non linear observer based on the euler discretization in this paper we present an estimator based on the euler discretization first we show that the proposed estimator is an exponential observer in the case when the error between trajectories of continuous time and its associated euler discretized system can be neglected otherwise we show that the error of estimation is exponentially attracted by some neighbourhood of the origin which depends only on the sampling time finally numerical simulations using a bioreactor model are given in order to highlight the performance of the proposed estimator

linearization of time delay systems by input output injection and output transformation in the present paper necessary and sufficient geometric conditions for the equivalence of a single input single output nonlinear time delay system under bicausal change of coordinates and regular output transformation to a linear weakly observable time delay system up to input output injection are given the obtained results are then applied to the observer design problem

direct transformation of nonlinear systems into state affine miso form for observer design this paper gives necessary and sufficient conditions to solve in a constructive way the transformation of a general multiple input single output nonlinear system into a state affine system this result is direct i e without solving the state elimination problem when computing the input output differential equation a kalman like observer can be designed for the obtained state affine system

krein type theorems and ordered structure for cauchy de branges spaces abstract we extend some results of m g krein to the class of entire functions which can be represented as ratios of discrete cauchy transforms in the plane as an application we obtain new versions of de branges ordering theorem for nearly invariant subspaces in a class of hilbert spaces of entire functions examples illustrating sharpness of the obtained results are given we also discuss applications to spectral theory of rank one perturbations of normal operators

observer design for autonomous discrete time nonlinear systems abstract we obtain a necessary and sufficient condition for a discrete time nonlinear system to be locally state equivalent to the nonlinear observer form the result looks similar to the continuous counterpart except for the fact that ad operation is utilized instead of ad operation

a block triangular observer form for non linear observer design this paper discusses observer design for unforced non linear multi output systems using a block triangular observer form btof the btof allows an established exact error linearization observer design method to be generalized to a larger class of multi output systems observer design proceeds in a decentralized manner or subsystem at a time starting with the uppermost subsystem designs for each subsystem effectively treat upper subsystem states as known measurements and are relatively simple given their reduced dimension exponential error stability results are given new necessary and sufficient existence conditions are given for the btof examples illustrate the construction of the btof coordinates and the advantages of a btof based design compared to a generally applicable method

a new procedure for time varying linearization up to output injection new necessary and sufficient conditions for time varying linearization up to output injection tvloi are presented they yield a straightforward tvloi procedure

time scaling for observer design with linearizable error dynamics in this paper we consider the problem of observer design for dynamical systems with scalar output by linearization of the error dynamics via coordinate change output injection and time scaling we present necessary and sufficient conditions which guarantee the existence of a coordinate change and output dependent time scaling such that in the new coordinates and with respect to the new time the system has linear error dynamics

schrodinger operators and de branges spaces abstract we present an approach to de branges s theory of hilbert spaces of entire functions that emphasizes the connections to the spectral theory of differential operators the theory is used to discuss the spectral representation of one dimensional schrodinger operators and to solve the inverse spectral problem

completeness and spectral synthesis of nonselfadjoint one dimensional perturbations of selfadjoint operators abstract we study spectral properties of nonselfadjoint rank one perturbations of compact selfadjoint operators the problems under consideration include completeness of eigenvectors relations between completeness of the perturbed operator and its adjoint and the spectral synthesis problem we obtain new criteria for completeness and spectral synthesis in this class as well as a series of counterexamples which show that the spectral structure of rank one perturbations is in general unexpectedly rich and complicated a parallel spectral theory is developed for one dimensional singular perturbations of unbounded selfadjoint operators our approach is based on a functional model for this class which translates the properties of operators to completeness problems for systems of reproducing kernels and their biorthogonals in some spaces of analytic entire functions

finite time observers application to secure communication in this paper control theory is used to formalize finite time chaos synchronization as a nonlinear finite time observer design issue this paper introduces a finite time observer for nonlinear systems that can be put into a linear canonical form up to an output injection the finite time convergence relies on the homogeneity properties of nonlinear systems the observer is then applied to the problem of secure data transmission based on the finite time chaos synchronization and the two channel transmission method

