robust stability and stabilization of linear switched systems with dwell time sufficient conditions are given for the stability of linear switched systems with dwell time and with polytopic type parameter uncertainty a lyapunov function in quadratic form which is non increasing at the switching instants is assigned to each subsystem during the dwell time this function varies piecewise linearly in time after switching occurs it becomes time invariant afterwards this function leads to asymptotic stability conditions for the nominal set of subsystems that can be readily extended to the case where these subsystems suffer from polytopic type parameter uncertainties the method proposed is then applied to stabilization via state feedback both for the nominal and the uncertain cases

on the convergence of quadrature formulas for complex weight functions abstract we consider quadrature formulas for complex weights and prove their convergence for a large class of functions

orthogonal polynomials and gaussian quadrature rules related to oscillatory weight functions in this paper we consider polynomials orthogonal with respect to an oscillatory weight function w x xeim x on 1 1 where m is an integer the existence of such polynomials as well as several of their properties three term recurrence relation differential equation etc are proved we also consider related quadrature rules and give applications of such quadrature rules to some classes of integrals involving highly oscillatory integrands

frequency limited h controller order reduction for linear parameter varying systems abstractin this paper a controller order reduction method for linear parameter varying systems is presented the proposed method is based on the frequency weighted balanced truncation technique which has the advantage to reduce the order in a specific frequency range the approach is discussed and is proved to preserve the closed loop stability with a guaranteed upper error bound effectiveness and performance of the obtained reduced order controller are investigated by applying it to an automotive semi active suspension control the obtained simulation results show that objectives such as the road handling and the passenger comfort realised with the reduced order controller are kept in the same performance level as with the full order controller moreover a comparison with an other order reduction method is shown and confirms the advantage of the developed method

notions of stabilizability and controllability for a class of uncertain linear systems abstract this paper investigates the relationship between stabilizability and certain notions of controllability for a class of uncertain linear systems containing time varying unknown but bounded uncertain parameters the paper introduces a notion of controllability invariance roughly speaking an uncertain system is controllability invariant if it is controllable in the usual sense for each fixed value of the uncertain parameters the paper describes a class of uncertain systems for which controllability invariance implies stabilizability

on inexact lpv control design of continuous time polytopic systems robust dynamic output design most often relies on nonconvex problems this is precisely the case with linear parameter varying lpv control when the measured varying parameters do not exactly fit the real ones this paper provides a solution in the convex programming framework with the use of linear matrix inequality lmi solvers in the case of polytopic parameter dependence a bounded uncertainty set is defined from the difference between the measured and the true parameters from which lmi stabilization and performance conditions are obtained after bounding as a desired property the proposed conditions reduce to the classical lpv ones whenever the true parameters are available for control synthesis

passivity preserving model reduction with finite frequency h approximation performance this paper is concerned with model reduction for passive systems for a given linear time invariant system that is stable and positive real pr our goal is to find a pr reduced order model to approximate it and our attention is focused on reducing the error with respect to a finite frequency h performance which is the most remarkable difference between the proposed approach and the existing ones first by applying multiplier expansion new conditions in terms of linear matrix inequalities are derived for characterizing the positive realness of the reduced order model and the finite frequency h performance of the error system a necessary and sufficient condition is then established for parameterizing a pr reduced order model with finite frequency h approximation performance based on which an iterative algorithm is constructed for numerically exploring such a reduced order model particularly a partial multiplier expansion treatment is introduced which greatly reduces the decision variables but does not cause conservatism to the derived conditions the proposed method is also extended to robust passivity reserving model reduction with polytopic uncertainty finally we provide two numerical examples about rlc circuits to show the effectiveness and advantages of the proposed model reduction method

a multiloop generalization of the circle criterion for stability margin analysis in order to provide a theoretical tool well suited for use in characterizing the stability margins e g gain and phase margins of multiloop feedback systems multiloop input output stability results generalizing the circle stability criterion are considered generalized conic sectors with centers and radii determined by linear dynamical operators are employed to enable an engineer to specify the stability margins which he desires as a frequency dependent convex set of modeling errors including nonlinearities gain variations and phase variations which the system must be able to tolerate in each feedback loop without instability the resulting stability criterion gives sufficient conditions for closed loop stability in the presence of such frequency dependent modeling errors even when the modeling errors occur simultaneously in all loops so for example stability is assured as loop gains and phases vary throughout a set of nonzero measure whose boundaries are frequency dependent the stability conditions yield an easily interpreted scalar measure of the amount by which a muitiloop system exceeds or falls short of its stability margin specifications

