quadratic stabilizability of uncertain linear systems existence of a nonlinear stabilizing control does not imply existence of a linear stabilizing control this note is concerned with the problem of stabilizing an uncertain linear system via state feedback control an uncertain system which admits a stabilizing state feedback control and some associated quadratic lyapunov function is said to be quadratically stabilizable in a number of recent papers conditions are given under which quadratic stabilizability via nonlinear control implies quadratic stabilizability via linear control these papers restrict the manner in which the uncertain parameters are permitted to enter structurally into the state equation in order to establish this result this note presents an example which shows that this implication is not true for more general uncertain linear systems to this end we describe an uncertain linear system which is quadratically stabilizable via nonlinear control but not quadratically stabilizable via linear control

exponential stabilization of a class of nonlinear systems a generalized gronwall bellman lemma approach in this paper stabilizing control design for a class of nonlinear affine systems is presented by using a new generalized gronwall bellman lemma approach the nonlinear systems under consideration can be non lipschitz two cases are treated for the exponential stabilization the static state feedback and the static output feedback the robustness of the proposed control laws with regards to parameter uncertainties is also studied a numerical example is given to show the effectiveness of the proposed method

design of robust controllers for time delay systems the problem of stabilizing linear dynamical time delay systems subject to bounded uncertainties is investigated two memoryless feedback controllers are considered it is established that when the matching conditions are met and certain bounding relations are satisfied then the linear controller renders the zero response of the system asymptotically stable saturation type controllers are shown to guarantee that all system responses are uniformly ultimately bounded

robust stabilization of a system with delays in control a robust stabilization problem is discussed for a system with delays in control the authors derive a robust stabilizing law against additive perturbations then motivated by the feature of predictive controllers they investigate the structure of robust stabilizing law and provide some interpretations on the relation between the value of time delay and the achievable margin of robust stabilizability

robust h 2 and h control of discrete time systems with polytopic uncertainties via dynamic output feedback this paper addresses the problem of robust h 2 and h control of discrete linear time invariant lti systems with polytopic uncertainties via dynamic output feedback the problem has been known to be difficult when a parameter dependent lyapunov function is to be applied for a less conservative design due to non convexity our approach is based on a novel bounding technique that converts the non convex optimization into a convex one together with a line search which is simple but may be conservative to further reduce the design conservatism an algorithm based on the sequentially linear programming method slpmm is proposed a numerical example is given which demonstrates the feasibility of the proposed design methods

h sub spl infin control of systems under norm bounded uncertainties in all system matrices this paper concerns h sub spl infin control of systems under norm bounded uncertainties in all the system matrices this is an extension of the work by xie et al 1992 where only the a matrix is allowed to be uncertain it is found that the problem shares the same formulation with the h sub spl infin control problem for systems without uncertainties it can also be viewed as reducing the problem of dealing with systems with both structured uncertainties and unstructured uncertainties to one with unstructured uncertainties only

model checking for roc regression analysis the receiver operating characteristic roc curve is a prominent tool for characterizing the accuracy of a continuous diagnostic test to account for factors that might influence the test accuracy various roc regression methods have been proposed however as in any regression analysis when the assumed models do not fit the data well these methods may render invalid and misleading results to date practical model checking techniques suitable for validating existing roc regression models are not yet available in this article we develop cumulative residual based procedures to graphically and numerically assess the goodness of fit for some commonly used roc regression models and show how specific components of these models can be examined within this framework we derive asymptotic null distributions for the residual processes and discuss resampling procedures to approximate these distributions in practice we illustrate our methods with a dataset from the cystic fibrosis registry

partial auc estimation and regression accurate diagnosis of disease is a critical part of health care new diagnostic and screening tests must be evaluated based on their abilities to discriminate diseased from nondiseased states the partial area under the receiver operating characteristic roc curve is a measure of diagnostic test accuracy we present an interpretation of the partial area under the curve auc which gives rise to a nonparametric estimator this estimator is more robust than existing estimators which make parametric assumptions we show that the robustness is gained with only a moderate loss in efficiency we describe a regression modeling framework for making inference about covariate effects on the partial auc such models can refine knowledge about test accuracy model parameters can be estimated using binary regression methods we use the regression framework to compare two prostate specific antigen biomarkers and to evaluate the dependence of biomarker accuracy on the time prior to clinical diagnosis of prostate cancer

