invariance properties in hermite pade approximation theory abstract the pade approximant is invariant under both linear fractional transformations of the function value and linear fractional transformations origin fixed of the argument the paper reports on an investigation of these invariance properties to the class of hermite pade approximants based on the class of general ordinary nonlinear differential equations further the paper characterizes the class with these invariance properties uniqueness is discussed examples are given such as the pade riccati approximants and allowed types of singular points are discussed

parameter estimates of general failure rate model a bayesian approach abstract the failure rate function plays an important role in studying the lifetime distributions in reliability theory and life testing models a study of the general failure rate model r t a b t 1 under squared error loss function taking a and b independent exponential random variables has been performed in the literature in this article we consider a and b not necessarily independent the estimates of the parameters a and b under squared error loss linex loss and entropy loss functions are obtained and further examined using simulated and real data sets

h control for descriptor systems a matrix inequalities approach abstract this paper considers the h control problem for descriptor systems that possibly have impulsive modes and or j axis zeros first we propose matrix inequalities that give a generalized stability condition and an h norm condition for descriptor systems using these matrix inequalities we show that the solvability of a set of matrix inequalities is necessary and sufficient to the existence of a proper controller that satisfies a prescribed h norm condition as well as stabilizing the closed loop system and eliminating all impulsive modes these inequalities are equivalent to certain linear matrix inequalities to which we can get solutions whenever they exist using efficient polynomial time algorithms

definition and uniqueness of integral approximants abstract definitions are given for the integral approximant polynomials which insure their existence and uniqueness a specification of minimality is required in these definitions existence of infinite subsequences of integral polynomials without common factors of z is proven an equivalence theorem between the property of agreement of all high order integral polynomials and the property that the function being approximated belongs to a particular function class is proved the accuracy through order property is found to hold for all the cases we have investigated for the integral approximant an example is given which proves that the series coefficients which uniquely determine the integral polynomials may not uniquely determine the integral approximant

brief paper actuator fault robust estimation and fault tolerant control for a class of nonlinear descriptor systems for lipschitz nonlinear descriptor systems with bounded input disturbances by solving a lyapunov equation a robust state space observer is proposed to simultaneously estimate descriptor system states actuator faults their finite times derivatives and attenuate input disturbances in any desired accuracy the considered faults can be unbounded provided that their qth derivatives are bounded the present fault estimation approaches can handle a large class of faults by using the estimates of descriptor states and faults and the linear matrix inequality lmi technique a fault tolerant control scheme is worked out the nonlinear fault tolerant control system can be made solvable causal asymptotically stable and attenuate input uncertainties in terms of the prescribed performance index only original coefficient matrices are used in the proposed state space observers and fault tolerant controllers therefore the present design approaches are preferable in applications finally a numerical example is given to illustrate the design procedure and simulations demonstrate the efficiency of the proposed design

observer based control of systems with slope restricted nonlinearities an observer design is presented which makes use of bounds on the slope of system nonlinearities necessary and sufficient conditions are derived for the feasibility of the design a class of state feedback control laws are characterized which when implemented with the observer states ensure global asymptotic stability one such certainty equivalence design is illustrated on an active magnetic bearing example

fault estimation for a class of nonlinear systems based on intermediate estimator this technical note investigates the problem of fault estimation for a class of nonlinear systems with lipschitzian nonlinearities in most of the existing fault estimation approaches the observer matching condition should be satisfied however this condition is hard to meet for many systems to overcome this restriction a new fault estimation method is proposed where an intermediate variable is introduced and a specially designed intermediate estimator is proposed to estimate the state and the faults simultaneously by exploiting the properties of fault distribution matrix it is proved that the states of the error system are uniformly ultimately bounded simulation examples verify the effectiveness of the proposed method

