construction of lyapunov krasovskii functionals for switched nonlinear systems with input delay abstract this paper studies the stability issue for switched nonlinear systems with input delay and disturbance it is assumed that for the nominal system an exponential stabilizing controller is predesigned such that the switched system is stable under a certain switching signal and a piecewise lyapunov function for the corresponding closed loop system is known however in the presence of input delay and disturbance the system may be unstable under the same switching signal for this case a new lyapunov krasovskii functional is firstly constructed based on the known lyapunov function then by employing this new functional a new switching signal satisfying the new average dwell time conditions is constructed to guarantee the input to state stability of the system under a certain delay bound the bound on the average dwell time is closely related to the bound on the input delay finally numerical examples are given to illustrate the effectiveness of the proposed theory

matching on the estimated propensity score propensity score matching estimators rosenbaum and rubin 1983 are widely used in evaluation research to estimate average treatment effects in this article we derive the large sample distribution of propensity score matching estimators our derivations take into account that the propensity score is itself estimated in a first step prior to matching we prove that first step estimation of the propensity score affects the large sample distribution of propensity score matching estimators and derive adjustments to the large sample variances of propensity score matching estimators of the average treatment effect ate and the average treatment effect on the treated atet the adjustment for the ate estimator is negative or zero in some special cases implying that matching on the estimated propensity score is more efficient than matching on the true propensity score in large samples however for the atet estimator the sign of the adjustment term depends on the data generating process and ignoring the estimation error in the propensity score may lead to confidence intervals that are either too large or too small

new control design for bounded backstepping under input delays we provide a new backstepping result for time varying systems with input delays the novelty of our work is in the bounds on the controls and the facts that i one does not need to compute any lie derivatives to apply our controls ii the controls have no distributed terms and iii we do not require any differentiability conditions on the available controls for the subsystems

input output feedback linearization of time delay systems in this note the input output linearization problem iolp for a class of single input single output nonlinear systems with multiple delays in the input the output and the state is studied the problem is solved by means of various static or dynamic compensators including state and output feedback the mathematical setting is based on some noncommutative algebraic tools and the introduction of a nonlinear version of the so called roesser models for this class of systems these are claimed to be the cornerstones for studying nonlinear time delay systems necessary and sufficient conditions are given for the existence of a static or pure shift output feedback which solves the iolp sufficient conditions for the existence of a dynamic state feedback solution are included as well

analysis of polynomial systems with time delays via the sum of squares decomposition we present a methodology for analyzing robust independent of delay and delay dependent stability of equilibria of systems described by nonlinear delay differential equations by algorithmically constructing appropriate lyapunov krasovskii functionals using the sum of squares decomposition of multivariate polynomials and semidefinite programming we illustrate the methodology using an example from population dynamics

regression models using parametric pseudo observations pseudo observations based on the nonparametric kaplan meier estimator of the survival function have been proposed as an alternative to the widely used cox model for analyzing censored time to event data using a spline based estimator of the survival has some potential benefits over the nonparametric approach in terms of less variability we propose to define pseudo observations based on a flexible parametric estimator and use these for analysis in regression models to estimate parameters related to the cumulative risk we report the results of a simulation study that compares the empirical standard errors of estimates based on parametric and nonparametric pseudo observations in various settings our simulations show that in some situations there is a substantial gain in terms of reduced variability using the proposed parametric pseudo observations compared with the nonparametric pseudo observations the gain can be measured as a reduction of the empirical standard error by up to about one third corresponding to an additional 125 larger sample size we illustrate the use of the proposed method in a brief data example

design of stabilizing controllers of upper triangular nonlinear time delay systems abstract in this paper it is considered the state feedback controller design for a class of upper triangular nonlinear systems with simultaneous input and state delays by using the state transformation of nonlinear systems the problem of designing controller can be converted into that of designing a dynamic parameter which is dynamically regulated by a dynamic equation then by appraising the nonlinear terms of the given systems a dynamic equation can be delicately constructed at last with the help of lyapunov stability theorem it is provided the stability analysis for the closed loop system consisting of the designed controller and the given systems both discrete delays and continuous delays with integral form are considered here different from many existing control designs for upper triangular nonlinear systems neither forwarding recursive nor saturation computation is utilized here and thus our design procedure is simpler a simulation example is given to demonstrate the effectiveness of the proposed design procedure

generalised linear models for correlated pseudo observations with applications to multi state models will be in a given state at some time is a complex nonlinear function of the intensity regression coefficients we present a technique which models the state probabilities directly this method is based on the pseudo values from a jackknife statistic constructed from simple summary statistic estimates of the state probabilities these pseudo values are then used in a generalised estimating equation to obtain estimates of the model parameters we illustrate how this technique works by studying examples of common regression problems we apply the technique to model acute graft versus host disease in bone marrow transplants