analysing the efficiency of some modifications of the secant method some modifications of the secant method for solving nonlinear equations are revisited and the local order of convergence is found in a direct symbolic computation to do this a development of the inverse of the first order divided differences of a function of several variables in two points is presented a generalisation of the efficiency index used in the scalar case to several variables is also analysed in order to use the most competitive algorithm

an iterative algorithm for pole placement by output feedback an iterative algorithm is proposed for solving the pole assignment by output feedback problem for an nth order l input m output linear system the algorithm uses a full rank feedback gain matrix and requires only linear equations of low dimension to be solved at each iteration application of the proposed algorithm allows all n closed loop poles to be almost exactly assigned provided that the iterations converge so that deviations of the resulting closed loop poles from the respective desired values become less than some user specified tolerance and m spl times t spl ges n examples are provided to illustrate the applicability of the proposed method

probabilistic index models summary we present a semiparametric statistical model for the probabilistic index which can be defined as p y y a where y and y a are independent random response variables associated with covariate patterns x and x a respectively a link function defines the relationship between the probabilistic index and a linear predictor asymptotic normality of the estimators and consistency of the covariance matrix estimator are established through semiparametric theory the model is illustrated with several examples and the estimation theory is validated in a simulation study

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

a parametric extension of mixed time frequency robust identification a parametric extension to the time frequency robust identification framework is presented the results can be applied to stable linear time invariant systems on which time and or frequency experiments have been performed the parametric portion of the model should be affine in the unknown parameters which includes practical applications such as flexible structures the consistency problem is cast as a constrained finite dimensional convex optimization problem that can be formulated as a linear matrix inequality the proposed procedure provides an interpolating identification algorithm convergent and optimal up to a factor of two with respect to central algorithms

stability and performance for saturated systems via quadratic and nonquadratic lyapunov functions in this paper we develop a systematic lyapunov approach to the regional stability and performance analysis of saturated systems in a general feedback configuration the only assumptions we make about the system are well posedness of the algebraic loop and local stability problems to be considered include the estimation of the domain of attraction the reachable set under a class of bounded energy disturbances and the nonlinear l2 gain the regional analysis is established through an effective treatment of the algebraic loop and the saturation deadzone function this treatment yields two forms of differential inclusions a polytopic differential inclusion pdi and a norm bounded differential inclusion ndi that contain the original system adjustable parameters are incorporated into the differential inclusions to reflect the regional property the main idea behind the regional analysis is to ensure that the state remain inside the level set of a certain lyapunov function where the pdi or the ndi is valid with quadratic lyapunov functions conditions for stability and performances are derived as linear matrix inequalities lmis to obtain less conservative conditions we use a pair of conjugate non quadratic lyapunov functions the convex hull quadratic function and the max quadratic function these functions yield bilinear matrix inequalities bmis as conditions for stability and guaranteed performance level the bmi conditions cover the corresponding lmi conditions as special cases hence the bmi results are guaranteed to be as good as the lmi results in most examples the bmi results are significantly better than the lmi results

on the local convergence of a family of two step iterative methods for solving nonlinear equations a local convergence analysis for a generalized family of two step secant like methods with frozen operator for solving nonlinear equations is presented unifying earlier methods such as secant s newton chebyshev like steffensen and other new variants the family of iterative schemes is built up where a profound and clear study of the computational efficiency is also carried out numerical examples and an application using multiple precision and a stopping criterion are implemented without using any known root finally a study comparing the order efficiency and elapsed time of the methods suggested supports the theoretical results claimed

adjusting for covariate effects on classification accuracy using the covariate adjusted receiver operating characteristic curve recent scientific and technological innovations have produced an abundance of potential markers that are being investigated for their use in disease screening and diagnosis in evaluating these markers it is often necessary to account for covariates associated with the marker of interest covariates may include subject characteristics expertise of the test operator test procedures or aspects of specimen handling in this paper we propose the covariate adjusted receiver operating characteristic curve a measure of covariate adjusted classification accuracy nonparametric and semiparametric estimators are proposed asymptotic distribution theory is provided and finite sample performance is investigated for illustration we characterize the age adjusted discriminatory accuracy of prostate specific antigen as a biomarker for prostate cancer