observer design for mimo non uniformly observable systems the design of high gain observers is usually based on normal forms of observability if the system is observable for every input uniform observability the gain of the observer does not required a solution to differential equation for multiple input multiple output mimo non uniformly observable systems we give here a sufficient condition that the input must satisfy in order to design an observer unlike uniformly observable systems the observer gain of non uniformly observable systems is derived from a lyapunov differential equation

algebraic conditions for state equivalence to a discrete time nonlinear observer canonical form abstract algebraic necessary and sufficient conditions for a single output discrete time system to be state equivalent to a generalized nonlinear observer canonical form with or without output transformation are derived our algebraic conditions are easier to verify for researchers unaccustomed to differential geometry in addition our proofs are constructive and contain the state and output transformations for generalized nonlinear observer canonical forms

robust detection filter design in the presence of time varying system perturbations this paper discusses the problem of designing detection filters for a class of linear time varying systems the basic contribution of the paper is that by applying a time invariant equivalent representation of the original time varying system it is possible to construct a detection filter such that the solution of the design problem can be solved using algebraic methods and geometric concepts similar to the case of time invariant situations

a nonlinear luenberger like observer for nonlinear singular systems this paper investigates observer design problem for a large class of nonlinear singular systems with multiple outputs we firstly regularize the singular system by injecting the derivative of outputs into the system then differential geometric method is applied to transform the regularized system into a simple normal form for which a luenberger like observer is proposed

multiple time scalings of a multi output observer form time scalings in the multi output observer form for uncontrolled nonlinear continuous time systems are considered in this technical note it is the multi output version of an existing single input result time scaling broadens the class of systems which admits an exact error linearization observer design by including time scaling transformations the existence conditions of the time scaling transformation and the change of state coordinates to time scaled observer form are provided

dynamic observer error linearization in this paper a new framework of observer error linearization problem is proposed the main idea of our approach is twofold the one is to introduce an auxiliary dynamics whose input is the system output and the other is to transform the augmented system into an observable linear system with an injection term which contains the system output as well as the state of the auxiliary dynamics it is a natural extension of the recently developed dynamic observer error linearization where the injection term contains only newly defined output it is also shown that whenever an n dimensional system is immersible into an n d dimensional linear system up to an output injection then it can be also dynamically observer error linearizable in our sense with a d dimensional auxiliary dynamics moreover we show that the converse is not true by providing a counterexample which implies that our approach is applicable to a strictly wider class of systems than that of the system immersion method

discrete time observer error linearizability via restricted dynamic systems in this technical note we define the observer error linearization problem of a discrete time autonomous nonlinear system via a restricted dynamic system this is the dual to restricted dynamic feedback linearization in a loose sense necessary and sufficient conditions for this problem are obtained in terms of the index

brief paper observer forms for perspective systems the estimation of three dimensional position information from two dimensional images in computer vision systems can be formulated as a state estimation problem for a nonlinear perspective dynamic system the multi output state estimation problem has been treated by several authors using methods for nonlinear observer design this paper shows that a perspective system can be transformed to two observer forms and provides constructive methods for arriving at the transformations these observer forms lead to straightforward observer designs first it is shown that using an output transformation the system admits an observer form which leads to an observer with linear error dynamics a second observer design is based on a time scaled block triangular form both designs assume a commonly used observability condition the designs are demonstrated in simulation

nonlinear estimation in a class of gene transcription process in this work the goodwin model applied to gene transcription is employed as a benchmark system for estimation purposes considering two dynamic behaviors monotone decreasing and sustained oscillations each one under a specific parameter s set the preceding observability analysis of the goodwin model was done via linear observability and the differential algebraic framework where is proved that the system is fully observable from mrna concentration measurements therefore a class of nonlinear observer which considers a class of sigmoid and linear functions of the output feedback considering model uncertainties is proposed and a sketch of proof of the observer s convergence is provided under the background of the lyapunov theory in order to demonstrate asymptotic convergence numerical experiments are carrying out in order to show the performance of the proposed methodology which is compared with a standard luenberger proportional observer and a proportional sliding mode observer psmo