determinants and the structure of the integral approximant table abstract the structure of the table of integral approximants based on our minimality definition is studied the key elements are simplices containing only a single linearly independent solution for the integral polynomials we prove some new identities among determinants of the coefficients of the determining equations for integral polynomials of different types relations between the simplices and these determinants are also derived we give determinantal conditions which are both necessary and sufficient for a full simplex to contain just one approximant a nullity lemma is proved limiting the change between contiguous types in the number of linearly independent solutions for integral polynomials virtually all of our results are equally valid for the more general case of the hermite pade approximants of the latin type

observer design and detection for nonlinear descriptor systems a nonlinear observer is considered for a class of continuous nonlinear descriptor systems subject to unknown inputs and faults this class is partly characterized by globally lipschitz nonlinearities and a member system may be singular and possibly non causal the observer structure chosen makes it useful for both state estimation for feedback controls and residual generation for fault detection results on the existence of solutions are given and some useful bounds are derived which are important in the observer design which is based on a transformed system and on the solution of a riccati equation the existence convergence properties and robustness of the observer are investigated by the use of a quadratic lyapunov function conditions are given for a bound to hold on the norm of the transfer function relating the residual error to the disturbance linear case a design algorithm is given and applied to the estimation of the states of a flexible joint robot

some convergence and divergence theorems for hermite pade approximants abstract we prove that under stated conditions the algebraic approximants converge to the function being approximated we also prove that the separation property convergence theorem of baker et al 1988 is sharp by proving a divergence theorem in addition we prove their missing lemma

state noise estimator for descriptor systems with application to sensor fault diagnosis for descriptor systems with measurement output noises input disturbances may exist at the same time a new descriptor estimator technique is developed the necessary and sufficient condition for the existence of the present estimator is derived and a systematic design approach is addressed the effect of uncertainties is decoupled completely and the asymptotic estimates of the descriptor system state and the output noise are obtained simultaneously furthermore a normal state disturbance estimator is also given for a class of nonlinear descriptor systems with both output noises and input uncertainties a nonlinear descriptor estimator is derived by using the proposed design approach together with the linear matrix inequality technique the existence and convergence of the nonlinear descriptor estimator is proven the asymptotic estimates of the descriptor nonlinear system state and the output noise are obtained at the same time the present estimators are applied to the sensor fault diagnosis and hence the sensor fault can be estimated asymptotically finally two numerical examples are included to illustrate the proposed design procedures and applications

functional unknown input reconstruction of descriptor systems the problem of finding conditions for the reconstruction of a linear combination of the vector of unknown inputs is tackled appropriate definitions are given in order to address formally the analysis thus necessary and sufficient conditions are obtained for two cases when the reconstruction may be achieved in finite time and when it is possible to do it asymptotically the results are applied for the fault detection with the respective deduction of analogous conditions

finite horizon h_ infty filtering with missing measurements and quantization effects in this paper a new h filtering approach is developed for a class of discrete time varying systems subject to missing measurements and quantization effects the missing measurements are modeled via a diagonal matrix consisting of a series of mutually independent random variables satisfying certain probabilistic distributions on the interval 0 1 the measured output is quantized by a logarithmic quantizer attention is focused on the design of a stochastic h filter such that the h estimation performance is guaranteed over a given finite horizon in the simultaneous presence of probabilistic missing measurements quantization effects as well as external non gaussian disturbances a necessary and sufficient condition is first established for the existence of the desired time varying filters in virtue of the solvability of certain coupled recursive riccati difference equations rdes owing to its recursive nature the proposed rde approach is shown to be suitable for online application without the need of increasing the problem size the simulation experiment is carried out for the mobile robot localization problem with non gaussian disturbances missing measurements and quantization effects the effectiveness of the proposed method is demonstrated in the numerical example

robust fault diagnosis for non linear difference algebraic systems a new robust fault diagnosis method based on linear matrix inequality lmi for non linear difference algebraic systems das with uncertainties is proposed based on the known nominal model of das it firstly constructs an auxiliary system consisting of a difference equation and an algebraic equation then converts the problem of fault identification into the problem of parameter estimation and finally realizes fault identification using an lmi method this method can not only detect isolate and identify faults for das but also give the upper bounds of fault identification error simulation indicates that it can give satisfactory diagnostic results for both abrupt and incipient faults