robust h sub spl infin performance for linear delay differential systems with time varying uncertainties the present paper concerns robust h spl infin performance for linear delay differential systems which involve an uncertain time delay and time varying norm bounded parameter uncertainties based on the lyapunov functional a simple criterion is proposed which assures the pseudo quadratic stability as a well as an h sub spl infin norm bound the criterion is given in the form of a linear matrix inequality which is affine or convex in additional scalar parameters a simple criterion is presented to evaluate the extent of the performance robustness

memoryless stabilization of uncertain dynamic delay systems riccati equation approach the authors present a procedure for obtaining the memoryless linear state feedback control of uncertain dynamic delay systems the uncertainties are time varying and within a given compact set this method is an extension of the riccati equation approach proposed by i r petersen and c v hollot 1986 the extension is straightforward also the uncertainties do not need to satisfy the matching conditions

robust analysis and synthesis for a class of uncertain nonlinear systems with multiple equilibria abstract this paper focuses on a class of uncertain nonlinear systems which are subject to norm bounded parameter uncertainty in the forward path and a vector valued periodic nonlinearity in the feedback path and addresses robust analysis and synthesis problems for such systems sufficient conditions for global asymptotic stability are derived in terms of linear matrix inequalities lmis and a technique for the estimation of the uncertainty bound is proposed by solving a generalized eigenvalue minimization problem the problem of robust synthesis is concerned with designing a feedback controller such that the resulting closed loop system is globally asymptotically stable for all admissible uncertainties it is shown that a solution to the robust synthesis problem for the uncertain system can be obtained by solving a synthesis problem for an uncertainty free system a concrete example is presented to demonstrate the applicability and validity of the proposed approach

technical communique h state feedback control for generalized continuous discrete time delay system in this paper we consider the problem of designing h state feedback controller for the generalized time delay systems with delayed states and control inputs in continuous and discrete time cases respectively the generalized time delay system problems are solved on the basis of linear matrix inequality lmi technique considering time delays the sufficient condition for the existence of controller and h state feedback controller design methods are presented also using some changes of variables and schur complements the obtained sufficient condition can be rewritten as an lmi form in terms of transformed variables the proposed controller design method can be extended into the problem of robust h state feedback controller design method easily

letter to the editor frozen divided difference scheme for solving systems of nonlinear equations the development of an inverse first order divided difference operator for functions of several variables as well as a direct computation of the local order of convergence of an iterative method is presented a generalized algorithm of the secant method for solving a system of nonlinear equations is studied and the maximum computational efficiency is computed furthermore a sequence that approximates the order of convergence is generated for the examples and it confirms in a numerical way that the order of the methods is well deduced

semi parametric maximum likelihood estimates for roc curves of continuous scale tests in this paper we propose a new semi parametric maximum likelihood ml estimate of a receiver operating characteristic roc curve that satisfies the property of invariance of the roc curve and is easy to compute we show that our new estimator is sqrt n consistent and has an asymptotically normal distribution our extensive simulation studies show that the proposed method is efficient and robust finally we illustrate the application of the proposed estimator in a real data set

conic bounds for systems subject to delays linear matrix inequality conditions implying conic bounds are developed for stable linear time invariant systems with input output and or state delays combined with the conic sector theorem this enables the design of output feedback controllers ensuring closed loop input output stability that is robust to certain maximum delays these contributions are used in a numerical example to design a nearly optimal controller with guaranteed input output stability for a range of delays and improved performance relative to an mathcal h 2 optimal controller designed for the nominally undelayed system