multiobjective output feedback control via lmi optimization this paper presents an overview of a linear matrix inequality lmi approach to the multiobjective synthesis of linear output feedback controllers the design objectives can be a mix of h sub spl infin performance h sub 2 performance passivity asymptotic disturbance rejection time domain constraints and constraints on the closed loop pole location in addition these objectives can be specified on different channels of the closed loop system when all objectives are formulated in terms of a common lyapunov function controller design amounts to solving a system of linear matrix inequalities the validity of this approach is illustrated by a realistic design example

a direct characterization of l sub 2 gain controllers for lpv systems in this paper a class of linear parameter dependent output feedback controllers that satisfy quadratic stability and an induced l sub 2 norm bound for a given linear parameter varying lpv plant is considered by using a parameter independent common lyapunov function the solvability conditions are expressed in terms of finite dimensional linear matrix inequalities lmi evaluated at the extreme points of the admissible parameter set conditions under which strictly proper controllers can be used are obtained by restricting some of the controller matrices to be constant the input and output matrices can be parameter varying without destroying the problem s convexity cases where the controller matrices can be obtained without interpolation are also discussed thereby simplifying the implementation of the controller a numerical example is included which demonstrates the application of the results

orthogonal laurent polynomials corresponding to certain strong stieltjes distributions with applications to numerical quadratures in this paper we shall be mainly concerned with sequences of orthogonal laurent polynomials associated with a class of strong stieltjes distributions introduced by a s ranga algebraic properties of certain quadratures formulae exactly integrating laurent polynomials along with an application to estimate weighted integrals on 1 1 with nearby singularities are given finally numerical examples involving interpolatory rules whose nodes are zeros of orthogonal laurent polynomials are also presented

all optimal hankel norm approximations of linear multivariable systems and their l error bounds the problem of approximating a multivariable transfer function g s of mcmillan degree n by s of mcmillan degree k is considered a complete characterization of all approximations that minimize the hankel norm is derived the solution involves a characterization of all rational functions s f s that minimize where s has mcmillan degree k and f s is anticavisal the solution to the latter problem is via results on balanced realizations all pass functions and the inertia of matrices all in terms of the solutions to lyapunov equations it is then shown that where k 1 g s is the k l st hankel singular value of g s and for one class of optimal hankel norm approximations the method is not computationally demanding and is applied to a 12 state model

h control of linear time varying systems a state space approach in this paper the standard problem of h infty control theory for finite dimensional linear time varying continuous time plants is considered the problem is given a real number gamma 0 f

structured and simultaneous lyapunov functions for system stability problems abstract it is shown that many system stability and robustness problems can be reduced to the question of when there is a quadratic lyapunov function of a certain structure which establishes stability of x ax for some appropriate a the existence of such a lyapunov function can be determined by solving a convex program we present several numerical methods for these optimization problems a simple numerical example is given

balanced truncation of linear time varying systems in this paper balanced truncation of linear time varying systems is studied in discrete and continuous time based on relatively basic calculations with time varying lyapunov equations inequalities we are able to derive both upper and lower error bounds for the truncated models these results generalize well known time invariant formulas the case of time varying state dimension is considered input output stability of all truncated balanced realizations is also proven the method is finally successfully applied to a high order model

bounded amplitude performance of switched lpv systems with applications to hybrid systems this paper discusses recent results on multiple linear agent control for systems satisfying a bounded amplitude performance constraint the plant is assumed to be a linear parameter varying lpv system scheduled along a nominal parameter trajectory in this respect the control problem represents a plant operating between a prespecified set of operating conditions linear controllers are designed at setpoints along this scheduling trajectory to satisfy bounded amplitude performance constraints this paper discusses an approach to analyze the switched system behavior under practical assumptions on the structure of the switching rule the approach combines the scheduling parameter with lpv system properties to derive bounds on the switching behavior of the system these estimates are then used to construct a logical model of the switched system behavior in the form of a timed automaton in this respect this paper presents a way of extracting logical models of continuous time system behavior