a time domain approach to robust fault detection of linear time varying systems this paper gives the optimal solutions to several robust fault detection problems such as 2 and problems for linear time varying systems in a time domain which extends the previous results on linear time invariant systems in a frequency domain it is shown that all three problems have the same optimal detection filter and the filter is a simple observer obtained by solving a standard differential riccati equation finally an example is given to illustrate our results

estimation of system components reliabilities using masked data consider a system of m independent and non identical components connected in series such system fails whenever at least one of the components has failed due to the cost and time constraints however the exact cause of system failure might be unknown instead it is assumed that the cause of system failure may be due to a component that belongs to a subset of the m components such type of observation is referred to as being masked confronted with this phenomenon we use the maximum likelihood procedure to estimate the parameters indexed to the lifetime distributions of the system components further the system component reliabilities at a specified time will be estimated we focused on series systems with two and three components the system components lifetimes are assumed to be weibull distributed we show that closed form solutions for the maximum likelihood estimates can be obtained under certain assumptions further numerical simulation study is presented

on a system of classical polynomials of simultaneous orthogonality abstract we introduce a system of classical polynomials of simultaneous orthogonality study the differential equation of third order recurrence relation and precise the ratio asymptotic and zeros distribution of polynomials

the structure of the singular solution table of the m pade approximation problem abstract a general interpolation problem is defined which contains as special cases the m pade approximation problem as well as classical interpolation problems e g newton pade approximation to study the structure of the solution table a new concept the minimal solution is introduced statements on the local and global structure of the solution table are obtained as a special case the well known block structure of the pade table is derived finally a characterization of the solution set is given

observer design for a class of mimo nonlinear systems a simple observer is proposed for a large class of mimo nonlinear systems which includes many physical models the main characteristic of the proposed observer lies in the easiness of its implementation and calibration indeed the gain of this observer does not necessitate the resolution of any dynamical system and its expression is given moreover its calibration is achieved through the choice of a single parameter a simulation example is given in order to illustrate the performance of the proposed observer

parameter estimations in linear failure rate model using masked data estimations of the parameters included in the lifetime distributions of the individual components in a series system with independent and nonidentical components are introduced in this paper by using masked system life data particularly we deduce the maximum likelihood and bayes estimates of these parameters when the failure rates of the system components are assumed to be linear with different parameters in bayes approach it is assumed that the unknown parameters to be estimated behave as independent random variables having symmetrical triangular prior distributions the problem is illustrated on a two component series system to show how one can apply the theoretical results obtained here numerical simulation study is introduced also in such simulation study a comparison between the procedures used is discussed

fault estimation and tolerant control for fuzzy stochastic systems this paper deals with the problem of fault estimation and fault tolerant control for takagi sugeno t s fuzzy stochastic systems with sensor failures where the system under consideration contains ito type stochastic disturbances a new robust observer technique is presented to obtain the estimates of the system states and the sensor faults simultaneously and a fuzzy fault tolerant control scheme is developed to guarantee the closed loop system to be exponentially stable in mean square sufficient conditions are obtained for the existence of admissible controllers and it is shown that the reachability of the sliding mode dynamics can be guaranteed under the proposed control techniques finally a numerical example is provided to illustrate the effectiveness and applicability of the theoretic results obtained

observer design for discrete time descriptor systems an lmi approach abstract in this paper the observer design problem for discrete time descriptor systems is considered for the discrete time linear descriptor systems the necessary and sufficient conditions for the existence and convergence of the proposed observer are given and proved and a systemic design approach is presented via the linear matrix inequalities formulation furthermore an extension to a class of nonlinear descriptor systems with lipschitz constraints is investigated simulation examples are given to illustrate the estimation performance of the proposed method