empirical likelihood inference for the area under the roc curve for a continuous scale diagnostic test the most commonly used summary index of the receiver operating characteristic curve roc is the area under the curve auc that measures the accuracy of the diagnostic test in this article we propose an empirical likelihood el approach for the inference on the auc first we define an el ratio for the auc and show that its limiting distribution is a scaled chi square distribution we then obtain an el based confidence interval for the auc using the scaled chi square distribution this el inference for the auc can be extended to stratified samples and the resulting limiting distribution is a weighted sum of independent chi square distributions additionally we conduct simulation studies to compare the relative performance of the proposed el based interval with the existing normal approximation based intervals and bootstrap intervals for the auc

on the statistical analysis of roc curves we introduce a new accuracy index for receiver operating characteristic roc curves namely the partial area under the binormal roc graph over any specified region of interest we propose a simple but general procedure based on a conventional analysis of variance for comparing accuracy indices derived from two or more different modalities the proposed method is related to and compared with existing methodology and is illustrated by results from an experiment on optimization of density and contrast yielded by multiform photographic images used for scintigraphy

variants of a classic traub s result we present a generalization of a modification of a classic traub s result which allows constructing from a given iterative method with order of convergence p efficient iterative methods with order of convergence at least pq 1 q p 1 q n

semiparametric regression for the area under the receiver operating characteristic curve medical advances continue to provide new and potentially better means for detecting disease such is true in cancer for example where biomarkers are sought for early detection and where improvements in imaging methods may pick up the initial functional and molecular changes associated with cancer development in other binary classification tasks computational algorithms such as neural networks support vector machines and evolutionary algorithms have been applied to areas as diverse as credit scoring object recognition and peptide binding prediction before a classifier becomes an accepted technology it must undergo rigorous evaluation to determine its ability to discriminate between states characterization of factors influencing classifier performance is an important step in this process analysis of covariates may reveal subpopulations in which classifier performance is greatest or identify features of the classifier that improve accuracy we develop regression methods for the nonparametric area

a regression modelling framework for receiver operating characteristic curves in medical diagnostic testing summary receiver operating characteristic curves roc s are used to evaluate diagnostic tests when test results are not binary they describe the inherent capacity of the test for distinguishing between truly diseased and nondiseased subjects although methodology for estimating and for comparing roc s is well developed to date no general framework exists for evaluating covariate effects on roc s we formulate a general regression model which allows the effects of covariates on test accuracy to be succinctly summarised such covariates might include for example characteristics of the patient or test environment test type or severity of disease the regression models are shown to arise naturally from some classic models for continuous or ordinal test data regression parameters are fitted using an estimating equation approach the method is illustrated on data from a study of multiformat photographic images used for scintigraphy

absolute stability in linear delay differential systems ill posedness and robustness the author considers matrix delay differential systems which are polynomial in several delay operators using a necessary and sufficient criterion for stability independent of delay or absolute stability the author shows that system stability for all values of the delay vector lying in a sector will imply absolute stability we then show that absolute stability is ill posed with respect to arbitrarily small perturbations of the delay ratios if a certain extended delay differential system which is formed from the original is not also absolutely stable

on stability independent of delay for linear systems a new criterion for asymptotic stability of solutions of certain linear differential difference equations independent of the delay duration is given in terms of solutions of a complex lyapunov matrix equation

memoryless stabilization of uncertain linear systems including time varying state delays the problem of stabilizing a class of uncertain time delay systems via memoryless linear feedback is examined the systems under consideration are linear systems with time varying state delays they also contain uncertain parameters possibly time varying whose values are known only to within a prescribed compact bounding set the main contribution given is to enlarge the class of time delay systems for which one can construct a stabilizing memoryless linear feedback controller within this framework a novel notion of robust memoryless stabilizability is first introduced via the method of lyapunov functionals then a sufficient condition for the stabilizability is proposed it is shown that solvability of a parameterized riccati equation can be used to determine whether the time delay system satisfies the sufficient condition if there exists a positive definite symmetric solution satisfying the riccati equation a suitable memoryless linear feedback law can be derived