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

a new frequency weighted balanced truncation method and an error bound in this paper a new frequency weighted model reduction method with an a priori error bound is proposed the method is a generalization of enns technique 1984 and yields stable models even when both input and output weightings are included the proposed method is compared with other existing methods using numerical examples

gain scheduling via linear fractional transformations abstract a linear finite dimensional plant with rational state space parameter dependence is controlled using a parameter dependent controller the parameters are known to take on values in a unit ball and are known in real time the goal of control is to stabilize the parameter dependent closed loop system and provide disturbance error attenuation as measured in induced l 2 norms the approach taken uses the optimally scaled small gain theorem and solves the control synthesis problem by reformulating the existence conditions into a finite dimensional convex optimization

foreword to the proceedings of the orthoquad 2014 conference orthoquad 2014 was an international symposium on orthogonality quadrature and related topics held on january 20 24 2014 in puerto de la cruz tenerife spain it was held in memory of professor pablo gonzalez vera 1955 2012

controller reduction concepts and approaches the problem of passing from a linear time invariant high order controller designed for a linear time invariant plant of presumably high order to a low order approximation of the controller is discussed the approximation problem is often best posed as a frequency weighted l sub infinity approximation problem many different controller representations are possible giving different performances of the various reduction algorithms

on the convergence of two point pade type approximants for a given function f holomorphic in a domain omega containing the origin and the point at infinity rational interpolants with prescribed poles are constructed and their convergence properties analyzed numerical results are also given

approximate solution of nonlinear double scattering inversion for true amplitude imaging abstractlinearized inversion algorithms are the main techniques in seismic imaging that apply the single scattering born approximation to the scattered field and therefore have difficulty handling the strong perturbation of model parameters and nonlinear multiple scattering effects to theoretically overcome these drawbacks in the linearization of the inverse scattering problem we have developed an approach to deal with nonlinear double scattering inversion we first used an integral equation formulation associated with the scattered field consisting of single and double scattering in an acoustic earth model based on the second order born approximation and we found that the approximation of the scattered field can be naturally related to the generalized radon transform grt we then adopted the inverse grt to obtain the corresponding quadratic approximate inversion solution our inversion scheme can appropriately handle the first order transmission effects from double scattering in a local area wh

on the stabilization of uncertain linear systems via bound invariant lyapunov functions this paper considers the problem of stabilizing a class of systems with an arbitrarily large uncertainty bounding set in particular the stabilization of linear uncertain systems via a bound invariant lyapunov function is examined necessary and sufficient conditions for the existence of a bound invariant lyapunov function are derived for systems with block structured uncertainty and a class of systems with scalar linear uncertainty

the sensitivity of born inversion to the choice of reference velocity a simple example we examine the sensitivity of the born model to the input background velocity we use a one dimensional analytic example to point out the difference between a corrective procedure and merely a perturbative one we examine various aspects of the sensitivity issue including the trade off between velocity determination and mapping of reflector location although this problem is discussed within the context of the born model it is an issue common to all perturbative methods e g migration methods which transform surface reflection data into a map of subsurface reflectors

error bound for transfer function order reduction using frequency weighted balanced truncation abstract an error bound for transfer function order reduction is derived when frequency weighted balanced truncation is the order reduction method the bound is valid for both one sided input or output and two sided weighted balancing approximations with stable weights which can otherwise be arbitrary the error bound formula is valid for both discrete time and continuous time problems examples are studied to demonstrate effectiveness of the error bound

a frequency weighted model order reduction technique and error bounds a new frequency weighted technique for balanced model reduction is proposed the proposed technique not only provides stable reduced order models for the case when both input and output weightings are included but also yields frequency response error bounds the method is illustrated using numerical examples and the results are compared with other frequency weighted model reduction techniques

optimal disturbance attenuation for discrete time switched and markovian jump linear systems an exact condition for uniform stabilization and disturbance attenuation for switched linear systems is given in the discrete time domain via the union of an increasing family of linear matrix inequality conditions associated with each markovian jump linear system is a switched linear system so we obtain a necessary and sufficient condition for almost sure uniform stabilization and disturbance attenuation for markovian jump linear systems as well the results lead to semidefinite programming based controller synthesis techniques from which optimal finite path dependent linear dynamic output feedback controllers arise naturally in particular under the notion of path by path optimal disturbance attenuation finite path dependent controllers can outperform the usual mode dependent ones