a further result on global stabilization of oscillators with bounded delayed input this note revisits the problem of globally stabilizing an oscillator with a bounded delayed input it establishes that an oscillator with input saturation can be globally asymptotically stabilized by a linear state feedback even in the presence of an arbitrarily large delay in the input this result strengthens a recent result in the literature which shows that such an oscillator can be globally asymptotically stabilized with a sufficiently small control input and the magnitude of the control input goes to zero as the delay increases to infinity the controller constructed in this note thus improves the efficiency of the closed loop system by fully utilizing the actuator capacity

global stabilization of multiple integrators with bounded controls this paper deals with the global stabilization of a chain of integrators by means of bounded feedback two nonlinear control laws made of summation of saturation of the state are proposed the first one extends that of sussmann sontag and yang 1994 ieee transactions on automatic control 39 12 2411 2425 and the second proposes variable saturation level to improve the performance both remain very simple and significantly improve the efficiency of the approach which is very competitive with respect to the other existing methods especially for its performance complexity ratio the robustness with respect to measurement delay and model uncertainty is numerically tested

affinely invariant matching methods with ellipsoidal distributions matched sampling is a common technique used for controlling bias in observational studies we present a general theoretical framework for studying the performance of such matching methods specifically results are obtained concerning the performance of affinely invariant matching methods with ellipsoidal distributions which extend previous results on equal percent bias reducing methods additional extensions cover conditionally affinely invariant matching methods for covariates with conditionally ellipsoidal distributions these results decompose the effects of matching into one subspace containing the best linear discriminant and the subspace of variables uncorrelated with the discriminant this characterization of the effects of matching provides a theoretical foundation for understanding the performance of specific methods such as matched sampling using estimated propensity scores calculations for such methods are given in subsequent articles

asymptotic theory of generalized estimating equations based on jack knife pseudo observations a general asymptotic theory of estimates from estimating functions based on jack knife pseudo observations is established by requiring that the underlying estimator can be expressed as a smooth functional of the empirical distribution using results in p variation norms the theory is applied to important estimators from time to event analysis namely the kaplan meier estimator and the aalen johansen estimator in a competing risks model and the corresponding estimators of restricted mean survival and cause specific lifetime lost under an assumption of completely independent censorings this allows for estimating parameters in regression models of survival cumulative incidences restricted mean survival and cause specific lifetime lost considering estimators as functionals and applying results in p variation norms is apparently an excellent way of studying the asymptotics of such estimators

technical communique robust stabilization of uncertain input delayed systems using reduction method this paper concerns a robust stabilization problem that arises when applying the so called reduction method to multiple input delayed systems with parametric uncertainties a robust stabilizing controller that can be constructed easily by solving convex problems in terms of linear matrix inequalities is presented numerical examples are provided to show that in many cases the proposed controller is less conservative and easier to obtain than the existing controllers

stability analysis of implicit polynomial systems this technical note develops a robust stability analysis method for a class of implicit polynomial systems subject to uncertain constant parameters a polynomial with respect to the state and uncertain parameters lyapunov function is computed to assess the robust local stability of the system and to provide a robust estimate of the domain of attraction the results are given in terms of linear matrix inequalities that are affinely dependent on the system state and uncertain parameters numerical examples illustrate the effectiveness of the developed approach

estimation of causal effects of binary treatments in unconfounded studies estimation of causal effects in non randomized studies comprises two distinct phases design without outcome data and analysis of the outcome data according to a specified protocol recently gutman and rubin 2013 proposed a new analysis phase method for estimating treatment effects when the outcome is binary and there is only one covariate which viewed causal effect estimation explicitly as a missing data problem here we extend this method to situations with continuous outcomes and multiple covariates and compare it with other commonly used methods such as matching subclassification weighting and covariance adjustment we show using an extensive simulation that of all methods considered and in many of the experimental conditions examined our new multiple imputation using two subclassification splines method appears to be the most efficient and has coverage levels that are closest to nominal in addition it can estimate finite population average causal effects as well as non linear causal estimands this type of analysis also allows the identification of subgroups of units for which the effect appears to be especially beneficial or harmful copyright 2015 john wiley sons ltd