h sub spl infin filtering for fuzzy singularly perturbed systems with pole placement constraints an lmi approach this paper addresses the problem of designing an h sub spl infin filter for a class of nonlinear singularly perturbed systems described by a takagi sugeno ts fuzzy model based on a linear matrix inequality lmi approach we develop a fuzzy h sub spl infin controller that guarantees that i the l sub 2 gain from an exogenous input to a filter error is less than or equal to a prescribed value and ii the poles of each local filter are within a prespecified region in order to alleviate the ill conditioning resulting from the interaction of slow and fast dynamic modes solutions to the problem are given in terms of linear matrix inequalities which are independent of the singular perturbation spl epsiv when spl epsiv is sufficiently small the proposed approach does not involve the separation of states into slow and fast ones and it can be applied not only to standard but also to nonstandard singularly perturbed nonlinear systems a numerical example is provided to illustrate the design developed in this paper

the analysis of placement values for evaluating discriminatory measures summary the idea of using measurements such as biomarkers clinical data or molecular biology assays for classification and prediction is popular in modern medicine the scientific evaluation of such measures includes assessing the accuracy with which they predict the outcome of interest receiver operating characteristic curves are commonly used for evaluating the accuracy of diagnostic tests they can be applied more broadly indeed to any problem involving classification to two states or populations d 0 or 1 we show that the roc curve can be interpreted as a cumulative distribution function for the discriminatory measure y in the affected population d 1 after y has been standardized to the distribution in the reference population d 0 the standardized values are called placement values if the placement values have a uniform 0 1 distribution then y is not discriminatory because its distribution in the affected population is the same as that in the reference population the degree to which the distribution of the standardized measure differs from uniform 0 1 is a natural way to characterize the discriminatory capacity of y and provides a nontraditional interpretation for the roc curve statistical methods for making inference about distribution functions therefore motivate new approaches to making inference about roc curves we demonstrate this by considering the roc glm regression model and observing that it is equivalent to a regression model for the distribution of placement values the likelihood of the placement values provides a new approach to roc parameter estimation that appears to be more efficient than previously proposed methods the method is applied to evaluate a pulmonary function measure in cystic fibrosis patients as a predictor of future occurrence of severe acute pulmonary infection requiring hospitalization finally we note the relationship between regression models for the mean placement value and recently proposed models for the area under the roc curve which is the classic summary index of discrimination

inference of the youden index and associated threshold using empirical likelihood for quantiles the youden index is a widely used measure in the framework of medical diagnostics where the effectiveness of a biomarker screening marker or predictor for classifying a disease status is studied when the biomarker is continuous it is important to determine the threshold or cut off point to be used in practice for the discrimination between diseased and healthy populations we introduce two methods aimed at estimating the youden index and its associated threshold the first one is a modified version of a recent approach based on the delta method and the second one is based on the adjusted empirical likelihood for quantiles in the setting of a two sample problem we also include cis for both of them in the simulation study we compare both methods under different scenarios finally a real example of prostatic cancer well known in the literature is analysed to provide the reader with a better understanding of the new methodology copyright 2011 john wiley sons ltd

memoryless h sup spl infin controllers for state delayed systems in this note a memoryless h sup spl infin controller for the state delayed system is presented the controller is a delay independent stabilizer for the state delayed system which also reduces the h sup spl infin norm of the closed loop transfer function from the disturbance to the controlled output to a prescribed level the controller can be obtained by solving a modified riccati equation

semilocal convergence of secant like methods for differentiable and nondifferentiable operator equations abstract from well known secant like methods we observe that we can construct a new family of secant like methods that includes the secant method and kurchatov s method we analyse the local orders of convergence and the efficiencies of the methods of the family and study the semilocal convergence for differentiable and nondifferentiable operators finally we apply our results to conservative problems

robust stabilization of uncertain linear systems quadratic stabilizability and h sup infinity control theory the problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time domain results on the quadratic stabilization of uncertain systems and the frequency domain results on h sup infinity optimization a complete solution to a certain quadratic stabilization problem in which uncertainty enters both the state and the input matrices of the system is given relations between these robust stabilization problems and h sup infinity control theory are explored it is also shown that in a number of cases if a robust stabilization problem can be solved via lyapunov methods then it can be also be solved via h sup infinity control theory based methods