fault detection for t s fuzzy systems with partly unmeasurable premise variables abstract this paper studies the fault detection problem for t s fuzzy systems with partly unmeasurable premise variables by using measurable premise variables and estimations of unmeasurable premise variables of fuzzy models as the premise variables of observers a novel fuzzy fault detection observer scheme is constructed and the corresponding design condition is proposed via a set theoretic description different from the conventional fault detection observer schemes where all premise variables of the observer are the estimations of the premise variables in the fuzzy systems the proposed method can take full advantage of the partly measurable premise variables for achieving a better fault detection performance a numerical example is given to illustrate the effectiveness of the proposed method

convergent fault estimation for linear systems with faults and disturbances the problem of convergent fault estimation for a class of linear systems with faults and disturbances is addressed for the first time in this technical note a differential equation based convergence theorem of mean sequence of estimates is proposed which provides an iterative mean estimation technique that has not been fully reported yet in the literature based on the technique a convergent fault estimation strategy for the linear system in consideration is designed and the convergence of mean sequence of fault estimates is proved theoretically an iterative algorithm is given subsequently to compute the fault estimates numerical simulation results demonstrate the effectiveness and merits of the proposed method

estimation of components reliability in a parallel system using masked system life data in this paper we estimate the reliability of the individual components that belong to a parallel system using masked system life test data in particular we compute the maximum likelihood and bayes estimates of component reliabilities the considered system consists of j independent components having non identical complementary exponential lifetime distributions it is assumed for bayes estimates that the unknown parameters are independent random variables having symmetrical triangle probability density functions the approaches are illustrated with a two component parallel system a numerical simulation study is introduced to show how one can use the present approaches to compute these estimations for a practical problem also in the numerical simulation study a comparison between bayes and maximum likelihood estimates is introduced

vector orthogonal polynomials abstract the following well known framework will be applied to hermite pade approximants first the hermite pade type approximants will be defined from the error of approximation some supplementary conditions will be fixed in order to obtain hermite pade forms vector orthogonal polynomials will be deduced from these conditions their existence and uniqueness are studied in the normal case these results are ensured then some properties of vector orthogonal polynomials will be proved

finite horizon estimation of randomly occurring faults for a class of nonlinear time varying systems this paper is concerned with the finite horizon estimation problem of randomly occurring faults for a class of nonlinear systems whose parameters are all time varying the faults are assumed to occur in a random way governed by two sets of bernoulli distributed white sequences the stochastic nonlinearities entering the system are described by statistical means that can cover several classes of well studied nonlinearities the aim of the problem is to estimate the random faults over a finite horizon such that the influence from the exogenous disturbances onto the estimation errors is attenuated at the given level quantified by an h norm in the mean square sense by using the completing squares method and stochastic analysis techniques necessary and sufficient conditions are established for the existence of the desired finite horizon h fault estimator whose parameters are then obtained by solving coupled backward recursive riccati difference equations rdes a simulation example is utilized to illustrate the effectiveness of the proposed fault estimation method

fuzzy model based fault tolerant design for nonlinear stochastic systems against simultaneous sensor and actuator faults this paper addresses the problem of fault estimation and fault tolerant control for a class of takagi sugeno t s fuzzy ito stochastic systems subject to simultaneously sensor and actuator faults the main difficulty in this study is that sensor faults actuator faults and stochastic noise that are governed by brownian motion are taken into simultaneous consideration in a unified framework and traditional fault tolerant approaches are not effective to solve this research issue a new descriptor fuzzy sliding mode observer approach is presented in this paper to obtain the simultaneous estimates of system state sensor fault and actuator fault vectors based on the state estimates an observer based fault tolerant control ftc scheme is developed to stabilize the resulting closed loop system finally a simulation example is provided to show the effectiveness of the proposed fault tolerant approach