reduced order dynamic observer error linearisation a natural extension of observer error linearisation this paper introduces the concept of reduced order dynamic observer error linearisation rdoel for multi output systems which is the problem of transforming a nonlinear system into a nonlinear observer canonical form with the aid of auxiliary dynamics the proposed rdoel framework is not only a modified version of dynamic observer error linearisation doel but also a natural extension of observer error linearisation oel we provide three necessary conditions for the rdoel problem and then derive a necessary and sufficient condition described in terms of lie algebras of vector fields furthermore from the result we also give a geometric necessary and sufficient condition for the oel problem which has not yet been completely established in the case where a diffeomorphism on the output of general form is considered

multi output dependent observability normal form abstract this article gives a sufficient condition which guarantees the existence of a reference frame in which a multi output nonlinear system is linearizable with a linear part depending on its outputs our method is based on the design of a reference frame associated with nonlinear observable systems moreover we give a generalization of the result obtained in d boutat g zheng j p barbot observer error linearization multi output depending in proc of ieee cdc 06 2006 and g zheng d boutat j p barbot single output dependent observability normal form siam journal on control and optimization 46 6 2007 and some examples are given in order to illuminate our thinking

analytical redundancy relations for fault detection and isolation in algebraic dynamic systems this paper extends the analytical redundancy techniques well developed for linear systems to fdi in non linear dynamic systems modeled by polynomial differential algebraic equations the residual evaluation form is developed for sensor actuator and process component faults fault detectability and isolability conditions are given and the design of robust structured residuals is addressed

design techniques for orthogonal modulated filterbanks based on a compact representation this paper presents a method to design perfect reconstruction orthogonal modulated filterbanks having a very large number of subbands at first using the angular parameterization of the underlying lattice structure the problem is formulated as an unconstrained optimization problem then it is shown for two different optimization criteria the minimization of the out of band energy and the maximization of the time frequency localization that the optimized lattice coefficients can be interpolated in two different ways a first characterization takes advantage of the fact that the angles related to successive polyphase components of the prototype filter have a smooth behavior a new parameterization named compact representation is therefore introduced which shows that a linear increase of the number of parameters with respect to the number of subbands can be avoided with practically no loss of accuracy a second observation concerns the also smooth behavior of each angular parameter when considering an increasing number of subbands the efficiency of the two approaches is illustrated by the design of filterbanks with a large number of subbands going from 32 up to 4096 including prototype filters up to a length of 32 768

nonlinear observers with linearizable error dynamics we present a new method for designing asymptotic observers for a class of nonlinear systems the error between the state of the system and the state of the observer in appropriate coordinates evolves linearly and can be made to decay arbitrarily exponentially fast

partial state observers for nonlinear systems this note deals with the design of reduced order observers for a class of nonlinear systems the order reduction of the observer is achieved by only estimating a required partial set of the state vector necessary and sufficient conditions are derived for the existence of reduced order observers an observer design procedure based on linear matrix inequalities is given a numerical example is given to illustrate the design method

new algebraic geometric conditions for the linearization by input output injection the goal of this paper is twofold it unifies and generalizes existing results on input output injection linearization of nonlinear systems the problem is solved as a realization problem since it is based on the analysis of the structure of the input output differential equation the necessary and sufficient conditions are derived from a simplified and constructive procedure for clarity the paper is limited to the case of single output systems exterior differential systems are extensively used throughout the paper giving constructive conditions