robust h sub infinity control for linear systems with norm bounded time varying uncertainty robust h sub infinity control design for linear systems with uncertainty in both the state and input matrices is treated a state feedback control design which stabilizes the plant and guarantees an h sub infinity norm bound constraint on disturbance attenuation for all admissible uncertainties is presented the robust h sub infinity control problem is solved via the notion of quadratic stabilization with an h sub infinity norm bound necessary and sufficient conditions for quadratic stabilization with an h sub infinity norm bound are derived the results can be regarded as extensions of existing results on h sub infinity control and robust stabilization of uncertain linear systems

h optimization without assumptions on finite or infinite zeros explicit algebraic conditions are presented for the suboptimality of some parameter in the h infty optimization problem by output measurement control apart from two strict properness conditions no artificial assumptions restrict the underlying system in particular the plant may have zeros on the imaginary axis or at infinity these suboptimality characterizations are applied to show how to compute the optimal value by quadratically convergent algorithms and to solve the almost disturbance decoupling problem with internal stability

a riccati equation approach to the stabilization of uncertain linear systems this paper presents a method for designing a feedback control law to stabilize a class of uncertain linear systems the systems under consideration contain uncertain parameters whose values are known only to within a given compact bounding set furthermore these uncertain parameters may be time varying the method used to establish asymptotic stability of the closed loop system obtained when the feedback control is applied involves the use of a quadratic lyapunov function the main contribution of this paper involves the development of a computationally feasible algorithm for the construction of a suitable quadratic lyapunov function once the lyapunov function has been obtained it is used to construct the stabilizing feedback control law the fundamental idea behind the algorithm presented involves constructing an upper bound for the lyapunov derivative corresponding to the closed loop system this upper bound is a quadratic form by using this upper bounding procedure a suitable lyapunov function can be found by solving a certain matrix riccati equation another major contribution of this paper is the identification of classes of systems for which the success of the algorithm is both necessary and sufficient for the existence of a suitable quadratic lyapunov function

robust h sub spl infin compensator design for time delay systems with norm bounded time varying uncertainties considers robust h sub spl infin compensator design for linear systems that involve unknown time delays both in states and controls and time varying norm bounded parameter uncertainties sufficient conditions for designing robust compensators are obtained in terms of two riccati inequalities which are not mutually coupled through which a full order robust h sub spl infin compensator can be obtained finally a small example is given to show the applicability of the proposed approach

h control by state feedback for plants with zeros on the imaginary axis algebraic tests are derived for the suboptimality of some parameter in the h infty optimization problem by state feedback where the finite zero structure of the plant is not restricted as an application of these characterizations a quadratically convergent algorithm for the computation of the optimal value is presented the suboptimality tests are based on new solvability criteria for general algebraic riccati inequalities that are of independent interest

robust h state feedback control for linear systems with state delay and parameter uncertainty this paper addresses the problem of robust h state feedback control design for linear systems with state delay and parameter uncertainty based on a positive definite solution of a modified algebraic riccati equation the proposed robust h static state feedback controller stabilizes uncertain time delay systems independently of delays and guarantees an h norm bound constraint on disturbance attenuation for all admissible uncertainties furthermore it is shown that no advantage can be obtained from the use of a proper linear dynamic state feedback compared with the use of static state feedback illustrative examples are given to demonstrate the applicability of the proposed approach

h disturbance attenuation for state delayed systems in this note the differential game and dissipation inequality are applied to the disturbance attenuation or h control for linear systems with delayed state firstly a simple sufficient condition on the existence of a suboptimal h state feedback controller is given which is independent of delay and an observer based dynamic output feedback solution is presented in terms of riccati inequalities or riccati equations secondly a sufficient condition on the existence of a delay dependent state feedback is presented and the criterion is presented by a matrix inequality which can be solved by numerical methods

technical communique robust h control of discrete systems with uncertain parameters and unknown delays in this paper we address the problems of robust h performance analysis and control synthesis for a class of discrete time systems with norm bounded parameter uncertainty and unknown constant state delay through finite dimensional algebraic riccati equations we provide a necessary and sufficient condition for designing a memoryless state feedback controller which stabilizes the discrete time delay system under consideration and guarantees an h norm bound constraint on the disturbance attenuation for all admissible uncertainties and unknown delays an example is worked out to illustrate the developed theory