brief paper multivariable pid control with set point weighting via bmi optimisation the paper focuses on the design of multivariable pid controllers with set point weighting the advantage of this pid structure is that the responses of the system to disturbances and to changes in the set point can be adjusted separately the proposed design methods rely on the transformation of the tuning of the controller gains into a static output feedback sof problem hence multivariable pid controllers can be designed by solving an optimisation problem with bilinear matrix inequalities bmis the paper addresses the design of both time invariant and gain scheduled robust controllers all of the tuning methods discussed through the paper are based on a pid structure with filtered derivative term thus guaranteeing the well posedness of the closed loop system

a survey of model reduction by balanced truncation and some new results balanced truncation is one of the most common model reduction schemes in this note we present a survey of balancing related model reduction methods and their corresponding error norms and also introduce some new results five balancing methods are studied 1 lyapunov balancing 2 stochastic balancing 3 bounded real balancing 4 positive real balancing and 5 frequency weighted balancing for positive real balancing we introduce a multiplicative type error bound moreover for a certain subclass of positive real systems a modified positive real balancing scheme with an absolute error bound is proposed we also develop a new frequency weighted balanced reduction method with a simple bound on the error system based on the frequency domain representations of the system gramians two numerical examples are illustrated to verify the efficiency of the proposed methods

derivation of forward and adjoint operators for least squares shot profile split step migration the forward and adjoint operators for shot profile least squares migration are derived the forward operator is demigration and the adjoint operator is migration the demigration operator is derived from the born approximation the process begins with a green s function that allows for a laterally varying migration velocity model using the split step approximation next the earth is divided into horizontal layers and within each layer the migration velocity model is made to be constant with respect to depth for a given layer 1 the source side wavefield is propagated down to its top using the background wavefield this gives a background wavefield incident at the layer s upper boundary 2 the layer s contribution to the scattered wavefield is computed using the born approximation to the scattered wavefield and the background wavefield 3 next its scattered wavefield is propagated back up to the measurement surface using again the background wavefield the measured wavefield is approximated by the sum of scattered wavefields from each layer in the derivation of the measured wavefield the shot profile migration geometry is used for each shot the resulting wavefield modeling operator takes the form of a fredholm integral equation of the first kind and this is used to write down its adjoint the shot profile migration operator this forward adjoint pair is used for shot profile least squares migration shot profile least squares migration is illustrated with two synthetic examples the first uses data collected over a four layer acoustic model and the second uses data from the sigsbee 2a model

structurally balanced controller order reduction with guaranteed closed loop performance abstract this paper considers controller order reduction with the consideration of closed loop stability and performance a closed loop structurally balancing method is proposed to reduce the controller orders for a class of systems and controllers the resulting reduced order controllers if they exist are guaranteed to stabilize the corresponding systems error bounds are also derived for the closed loop performance degradation

a parameterised model order reduction method for parametric systems based on laguerre polynomials abstractthis paper presents a laguerre polynomials based parametrised model order reduction method for the parametric system in time domain the method allows that the parametric dependence in system matrices is nonaffine the method is presented via reducing an approximate polynomial parametric system based on taylor expansion and laguerre polynomials resulting in a parametric reduced system that can accurately approximate the time response of the original parametric system over a wide range of parameter the reduced parametric system obtained by proposed method can be implemented by two algorithms algorithm 1 is a direct way that is suitable for single input multi output parametric systems algorithm 2 is presented based on a connection to the krylov subspace which is efficient and suitable for multi input multi output parametric systems the effectiveness of the proposed method is illustrated with two benchmarks in practical applications

continuous time identification of periodically parameter varying state space models this paper presents a new frequency domain identification technique to estimate multivariate linear parameter varying lpv continuous time state space models where a periodic variation of the parameters is assumed or imposed the main goal is to obtain an lpv state space model suitable for control from a single parameter varying experiment although most lpv controller synthesis tools require continuous time state space models the identification of such models is new the proposed identification method designs a periodic input signal taking the periodicity of the parameter variation into account we show that when an integer number of periods is observed for both the input and the scheduling the state space model representation has a specific sparse structure in the frequency domain which is exploited to speed up the estimation procedure a weighted non linear least squares algorithm then minimizes the output error two initialization methods are explored to generate starting values the first approach uses a linear time invariant lti approximation the second estimates a linear time variant ltv input output differential equation from which a corresponding state space realization is computed