combining propensity score matching with additional adjustments for prognostic covariates abstract propensity score matching refers to a class of multivariate methods used in comparative studies to construct treated and matched control samples that have similar distributions on many covariates this matching is the observational study analog of randomization in ideal experiments but is far less complete as it can only balance the distribution of observed covariates whereas randomization balances the distribution of all covariates both observed and unobserved an important feature of propensity score matching is that it can be easily combined with model based regression adjustments or with matching on a subset of special prognostic covariates or combinations of prognostic covariates that have been identified as being especially predictive of the outcome variables we extend earlier results by developing approximations for the distributions of covariates in matched samples created with linear propensity score methods for the practically important situation where matching uses both the estimat

brief every stabilizing dead time controller has an observer predictor based structure this paper considers the stabilization problem for linear time invariant systems with a single delay h in the feedback loop two parametrizations of all stabilizing controllers are derived in terms of a state space realization of the rational part of the plant these parametrizations have simple structures and clear interpretations the first is in the form of a generalized dead time compensator smith predictor and the second is in the observer predictor form applications of the proposed parametrization to the h 2 optimization and the robust stabilization problems are discussed

computing output feedback controllers to enlarge the domain of attraction in polynomial systems the problem of computing controllers to enlarge the domain of attraction da of equilibrium points of polynomial systems is considered in order to deal with such a problem a technique for computing static nonlinear output feedback controllers which maximize the largest estimate of the da leda induced by a given polynomial lyapunov function is proposed the main contribution of the note is to show that a lower bound of the maximum achievable leda and a corresponding controller can be obtained through linear matrix inequality optimizations moreover a necessary condition for tightness of this lower bound is presented which is also a sufficient condition to establish the tightness of the lower bound of the leda for a given controller

efficient estimation of average treatment effects using the estimated propensity score we are interested in estimating the average effect of a binary treatment on a scalar outcome if assignment to the treatment is exogenous or unconfounded that is independent of the potential outcomes given covariates biases associated with simple treatmentcontrol average comparisons can be removed by adjusting for differences in the covariates rosenbaum and rubin 1983 show that adjusting solely for differences between treated and control units in the propensity score removes all biases associated with differences in covariates although adjusting for differences in the propensity score removes all the bias this can come at the expense of efficiency as shown by hahn 1998 heckman ichimura and todd 1998 and robins mark and newey 1992 we show that weighting by the inverse of a nonparametric estimate of the propensity score rather than the true propensity score leads to an efficient estimate of the average treatment effect we provide intuition for this result by showing that this estimator can be interpreted as an empirical likelihood estimator that efficiently incorporates the information about the propensity score

estimating and using propensity scores with partially missing data abstract investigators in observational studies have no control over treatment assignment as a result large differences can exist between the treatment and control groups on observed covariates which can lead to badly biased estimates of treatment effects propensity score methods are an increasingly popular method for balancing the distribution of the covariates in the two groups to reduce this bias for example using matching or subclassification sometimes in combination with model based adjustment to estimate propensity scores which are the conditional probabilities of being treated given a vector of observed covariates we must model the distribution of the treatment indicator given these observed covariates much work has been done in the case where covariates are fully observed we address the problem of calculating propensity scores when covariates can have missing values in such cases which commonly arise in practice the pattern of missing covariates can be prognostically important and

multivariate matching methods that are monotonic imbalance bounding we introduce a new monotonic imbalance bounding mib class of matching methods for causal inference with a surprisingly large number of attractive statistical properties mib generalizes and extends in several new directions the only existing class equal percent bias reducing epbr which is designed to satisfy weaker properties and only in expectation we also offer strategies to obtain specific members of the mib class and analyze in more detail a member of this class called coarsened exact matching whose properties we analyze from this new perspective we offer a variety of analytical results and numerical simulations that demonstrate how members of the mib class can dramatically improve inferences relative to epbr based matching methods

static output feedback stabilization necessary conditions for multiple delay controllers this note focuses on the static output feedback stabilization problem for a class of single input single output systems when the control law includes multiple distinct delays we are interested in giving necessary conditions for the existence of such stabilizing controllers illustrative examples second order system chain of integrators or chain of oscillators are presented and discussed

large sample properties of matching estimators for average treatment effects matching estimators for average treatment effects are widely used in evaluation research despite the fact that their large sample properties have not been established in many cases the absence of formal results in this area may be partly due to the fact that standard asymptotic expansions do not apply to matching estimators with a fixed number of matches because such estimators are highly nonsmooth functionals of the data in this article we develop new methods for analyzing the large sample properties of matching estimators and establish a number of new results we focus on matching with replacement with a fixed number of matches first we show that matching estimators are not n 1 2 consistent in general and describe conditions under which matching estimators do attain n 1 2 consistency second we show that even in settings where matching estimators are n 1 2 consistent simple matching estimators with a fixed number of matches do not attain the semiparametric efficiency bound third we provide a consistent estimator for the large sample variance that does not require consistent nonparametric estimation of unknown functions software for implementing these methods is available in matlab stata and r