transformation of nonlinear systems in observer canonical form with reduced dependency on derivatives of the input abstract the transformation of nonlinear multi input multi output systems x f x u y h x u into an observer canonical form with reduced dependency on derivatives of the input is studied necessary and sufficient conditions for its existence and a straightforward algorithm for obtaining the canonical model are derived the proposed method involves the solution of a nonlinear algebraic equation system and systems of first order linear partial differential equations the nonlinear canonical form obtained permits global observer error linearization and it is a stage in the design of nonlinear observers the method is illustrated by an example

cosine modulated filterbanks based on extended gaussian functions a new family of cosine modulated filterbanks based on functions called extended gaussian functions egfs is obtained the design is particularly simple since it is mainly based on a closed form expression nearly perfect reconstruction cosine modulated filterbanks are obtained as well as guidelines to estimate the filterbank parameters this analytical design method can be used to produce with a controlled accuracy filterbanks with practically no upper limitations in the number of coefficients and subbands furthermore a slight modification of the prototype filter coefficients is sufficient to satisfy exactly the perfect reconstruction constraints an analysis of the time frequency localization of the discrete prototype filters also shows that under certain conditions egf prototypes are at less than 0 3 from the optimal upper bound

analysis and design of ofdm oqam systems based on filterbank theory a discrete time analysis of the orthogonal frequency division multiplex offset qam ofdm oqam multicarrier modulation technique leading to a modulated transmultiplexer is presented the conditions of discrete orthogonality are established with respect to the polyphase components of the ofdm oqam prototype filter which is assumed to be symmetrical and with arbitrary length fast implementation schemes of the ofdm oqam modulator and demodulator are provided which are based on the inverse fast fourier transform non orthogonal prototypes create intersymbol and interchannel interferences isi and ici that in the case of a distortion free transmission are expressed by a closed form expression a large set of design examples is presented for ofdm oqam systems with the number of subcarriers going from four up to 2048 which also allows a comparison between different approaches to get well localized prototypes

brief paper robust fault detection based on observers for bilinear systems the design of a residual generator for robust fault detection in bilinear systems is considered two methods are presented the first one is based on a linear time invariant observer up to output injection while the second one relies on a so called kalman like observer it is shown via examples that the approach based on a kalman like observer allows one to handle a larger class of bilinear systems than the other observer based methods presented in the literature

linearization by output injection and nonlinear observers abstract observers can easily be constructed for those nonlinear systems which can be transformed into a linear system by change of state variables and output injection necessary and sufficient conditions for the existence of such a transformation are given

summability properties of gabor expansions abstract we show that there exist complete and minimal systems of time frequency shifts of gaussians in l 2 r which are not strong markushevich basis do not admit the spectral synthesis in particular it implies that there is no linear summation method for general gaussian gabor expansions on the other hand we prove that the spectral synthesis for such gabor systems holds up to one dimensional defect

a general formulation of modulated filter banks this paper presents a general framework for maximally decimated modulated filter banks the theory covers the known classes of cosine modulation and relates them to complex modulated filter banks the prototype filters have arbitrary lengths and the overall delay of the filter bank is arbitrary within fundamental limits necessary and sufficient conditions for perfect reconstruction pr are derived using the polyphase representation it is shown that these pr conditions are identical for all types of modulation modulation based on the discrete cosine transform dct both dct iii dct iv and dct i dct ii and modulation based on the modified discrete fourier transform mdft a quadratic constrained design method for prototype filters yielding pr with arbitrary length and system delay is derived and design examples are presented to illustrate the tradeoff between overall system delay and stopband attenuation subchannelization

observer based residual generation for fault diagnosis for non affine non linear polynomial systems this paper proposes an observer based residual generator obrg for diagnosing faults in a continuous non affine system with polynomial non linearities up to any finite degree where the fault and an unknown input affect both the system and part of the output firstly given certain assumptions and the use of defined extended vectors a parameterized polynomial system is considerred for which a compact set of sufficient conditions is given for the existence of a candidate obrg conditions for error stability by a lyapunov method and detectability are given the calculation steps in the design of the obrg are shown to involve the solution of three linear equations with parameterizations and the calculation of a set of constant matrices for detectability of faults a result is then given establishing that the design holds for a much wider class of systems the residual design is applied to a real three tank system