luenberger like interval observer design for discrete time descriptor linear system abstract in this paper the problem of luenberger like interval observer design for discrete time descriptor linear system is investigated in the first place two ways in which the original descriptor system is transformed into general systems are given and the detectability of the equivalent general systems is discussed in detail a new equivalent general system construction is developed and we prove that the detectability can be kept under this new equivalent transformation after this based on the new equivalent general system a luenberger like interval observer is proposed finally two simulation examples are given to demonstrate the correctness and the effectiveness of the proposed interval observer

bayesian estimation of the parameters in n non independent and non identical series system in this paper we have presented a bayesian approach for estimating the unknown parameters in a n non independent and non identical series system subjected to n 1 sources of fatal shocks also the estimators of the values of the survival functions are deduced the corresponding estimators of the similar system subjected to exponential fatal shocks are given and during this process the gamma prior density function is used special cases of the present results are obtained to show how the current results generalized the results in other literatures

a geometric approach to nonlinear fault detection and isolation we present a differential geometric approach to the problem of fault detection and isolation for nonlinear systems a necessary condition for the problem to be solvable is derived in terms of an unobservability distribution which is computable by means of suitable algorithms the existence and regularity of such a distribution implies the existence of changes of coordinates in the state and in the output space which induce an observable quotient subsystem unaffected by all fault signals but one for this subsystem a fault detection filter is designed

technical communique a note on the existence of a solution and stability for lipschitz discrete time descriptor systems this paper addresses the existence and uniqueness of a solution and stability for lipschitz discrete time descriptor systems by means of the fixed point principle a criterion is presented via a matrix inequality and the criterion guarantees the existence and uniqueness of a solution in addition a sufficient condition is also presented to ensure that the solution exists for any compatible initial condition and the system is globally exponentially stable simultaneously it is shown that the criterion presented in this paper is easy to verify and independent of the choices of decomposition matrices for the given system finally the approach is illustrated by a numerical example

existence of certain sequences of hermite pade approximants abstract we prove the existence of infinite sequences of unique minimal hermite pade polynomials of horizontal near partially diagonal and near diagonal character

approximants de pade hermite 2eme partie programmation in this second paper we propose an algorithm for the construction of the tables and of the pade hermite tables 3 then we present some numerical applications

brief paper lmi based sensor fault diagnosis for nonlinear lipschitz systems the problem of sensor fault diagnosis in the class of nonlinear lipschitz systems is considered a dynamic observer structure is used with the objective to make the residual converge to the faults vector achieving detection and estimation at the same time it is shown that unlike the classical constant gain structure this objective is achievable by minimizing the faults effect on the estimation error of the dynamic observer the use of appropriate weightings to solve the design problem in a standard convex optimization framework is also demonstrated an lmi design procedure solvable using commercially available software is presented

controllability and elimination of impulsive modes in descriptor systems as a refined notion impulsive mode controllability is suggested for the general class of linear continuous descriptor systems this notion reveals rich properties of the general descriptor systems in terms of admissibility of initial conditions admissibility of feedback control and impulsive mode elimination the condition for impulsive mode controllability is derived and proved to be necessary and sufficient for the existence of admissible feedback controls eliminating impulsive modes under impulsive mode controllability admissible feedback controls are constructed for eliminating impulsive modes on the basis of numerically reliable decompositions of the system s coefficient matrices

approximants de pade hermite 1ere partie theorie we present in this first paper a generalization of pade approximants which gives us as particular cases shafer s and baker sd log approximants first we define these approximants following an old idea of hermite then we prove some fundamental properties for their constructions

hermite pade approximation basic notions and theorems abstract our purpose is to give a brief exposition of basic notions and facts on hermite pade approximation theory a hermite pade form hpf is defined here in the same way as a pade approximant is as a consequence in some cases hpf does not exist even in the modified version hpf need not be unique therefore it was worthwhile to choose some hpf as the optimal one all criteria of existence unicity etc are phrased in a unified manner they base on few quantities depending on the power series under consideration and are usable in the theory rather than in the numerical practice