decomposition of number of life years lost according to causes of death we study the competing risks model and show that the cause j cumulative incidence function integrated from 0 to has a natural interpretation as the expected number of life years lost due to cause j before time this is analogous to the restricted mean lifetime which is the survival function integrated from 0 to it is discussed how the number of years lost may be related to subject specific explanatory variables in a regression model based on pseudo observations and the method is exemplified using data from a bone marrow transplantation study finally inclusion of standard mortality rates is discussed copyright 2013 john wiley sons ltd

characterizing the effect of matching using linear propensity score methods with normal distributions summary matched sampling is a standard technique for controlling bias in observational studies due to specific covariates since rosenbaum rubin 1983 multivariate matching methods based on estimated propensity scores have been used with increasing frequency in medical educational and sociological applications we obtain analytic expressions for the effect of matching using linear propensity score methods with normal distributions these expressions cover cases where the propensity score is either known or estimated using either discriminant analysis or logistic regression as is typically done in current practice the results show that matching using estimated propensity scores not only reduces bias along the population propensity score but also controls variation of components orthogonal to it matching on estimated rather than population propensity scores can therefore lead to relatively large variance reduction as much as a factor of two in common matching settings where close matches are possible approximations are given for the magnitude of this variance reduction which can be computed using estimates obtained from the matching pools related expressions for bias reduction are also presented which suggest that in difficult matching situations the use of population scores leads to greater bias reduction than the use of estimated scores

asymptotic stabilization of an input delayed chain of integrators with nonlinearity in this paper we consider a stabilization problem of an input delayed chain of integrators with nonlinearity in this system the nonlinear part cannot be directly canceled by the input due to time delay we design a stabilizing controller and show that the system stability is determined by the types of nonlinear functions

global asymptotic stabilization for chains of integrators with a delay in the input the problem of the global uniform asymptotic stabilization by bounded feedback of a chain of integrators with a delay in the input is solved no limitation on the size of the delay is imposed to validate the approach a third order example is presented

regional stabilization of input delayed uncertain nonlinear polynomial systems this paper addresses the problem of local stabilization of nonlinear polynomial control systems subject to time varying input delay and polytopic parameter uncertainty a linear matrix inequality approach based on the lyapunov krasovskii theory is proposed for designing a nonlinear polynomial state feedback controller ensuring the robust local uniform asymptotic stability of the system origin along with an estimate of its region of attraction two convex optimization procedures are presented to compute a stabilizing controller ensuring either a maximized set of admissible initial states for given upper bounds on the delay and its variation rate or a maximized lower bound on the maximum admissible input delay considering a given set of admissible initial states numerical examples demonstrate the potentials of the proposed stabilization approach

extended h 2 and h norm characterizations and controller parametrizations for discrete time systems this paper presents new synthesis procedures for discrete time linear systems it is based on a recently developed stability condition which contains as particular cases both the celebrated lyapunov theorem for precisely known systems and the quadratic stability condition for systems with uncertain parameters these new synthesis conditions have some nice properties a they can be expressed in terms of lmi linear matrix inequalities and b the optimization variables associated with the controller parameters are independent of the symmetric matrix that defines a quadratic lyapunov function used to test stability this second feature is important for several reasons first structural constraints as those appearing in the decentralized and static output feedback control design can be addressed less conservatively second parameter dependent lyapunov function can be considered with a very positive impact on the design of robust h 2 and h x control problems third the design of controller with mixed

a two step bayesian approach for propensity score analysis simulations and case study a two step bayesian propensity score approach is introduced that incorporates prior information in the propensity score equation and outcome equation without the problems associated with simultaneous bayesian propensity score approaches the corresponding variance estimators are also provided the two step bayesian propensity score is provided for three methods of implementation propensity score stratification weighting and optimal full matching three simulation studies and one case study are presented to elaborate the proposed two step bayesian propensity score approach results of the simulation studies reveal that greater precision in the propensity score equation yields better recovery of the frequentist based treatment effect a slight advantage is shown for the bayesian approach in small samples results also reveal that greater precision around the wrong treatment effect can lead to seriously distorted results however greater precision around the correct treatment effect parameter yields quite good results with slight improvement seen with greater precision in the propensity score equation a comparison of coverage rates for the conventional frequentist approach and proposed bayesian approach is also provided the case study reveals that credible intervals are wider than frequentist confidence intervals when priors are non informative