symbolic computing of nonlinear observable and observer forms observer design for highly nonlinear dynamics is an important issue particularly when the locally observable dynamics are not linearly observable in such circumstances the ability to reduce the system to observable or observer form is a useful first step to observer design we describe and illustrate symbolic computing tools to do that

state and input simultaneous estimation for a class of nonlinear systems this paper addresses the problem of estimating simultaneously the state and input of a class of nonlinear systems here the systems nonlinear part comprises a lipschitz nonlinear function with respect to the state and input and a state dependent unknown function including additive disturbance as well as uncertain nonlinear time varying terms upon satisfying some conditions the observer design problem can be solved via a riccati inequality or a lmi based technique with asymptotic estimation guaranteed a numerical example is included for illustration

theory and design of m channel maximally decimated quadrature mirror filters with arbitrary m having the perfect reconstruction property based on the concept of losslessness in digital filter structures this paper derives a general class of maximally decimated m channel quadrature mirror filter banks that lead to perfect reconstruction the perfect reconstruction property guarantees that the reconstructed signal hat x n is a delayed version of the input signal x n i e hat x n x n n 0 it is shown that such a property can be satisfied if the alias component matrix ac matrix for short is unitary on the unit circle of the z plane the number of channels m is arbitrary and when m is two the results reduce to certain recently reported 2 channel perfect reconstruction qmf structures a procedure based on recently reported fir cascaded lattice structures is presented for optimal design of such fir m channel filter banks design examples are included

observer design based on immersion technics and canonical form abstract a crucial problem in immersion based observer design is the case where the dimension of the immersed system is greater than that of the original system and the analytical expression of the inverse of the immersion is unknown in this paper we have proposed a method for constructing observers for such autonomous nonlinear systems

reduced order state reconstruction for nonlinear dynamical systems in the presence of model uncertainty abstract a new approach to the reduced order state reconstruction problem for nonlinear dynamical systems in the presence of model uncertainty is proposed the problem of interest is conveniently formulated and addressed within the context of singular first order non homogeneous partial differential equations pde theory leading to a reduced order nonlinear state estimator that is constructed through the solution of a system of singular pdes a set of necessary and sufficient conditions is derived that ensure the existence and uniqueness of a locally analytic solution to the above system of pdes and a series solution method is developed that is easily programmable with the aid of a symbolic software package such as maple furthermore the convergence of the estimation error or the mismatch between the actual unmeasurable states and their estimates is analyzed and characterized in the presence of model uncertainty finally the performance of the proposed reduced order state reconstruction method is evaluated in a case study involving a biological reactor that exhibits nonlinear dynamic behavior

oversampled paraunitary dft filter banks a general construction algorithm and some specific solutions oversampled filter banks are at the center of essential signal processing systems either for source coding or for transmission applications among this class of filter banks fbs the case of oversampled discrete fourier transform dft filter banks is particularly important since it leads to efficient algorithm implementations however up to now no general construction algorithm has been proposed to exhaustively cover the large set of the various solutions offered by this family of fbs the paper recalls in detail the precise features of the rectangular paraunitary matrices that are specific of this type of systems a parametrization method is proposed involving transformations being either rotations or shifts that depend upon the oversampling ratio and upon the prototype filter length this shows that several factorizations exist leading to solutions of different dimension orthogonal and paraunitary patterns are introduced and using a sequence of transformations applied to a pattern stap an algorithm is derived that allows us to get the exhaustive set of solutions for various values of the oversampling ratio and prototype filter length furthermore for some oversampling ratios explicit expressions of some solutions are also provided that are valid whatever the maximum length of the prototype filter finally design examples for linear and nonlinear phase prototype filters are presented