method of centers for minimizing generalized eigenvalues abstract we consider the problem of minimizing the largest generalized eigenvalue of a pair of symmetric matrices each of which depends affinely on the decision variables although this problem may appear specialized it is in fact quite general and includes for example all linear quadratic and linear fractional programs many problems arising in control theory can be cast in this form the problem is nondifferentiable but quasiconvex so methods such as kelley s cutting plane algorithm or the ellipsoid algorithm of shor nemirovsky and yudin are guaranteed to minimize it in this paper we describe relevant background material and a simple interior point method that solves such problems more efficiently the algorithm is a variation on huard s method of centers using a self concordant barrier for matrix inequalities developed by nesterov and nemirovsky nesterov and nemirovsky have also extended their potential reduction methods to handle the same problem since the problem is quasiconvex but not convex devising a nonheuristic stopping criterion i e one that guarantees a given accuracy is more difficult than in the convex case we describe several nonheuristic stopping criteria that are based on the dual of a related convex problem and a new ellipsoidal approximation that is slightly sharper in some cases than a more general result to nesterov and nemirovsky the algorithm is demonstrated on an example determining the quadratic lyapunov function that optimizes a decay rate estimate for a differential inclusion

model reduction via balanced state space representations a model reduction procedure based on balanced state space representations is studied in this paper the reduced order model is examined from the point of view of stability controllability and observability both continuous time and discrete time systems are considered

explicit controller formulas for lmi based h synthesis the set of h controllers with closed loop performance c can be implicitly parametrized by the solutions r s of a system of linear matrix inequalities lmi the matrices r and s play a role analogous to that of the riccati solutions x and y in classical riccati based h control useful applications include lmi based h synthesis mixed h 2h design and h design with a pole placement constraint this paper is concerned with the reliable computation of h controllers given a solution r s of the characteristic system of lmis explicit formulas are derived for both the regular and singular cases remarkably these formulas are extensions of the usual central controller formulas where the lmi solutions r and s replace the riccati solutions x and y simple and numerically appealing new formulas for discrete time h controllers are also derived

optimal constant i o similarity scaling for full information and state feedback control problems abstract in robust control problems capturing all robustness and performance objectives in a single h norm cost function is impossible an alternative approach still untilizing the h norm involves diagonal similarity scaling of certain closed loop transfer functions the set of allowable diagonal scalings is problem dependent and reflects assumptions about the uncertainty and desired performance objectives the scaling set considered here is a prescribed convex set of positive definite matrices we consider the optimal constant scaling problem for the full information h control problem the solution is obtained by transforming the original problem into a convex feasibility problem specifically a structured linear matrix inequality in special cases solvability of the full information problem is equivalent to solvability of the state feedback problem

positive interpolatory quadrature formulas and para orthogonal polynomials we establish a relation between quadrature formulas on the interval 1 1 that approximate integrals of the form j f 11 f x x dx and szego quadrature formulas on the unit circle that approximate integrals of the form i f f ei d the functions x and are assumed to be weight functions on 1 1 and respectively and are related by cos sin it is well known that the nodes of szego formulas are the zeros of the so called para orthogonal polynomials bn z n z n z 1 n z and n z being the orthogonal and reciprocal polynomials respectively with respect to the weight function furthermore for 1 we have recently obtained gauss type quadrature formulas on 1 1 see bultheel et al j comput appl math 132 1 2000 1 in this paper making use of the para orthogonal polynomials with 1 a one parameter family of interpolatory quadrature formulas with positive coefficients for j f is obtained along with error expressions for analytic integrands finally some illustrative numerical examples are also included

dc optimization approach to robust controls the optimal scaling value problem the optimal scaling problem osp for constant scaling in output feedback control is an inherently difficult nonconvex problem for which in general existing local search algorithms can at best locate a local solution however it can be restated as a problem of globally minimizing a convex function under dc constraints i e constraints that can be expressed in terms of differences of convex functions a particular structure of this dc optimization problem is that it becomes convex when a relatively small number of complicating variables are held fixed we propose alternative branch and bound algorithms for osp which exploit this structure by branching upon the complicating variables and use adaptive sub division strategies to speed up the convergence to the global solution

