing parameter there are two important extensions of this class the first allows a random smoothing parameter for example that specified by a cross validation method the second allows the smoothing parameter to be a function of location for example an estimator based on nearest neighbor distance in this paper a general method is presented which establishes uniform consistency for all of these estimators

robust stability bound for systems with structured and unstructured perturbations the robust stability problem of a system that is subjected to both structured and unstructured perturbations is investigated in particular the maximal allowable perturbation bound on the system parameters is characterized with a high frequency uncertainty imposed

robust strict positive real stabilization and asymptotic hyperstability robustness abstract this paper is devoted to the study of robust strict positive real stabilization of siso uncertain systems i e finding a single controller that not only robustly stabilizes a plant with uncertainties under unity feedback but also makes the closed loop system robustly strictly positive real it is proved that there must exist a stable controller achieving robust strict positive real stabilization of uncertain systems with both parameter variations and unstructured uncertainties under some reasonable assumptions the propemess of the controller is guaranteed when the largest relative degree of an uncertain system is retricted by applying these results to nonlinear systems some significant conclusions on asymptotic hyperstability robustness are given

robust strict positive real stabilization criteria for siso uncertain systems abstract this paper is devoted to the study of robust strict positive real stabilization criteria for siso uncertain systems i e considering the problem of when a single controller not only robustly stabilizes a plant with uncertainty under unity feedback but also enables the closed loop system to be robustly strictly positive real the uncertain system models with both parameter variation and unstructured perturbation are considered and some necessary and sufficient conditions for the problem are derived

a brief survey of bandwidth selection for density estimation abstract there has been major progress in recent years in data based bandwidth selection for kernel density estimation some second generation methods including plug in and smoothed bootstrap techniques have been developed that are far superior to well known first generation methods such as rules of thumb least squares cross validation and biased cross validation we recommend a solve the equation plug in bandwidth selector as being most reliable in terms of overall performance this article is intended to provide easy accessibility to the main ideas for nonexperts

u processes rates of convergence on introduit un nouveau processus stochastique une collection de statistiques u indicees par une famille de noyaux symetriques on obtient des conditions pour la convergence presque sure uniforme d une suite de tels processus

theoretical analysis of nonparametric filament estimation this paper provides a rigorous study of the nonparametric estimation of filaments or ridge lines of a probability density f points on the filament are considered as local extrema of the density when traversing the support of f along the integral curve driven by the vector field of second eigenvectors of the hessian of f we parametrize points on the filaments by such integral curves and thus both the estimation of integral curves and of filaments will be considered via a plug in method using kernel density estimation we establish rates of convergence and asymptotic distribution results for the estimation of both the integral curves and the filaments the main theoretical result establishes the asymptotic distribution of the uniform deviation of the estimated filament from its theoretical counterpart this result utilizes the extreme value behavior of non stationary gaussian processes indexed by manifolds m h h in 0 1 as h to 0

uniform in bandwidth consistency of kernel type function estimators we introduce a general method to prove uniform in bandwidth consistency of kernel type function estimators examples include the kernel density estimator the nadaraya watson regression estimator and the conditional empirical process our results may be useful to establish uniform consistency of data driven bandwidth kernel type function estimators

arbitrarily small sensitivity in multiple input output uncertain feedback systems abstract a square linear time invariant multiple input multiple output plant r is considered known only to belong to a set r the plant is embedded in a feedback structure designed such that the closed loop response belongs to a specified set for all r r this paper develops sufficient conditions on the uncertain set r such that arbitrarily small sensitivity and internal stability can be achieved by the horowitz synthesis method specifically we show that in addition to generalized single input single output like conditions there exists a condition on the pole zero excess of the controller

optimal spatial adaptation to inhomogeneous smoothness an approach based on kernel estimates with variable bandwidth selectors a new v ria e 1 s e 0r estimation is proposed the application of this bandwidth selector leads to kernel estimates that achieve optimal rates of convergence over b 3 sses this implies that the procedure adapts to spatially inhomogeneous s noothness in particu lar the estimates share optimality properties with wavelet estimates based on thresholding of empirical wavelet coefficients 1 introduction in nonparametric curve estimation the statistical anal ysis may focus on the inference of the qualitative structure of the analyzed curve often interesting features of the curve are connected with spatially inhomogeneous smoothness in this case curve estimates that are spatially adaptlve ar e appropriaie a variety of such procedures have been proposed in the literature in breiman friedman olshen and stone 1983 piecewise constant least squares estimates are considered with a data adaptive choice of the pieces cart more generally friedman and silverman 1989 friedman 1991 and luo and wahba 1995 use variable knot splines mars knot points are added removed and allocated recursively using cross validation techniques these methods have shown good performance in simulations and real data examples however no asymptotic theory is available mammen and van de geer 1997 discuss penalized least squares curve estimation for spatially inhomogeneous curves they propose penalty terms which allow more spatial inhomogeneity than the usual l2 norms of deriva tives of the curve the estimates turn out to be variable knot splines see also mammen 1991 results on rates of convergence and a pointwise asymptotic distribution theory are given miiller and stadtmiiller 1987 staniswalis 1989 and brockmann gasser and hermann 1993 propose kernel estimation with locally variable band width selectors the calculation of local bandwidths is based on pilot estima tion of local smoothness characteristics an asymptotic analysis is available

on almost sure convergence of conditional empirical distribution functions on etudie la convergence presque sure d une distribution empirique conditionnelle de type noyau a la fois en norme sup et en norme sup ponderee