vector orthogonal polynomials we give the relation between hermite pade approximants and vector orthogonal polynomials an algorithm for calculating vector orthogonal polynomials near the diagonal is described an exact multiple integral formula for vector orthogonal polynomials is proved an example is given showing how the recurrence relations of pade may be used to calculate hermite pade approximants of degrees m mu mu with mu increasing

a sliding mode observer for infinitely unobservable descriptor systems in existing work of sliding mode observers smos for descriptor systems a necessary condition is that the system must be infinitely observable this paper presents a scheme that circumvents that condition by reformulating the system as a reduced order system where certain structures in the system matrix are manipulated and certain states are treated as unknown inputs following that an smo is implemented on the reduced order system where state and fault estimation can be achieved necessary and sufficient conditions of this scheme are also presented finally a simulation example shows the effectiveness of the proposed scheme

ℋ ℋ fault detection filter for a class of nonlinear descriptor systems this article addresses the problem of designing a robust fault detection filter rfdf for a class of nonlinear descriptor systems whose nonlinear term is globally lipschitz and linear term is described by a linear parameter varying form the effect of perturbations on the residuals is minimised using the norm while the sensitivity performance is guaranteed using the index thanks to a particular lyapunov function which depends on the faults and the filter design problem is formulated as a convex optimisation problem solved via linear matrix inequality techniques performances of the proposed filter are shown through the application of an activated sludge process model

convergence theorems for rows of differential and algebraic hermite pade approximations abstract the authors investigate the asymptotic behaviour of hermite pade polynomials of latin type which are formed from differential or algebraic expressions involving a meromorphic function the degrees of the denominator polynomials are chosen to correspond to rows of the hermite pade table for special choices of denominator degrees these asymptotic are used to prove de montessus type theorems for hermite pade approximants formed by solving differential or algebraic equations

descriptor recursive estimation for multiple sensors with different delay rates in this article the problem of recursive estimation is studied for a class of descriptor systems measured by multiple sensors with different delay rates the delay phenomenon occurs in a random way and the delay rate for each sensor is characterised by an individual binary switching sequence obeying a conditional probability distribution the original descriptor system is transformed into two non descriptor stochastic subsystems with autocorrelated and cross correlated noises by using the singular value decomposition and the state augmentation applying an innovation analysis approach and the orthogonal projection theorem recursive estimators including filter predictor and smoother are first derived for each subsystem and the process noise then based on the newly obtained recursive state estimators and process noise estimators the recursive filter predictor and smoother are obtained for the original descriptor system measured by multiple sensors with different delay rates a numerical simulation ex

robust h h fault detection observer design for descriptor lpv systems with unmeasurable gain scheduling functions this paper addresses a design of a fault detection observer fdo for descriptor linear parameter varying d lpv systems in contrast with the conventional approach for d lpv systems the gain scheduling functions gsf are considered unmeasurable the fdo is investigated in the h h index framework in order to minimise the effects of the disturbance and maximise the effect of faults on the residuals and minimise the error caused by the unmeasurable gsf the stability is guaranteed based on a lyapunov approach sufficient conditions for the existence of the fdo are established in terms of linear matrix inequalities the effectiveness of the proposed method is illustrated by means of a simulation example

h h fault detection filter design for discrete time takagi sugeno fuzzy system abstract in this note a robust fault detection observer is designed for a t s takagi sugeno fuzzy model with sensor faults and unknown bounded disturbances the method applies the technique of descriptor systems by considering sensor faults as an auxiliary state variable the idea is to formulate the robust fault detection observer design as an h h problem based on nonquadratic lyapunov functions a solution of the considered problem is then given via a linear matrix inequality lmi formulation an example is proposed to illustrate the design conditions

application of the pade method to solving the noisy trigonometric moment problem some initial results the noisy trigonometric moment problem for a finite linear combination of box functions is considered and a research program possibly leading to a superresolving method is outlined and some initial steps are performed the method is based on the remark that the poles of the pade approximant to the z transform of the noiseless moments show asymptotically a regular pattern in the complex plane the pattern can be described by a set of arcs connecting points on the unit circle and a pole density function defined on the arcs when a moderate noise affects the moments more arcs are needed to describe the pole pattern but the noiseless pattern is slightly deformed still allowing its identification when this identification is possible a very effective noise filter and moment extrapolator should be easily constructed in this paper only some preliminary steps of the above research program are performed specifically the case of one box function is considered a method for computing the pole patterns