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

high gain observer for a class of non triangular systems this paper presents a high gain observer for a class of mimo nonlinear systems involving some uncertainties the latter is particularly composed of cascade subsystems where each subsystem is associated with a subset of the output variables and assumes a triangular dependence on its own state variables and may depend on the state variables of all other subsystems the main contribution consists in extending the available results to allow more interconnections between the subsystems of fundamental interest it is shown that the underlying observation error exponentially converges to zero in the absence of uncertainties moreover the observation error can be made as small as desired by properly specifying the observer design parameter in the case where uncertainties are considered

adaptive impulsive observers for nonlinear systems this paper revisits the design of adaptive impulsive observers aios for nonlinear systems the dynamics of observer state of the proposed aio is modelled by an impulsive differential equation by which the observer state is updated in an impulsive fashion the parameter estimation law is modelled by an impulse free time varying differential equation associated with the impulse time sequence for determining when the observer state is updated unlike the previous work the convergence analysis of the estimation error system is performed by applying a time varying lyapunov function based method in conjunction with the application of a generalized version of barbalat s lemma a sufficient condition for the existence of aios is also derived for some special cases it is shown that the sufficient condition can be formulated in terms of linear matrix inequalities lmis and the observer matrices can be attained by solving a set of lmis furthermore with an additional persistence of excitation type constraint it is proved that the sufficient condition can guarantee the convergence of parameter estimation two examples of chaotic oscillators are provided to illustrate the design procedure of the proposed aios

nonlinear observer design by observer error linearization this paper studies the observer design problem by the observer error linearization approach for nonlinear systems with and without inputs necessary and sufficient conditions for the existence of the linearization transformation are derived for nonlinear systems without inputs the conditions are shown to be corrections to an existing result a computation procedure and a different set of necessary and sufficient conditions based on the computation procedure are presented

brief paper full order observer design for a class of port hamiltonian systems we consider a special class of port hamiltonian systems for which we propose a design methodology for constructing globally exponentially stable full order observers using a passivity based approach the essential idea is to make the augmented system consisting of the plant and the observer dynamics to become strictly passive with respect to an invariant manifold defined on the extended state space on which the state estimation error is zero we first introduce the concept of passivity of a system with respect to a manifold by defining a new input and output on the extended state space and then perform a partial state feedback passivation which leads to the construction of the observer we then illustrate this observer design procedure on two physical examples the magnetic levitation system and the inverted pendulum on the cart system

linearization by generalized input output injection abstract the problem under interest is the linearization of nonlinear mimo systems by generalized input output injection in order to design observers with linear error dynamics the method is based on the study of the structure of the input output differential equations thus the problem is solved as a realization problem in this note one considers the linearization under two kinds of inout output injection in the first case the transformation depends on the output and time derivatives of the input whereas in the second case derivatives of both the input and the output are considered necessary and sufficient conditions are obtained which generalize the ones on standard input output injection linearization

a note on observer design for one sided lipschitz nonlinear systems in this note observer design of a class of nonlinear systems is considered based on the one sided lipschitz condition sufficient conditions for the existence of observers of the class of nonlinear systems are presented a design method of the observer that is dependent on the solution of the linear matrix inequality is then presented furthermore a gain matrix of the observer is given the method given in this note makes the applicable class larger than that given in the literature it should be noticed that the proposed method is applicable not only to the monotone nonlinearities and lipschitz nonlinearities but also to the one sided lipschitz nonlinearities which are neither monotone nonlinearities nor usual lipschitz nonlinearities finally we use the proposed method to design observers for three simulative examples and the effect of each state trajectory tracking is very satisfactory

a block triangular form for nonlinear observer design this note reconsiders existence conditions for an established block triangular form btf for a broad class of multi output nonlinear systems systems transformable into btf coordinates allow for decentralized observer design performed subsystem at a time effectively treating upper subsystem states as measurements sufficient conditions are given to ensure that the output is linear in btf coordinates an example illustrates the btf construction and a typical observer design