local bandwidth selection for kernel estimates abstract a kernel estimate of a curve that uses an adaptive procedure for local selection of the bandwidth is considered here a two step procedure is proposed for estimating the local bandwidth that minimizes the mean squared error mse of a kernel estimator for nonparametric regression first a consistent estimate of the exact mse is constructed then the bandwidth that minimizes the estimate of the mse is calculated sufficient conditions under which this bandwidth is asymptotically optimal and normally distributed are given the local bandwidth selection procedure was implemented on some simulated data and compared to a global bandwidth selection procedure proposed by rice 1984b a 68 91 reduction in the average mse of a kernel estimator was realized with the local bandwidth selection procedure such a scheme was also studied by muller 1985 and termed a direct pilot estimator approach muller derived sufficient conditions similar to those presented here under which the direct pilot estimator

a consistent bootstrap procedure for the maximum score estimator abstract in this paper we propose a new model based smoothed bootstrap procedure for making inference on the maximum score estimator of manski 1975 1985 and prove its consistency we provide a set of sufficient conditions for the consistency of any bootstrap procedure in this problem we compare the finite sample performance of different bootstrap procedures through simulation studies the results indicate that our proposed smoothed bootstrap outperforms other bootstrap schemes including the m out of n bootstrap additionally we prove a convergence theorem for triangular arrays of random variables arising from binary choice models which may be of independent interest

robust stabilizability for linear systems with both parameter variation and unstructured uncertainty the authors consider the problem of finding a single compensator which stabilizes a plant having both parameter variation and high frequency unstructured uncertainty an uncertain system model is proposed to characterize plants containing those two different uncertainties closed loop stability criteria are then proposed for the model robust stabilizability for single input single output siso systems is studied a number of assumptions describing the set of admissable siso plants are imposed the satisfaction of these assumptions guarantees the existence of a proper stable compensator c s achieving robust stabilization the algorithm used for controller design is recursive in nature and allows the designer to select one compensator coefficient at a time also the minimum order of the desired stabilizer c s depends only on the largest relative degree of the nominal plants which often leads to a lower order compensator

optimal pointwise adaptive methods in nonparametric estimation the problem of optimal adaptive estimation of a function at a given point from noisy data is considered two procedures are proved to be asymptotically optimal for different settings first we study the problem of bandwidth selection for nonparametric pointwise kernel estimation with a given kernel we propose a bandwidth selection procedure and prove its optimality in the asymptotic sense moreover this optimality is stated not only among kernel estimators with a variable bandwidth the resulting estimator is asymptotically optimal among all feasible estimators the important feature of this procedure is that it is fully adaptive and it works for a very wide class of functions obeying a mild regularity restriction with it the attainable accuracy of estimation depends on the function itself and is expressed in terms of the ideal adaptive bandwidth corresponding to this function and a given kernel the second procedure can be considered as a specialization of the first one under the qualitative assumption that the function to be estimated belongs to some holder class l with unknown parameters l this assumption allows us to choose a family of kernels in an optimal way and the resulting procedure appears to be asymptotically optimal in the adaptive sense in any range of adaptation with 2

a robust stability bound of linear systems with structured uncertainty the robust stability of linear uncertain systems with multiple uncertain parameters is considered a sphere norm bound condition on the uncertainties which assures stability of the systems is derived this bound is shown to be less conservative than existing ones a necessary condition to maximize this bound is also given

fractional representation algebraic geometry and the simultaneous stabilization problem an explicit relationship between the fractional representation approach feedback system design and the algebro geometric approach to system theory is formulated and used to derive a global solution to the feedback system problem these techniques are then applied to the simultaneous stabilization problem yielding a natural geometric criterion for a set of plants to be simultaneously stabilized by a single compensator

modeling of uncertain dynamics for robust controller design in state space abstract structured modeling of uncertain dynamics for robust controller design in state space is discussed it is shown that under mild conditions it is possible to obtain a rational transfer function matrix tfm possibly dependent on a parameter vector which varies over a subset of a finite dimensional real vector space to represent uncertain dynamics furthermore in many practical cases uncertain dynamics can be represented by a relatively low order tfm even if the actual dynamics are of very high order the procedure of determining such a tfm is discussed it is shown that a controller which stabilizes the nominal system including such a representation of uncertain dynamics also stabilizes the actual system furthermore desired performance or relative stability can also be guaranteed the presented approach gives a unified framework for the solution to the robust controller design problem for systems with both parameter uncertainties and uncertain dynamics an application to a robust controller design problem for a large flexible structure is also presented

on a feasible infeasible two population fi 2pop genetic algorithm for constrained optimization distance tracing and no free lunch abstract we explore data driven methods for gaining insight into the dynamics of a two population genetic algorithm ga which has been effective in tests on constrained optimization problems we track and compare one population of feasible solutions and another population of infeasible solutions feasible solutions are selected and bred to improve their objective function values infeasible solutions are selected and bred to reduce their constraint violations interbreeding between populations is completely indirect that is only through their offspring that happen to migrate to the other population we introduce an empirical measure of distance and apply it between individuals and between population centroids to monitor the progress of evolution we find that the centroids of the two populations approach each other and stabilize this is a valuable characterization of convergence we find the infeasible population influences and sometimes dominates the genetic material of the optimum solution since the infeasible population is not evaluated by the objective function it is free to explore boundary regions where the optimum is likely to be found roughly speaking the no free lunch theorems for optimization show that all blackbox algorithms such as genetic algorithms have the same average performance over the set of all problems as such our algorithm would on average be no better than random search or any other blackbox search method however we provide two general theorems that give conditions that render null the no free lunch results for the constrained optimization problem class we study the approach taken here thereby escapes the no free lunch implications per se