frequency limited mmb h _ infty model reduction for positive systems in this paper the problem of frequency limited mmb h infty model reduction for positive linear time invariant systems is investigated specifically our goal is to find a stable positive reduced order model for a given positive system such that the mmb h infty norm of the error system is bounded over a frequency interval of interest a new condition in terms of matrix inequality is developed for characterizing the frequency limited mmb h infty performance then an equivalent parametrization of a positive reduced order model is derived based on which an iterative algorithm is constructed for optimizing the reduced order model the algorithm utilizes coarse reduced order models resulting from generalized balanced truncation as the initial value both continuous and discrete time systems are considered in the same framework numerical examples clearly show the effectiveness and advantages of the proposed model reduction method

quadrature and orthogonal rational functions abstract classical interpolatory or gaussian quadrature formulas are exact on sets of polynomials the szeg quadrature formulas are the analogs for quadrature on the complex unit circle here the formulas are exact on sets of laurent polynomials in this paper we consider generalizations of these ideas where the laurent polynomials are replaced by rational functions that have prescribed poles these quadrature formulas are closely related to certain multipoint rational approximants of cauchy or riesz herglotz transforms of a positive or general complex measure we consider the construction and properties of these approximants and the corresponding quadrature formulas as well as the convergence and rate of convergence

affine characterizations of minimal and mode dependent dwell times for uncertain linear switched systems an alternative approach for minimum and mode dependent dwell time characterization for switched systems is derived while minimum dwell time results require the subsystems to be asymptotically stable mode dependent dwell time results can consider unstable subsystems and dwell times within a possibly unbounded range of values the proposed approach is related to lyapunov looped functionals a new type of functionals leading to stability conditions affine in the system matrices unlike standard results for minimum dwell time these conditions are expressed as infinite dimensional lmis which can be solved using recent polynomial optimization techniques such as sum of squares the specific structure of the conditions is finally utilized in order to derive dwell time stability results for uncertain switched systems several examples illustrate the efficiency of the approach

a convex characterization of gain scheduled h sub spl infin controllers an important class of linear time varying systems consists of plants where the state space matrices are fixed functions of some time varying physical parameters spl theta small gain techniques can be applied to such systems to derive robust time invariant controllers yet this approach is often overly conservative when the parameters spl theta undergo large variations during system operation in general higher performance can be achieved by control laws that incorporate available measurements of spl theta and therefore adjust to the current plant dynamics this paper discusses extensions of h sub spl infin synthesis techniques to allow for controller dependence on time varying but measured parameters when this dependence is linear fractional the existence of such gain scheduled h sub spl infin controllers is fully characterized in terms of linear matrix inequalities the underlying synthesis problem is therefore a convex program for which efficient optimization techniques are available the formalism and derivation techniques developed here apply to both the continuous and discrete time problems existence conditions for robust time invariant controllers are recovered as a special case and extensions to gain scheduling in the face of parametric uncertainty are discussed in particular simple heuristics are proposed to compute such controllers

orthogonality interpolation and quadratures on the unit circle and the interval 1 1 given a weight function s x on 1 1 or more generally a positive borel measure the erdos turan theorem assures the convergence in l 2 s norm to a function f of its sequence of interpolating polynomials at the zeros of the orthogonal polynomials or equivalently at the nodes of the gauss christoffel quadrature formulas associated with s in this paper we will extend this result to the nodes of the gauss radau and gauss lobatto quadrature formulas by passing to the unit circle and taking advantage of the results on interpolation by means of laurent polynomials at the zeros of certain para orthogonal polynomials with respect to the weight function w q s cos q sin q on p p as a consequence an application to the construction of certain product integration rules on finite intervals of the real line will be given several numerical experiments are finally carried out

guaranteed properties of gain scheduled control for linear parameter varying plants abstract gain scheduling has proven to be a successful design methodology in many engineering applications however in the absence of a sound theoretical analysis these designs come with no guarantees on the robustness performance or even nominal stability of the overall gain scheduled design this paper presents such an analysis for one type of gain scheduled system namely a linear parameter varying plant scheduling on its exogenous parameters conditions are given which guarantee that the stability robustness and performance properties of the fixed operating point designs carry over to the global gain scheduled design these conditions confirm and formalize popular notions regarding gain scheduled design such as the scheduling variable should vary slowly