finite time global stabilization by means of time varying distributed delay feedback the paper contains certain results concerning the finite time global stabilization for triangular control systems described by retarded functional differential equations by means of time varying distributed delay feedback these results enable us to present solutions to feedback stabilization problems for systems with delayed input the results are obtained by using the backstepping technique

stabilizing a chain of integrators using multiple delays this note addresses the output feedback stabilization problem of a chain of integrators using multiple delays we shall prove that either n distinct delays or a proportional delay compensator with n 1 distinct delays are sufficient to stabilize a chain including n integrators we present two different approaches both are constructive and rely on frequency domain techniques on a derivative feedback approximation idea and a pole placement idea respectively an illustrative example triple integrator is presented

linear systems with delayed controls a reduction linear systems with delayed control action are transformed into systems without delays under an absolute continuity condition the new system is an ordinary differential control equation in the general case the new system is a measure differential control system it is shown how the controllability stabilization and various optimization problems can be analyzed via the reduced systems

global stabilization of oscillators with bounded delayed input the problem of globally asymptotically stabilizing by bounded feedback of an oscillator with an arbitrary large delay in the input is solved a first solution follows from a general result on the global stabilization of null controllable linear systems with delay in the input by bounded control laws with a distributed term next it is shown through a lyapunov analysis that the stabilization can be achieved as well when neglecting the distributed terms it turns out that this main result is intimately related to the output feedback stabilization problem

ellipsoidally symmetric extensions of the general location model for mixed categorical and continuous data summary the general location model olkin tate 1961 krzanowski 1980 1982 little schluchter 1985 has categorical variables marginally distributed as a multinomial and continuous variables conditionally normally distributed with different means across cells defined by the categorical variables but a common covariance matrix across cells two extensions of the general location model are obtained the first replaces the common covariance matrix with different but proportional covariance matrices where the proportionality constants are to be estimated the second replaces the multivariate normal distributions of the first extension with multivariate t distributions where the degrees of freedom can also vary across cells and are to be estimated the t distribution is just one example of more general ellipsoidally symmetric distributions that can be used in place of the normal these extensions can provide more accurate fits to real data and can be viewed as tools for robust inference moreover the models can be very useful for multiple imputation of ignorable missing values maximum likelihood estimation using the aecm algorithm meng van dyk 1997 is presented as is a monotone data gibbs sampling scheme for drawing parameters and missing values from their posterior distributions to illustrate the techniques a numerical example is presented

connections between razumikhin type theorems and the iss nonlinear small gain theorem a razumikhin type theorem that guarantees input to state stability for functional differential equations with disturbances is established using the nonlinear small gain theorem the result is used to show that input to state stabilizability for nonlinear finite dimensional control systems is robust in an appropriate sense to small time delays at the input also relaxed razumikhin type conditions guaranteeing global asymptotic stability for differential difference equations are given

technical communique robust stabilization of uncertain systems with unknown input delay this paper is concerned with the robust controller design for uncertain input delayed systems the time delay is assumed to be an unknown constant a controller with delay feedback for the robust stabilization of the system is proposed the stability criterion of the closed loop system is derived in terms of linear matrix inequalities lmis examples show that in many cases our method can give less conservative results than those by the existing methods moreover for the same cases our controllers have lower feedback gains than the existing ones

backstepping for nonlinear systems with delay in the input revisited in this paper a new solution to the problem of globally asymptotically stabilizing a nonlinear system in feedback form with a known pointwise delay in the input is proposed the result covers a family of systems wider than those studied in the literature and endows with control laws with a single delay in contrast to those given in previous works which include two distinct pointwise delays or distributed delays the strategy of design is based on the construction of an appropriate lyapunov krasovskii functional an illustrative example ends the paper

affinely invariant matching methods with discriminant mixtures of proportional ellipsoidally symmetric distributions in observational studies designed to estimate the effects of interventions or exposures such as cigarette smoking it is desirable to try to control background differences between the treated group e g current smokers and the control group e g never smokers on covariates x e g age education matched sampling attempts to effect this control by selecting subsets of the treated and control groups with similar distributions of such covariates this paper examines the consequences of matching using affinely invariant methods when the covariate distributions are discriminant mixtures of proportional ellipsoidally symmetric dmpes distributions a class herein defined which generalizes the ellipsoidal symmetry class of rubin and thomas ann statist 20 1992 1079 1093 the resulting generalized results help indicate why earlier results hold quite well even when the simple assumption of ellipsoidal symmetry is not met e g biometrics 52 1996 249 264 extensions to conditionally affinely invariant matching with conditionally dmpes distributions are also discussed