observers for a class of lipschitz systems with extension to h performance analysis abstract in this paper observer design for a class of lipschitz nonlinear dynamical systems is investigated one of the main contributions lies in the use of the differential mean value theorem dmvt which allows transforming the nonlinear error dynamics into a linear parameter varying lpv system this has the advantage of introducing a general lipschitz like condition on the jacobian matrix for differentiable systems to ensure asymptotic convergence in both continuous and discrete time systems such sufficient conditions expressed in terms of linear matrix inequalities lmis are established an extension to h filtering design is obtained also for systems with nonlinear outputs a comparison with respect to the observer method of gauthier et al a simple observer for nonlinear systems applications to bioreactors ieee trans automat control 37 6 1992 875 880 is presented to show that the proposed approach avoids high gain for a class of triangular globally lipschitz systems in the last section academic examples are given to show the performances and some limits of the proposed approach the last example is introduced with the goal to illustrate good performances on robustness to measurement errors by avoiding high gain

h h fault detection observer in finite frequency domain for linear parameter varying descriptor systems abstract this paper considers h h fault detection observer design in the finite frequency domain for a class of linear parameter varying lpv descriptor systems we propose a novel fault detection observer with a non singular structure to make the residual sensitive to faults and robust against disturbances we develop a finite frequency h h design method based on a generalized kalman yakubovich popov lemma for lpv descriptor systems design conditions for the proposed fault detection observer are derived and converted as linear matrix inequalities simulation studies are conducted to demonstrate the performance of the proposed method

b splines and hermite pade approximants to the exponential function this paper is the continuation of a work initiated in p sablonniere an algorithm for the computation of hermite pade approximations to the exponential function divided differences and hermite pade forms numer algorithms 33 2003 443 452 about the computation of hermite pade forms hpf and associated hermite pade approximants hpa to the exponential function we present an alternative algorithm for their computation based on the representation of hpf in terms of integral remainders with b splines as peano kernels using the good properties of discrete b splines this algorithm gives rise to a great variety of representations of hpf of higher orders in terms of hpf of lower orders and in particular of classical pade forms we give some examples illustrating this algorithm in particular another way of constructing quadratic hpf already described by different authors finally we briefly study a family of cubic hpf

filtering and fault estimation of descriptor switched systems in this paper the problems of state and fault estimation are addressed for a class of switched descriptor systems subject to lipschitz nonlinearities and unknown inputs ui the ui appear both on the dynamic and on the measurement equations two problems are addressed by l 2 gain minimization with the use of switched lyapunov functions and formulated by lmi first a functional observer for switched lipschitz nonlinear descriptor system is proposed for robust state estimation second fault estimation is performed by filtering the output estimation error as usually done in the residual generation framework moreover frequency weighting functions can be used to shape the response to the fault and thus improve the estimation

parameter estimations in a general hazard rate model using masked data the general hazard rate model is a relevant model to specify the life time distributions in reliability theory and life testing in this paper we use masked data to obtain estimations of the unknown parameters included in life time distributions of the individual components belonging to a series system consists of j independent and non identical components it is assumed here that the failure rate of component j is general with the form h j t a j b jt c j 1 j 1 2 j where a j b j c j are non negative parameters maximum likelihood and bayes estimates of the parameters a j b j are obtained while c j are known symmetrical triangular prior distributions are assumed for the unknown parameters to be estimated in obtaining the bayes estimators for these parameters a large simulation study is done in order to i explain how one can utilize the theoretical results obtained and ii compare the two procedures used the problem of estimating the unknown parameters included in increasing linear failure rate model can be obtained as special case by setting c j 2 for all j 1 2 j