observer design for one sided lipschitz discrete time systems abstract this note focuses on state observer design for a general class of nonlinear discrete time systems that satisfies the one sided lipschitz condition it has been shown that this condition may encompass a large class of nonlinearities however challenging problems arise such as relevant choice of the lyapunov function or non convexity of the obtained stability conditions both full order and reduced order observer designs are considered in this work the main contribution is to provide first some mathematical artifacts on the lyapunov function to obtain simple and workable stability conditions furthermore we show how to obtain lmi conditions to ensure asymptotic convergence on the other hand we extend the obtained results to n p reduced order observer design high performances are shown through simulation results

output feedback control of a class of nonlinear systems a nonseparation principle paradigm considers the problem of global stabilization by output feedback for a family of nonlinear systems that are dominated by a triangular system satisfying a linear growth condition the problem has remained unsolved due to the violation of the commonly assumed conditions in the literature using a feedback domination design method which is not based on the separation principle we explicitly construct a linear output compensator making the closed loop system globally exponentially stable

local observer for infinitesimally observable nonlinear systems in this article we present a local observer based on infinitesimal observability along trajectories the gain of this observer derives from a dynamical lyapunov equation the inputs for which the observer converges are those which render the system observable at each point of the limit of the unknown trajectory infinitesimal observability at infinity along trajectories the performance of the proposed observer is illustrated with an application to dc machine

non linear observer design by reduced generalized observer canonical form a non linear canonical form observer design approach for multi input multi output systems y h x u with linearizable error dynamics is proposed in the paper the method involves a transformation of the original non linear system in a reduced generalized observer canonical form rgocf by a non linear state transformation the name reduced comes from the fact that this non linear canonical form has a reduced dependency on derivatives of the inputs necessary and sufficient conditions for transformability are derived and a transformation algorithm based on those conditions is developed the non linear observer is firstly designed in the canonical coordinates of the rgocf and then it is presented in the original and observability coordinates a final example including simulation is given for illustration

interval state estimation for a class of nonlinear systems the goal of this technical note is to design interval observers for a class of nonlinear continuous time systems the first part of this work shows that it is usually possible to design an interval observer for linear systems by means of linear time invariant changes of coordinates even if the system is not cooperative this result is extended to a class of nonlinear systems using partial exact linearisations the proposed observers guarantee to enclose the set of system states that is consistent with the model the disturbances and the measurement noise moreover it is only assumed that the measurement noise and the disturbances are bounded without any additional information such as stationarity uncorrelation or type of distribution the proposed observer is illustrated through numerical simulations

discrete hilbert transforms on sparse sequences weighted discrete hilbert transforms an n p n anvn z n from 2 to a weighted l 2 space are studied with n a sequence of distinct points in the complex plane and v vn a corresponding sequence of positive numbers in the special case when j nj grows at least exponentially bounded transforms of this kind are described in terms of a simple relative to the muckenhoupt a2 condition the special case when z is restricted to another sequenceis studied in detail it is shown that a bounded trans form satisfying a certain admissibility condition can be split into finitely many surjective transforms and precise geometric conditions are found for invertibility of such two weight transforms these results can be interpreted as statements about systems of reproducing kernels in certain hilbert spaces of which de branges spaces and model subspaces of h 2 are prime examples in particular a connection to the feichtinger conjecture is pointed out descriptions of carleson measures and riesz bases of normalized reproducing kernels for certain small de branges spaces follow from the results of this paper 1 introduction and main results this paper is concerned with the mapping properties of what we will call discrete hilbert transforms in the complex plane one aspect of this topic was treated in 7 where all unitary discrete hilbert transforms were described when we now turn to questions about boundedness surjectivity and invertibility results of the same generality seem at present out of reach the results to be presented below are complete only when the discrete hilbert transforms are defined on particularly sparse sequences we will nevertheless present the problems in the most general setting as we believe they merit further investigations we will emphasize the connection with topics such as carleson measures and riesz bases of normalized reproducing kernels in hilbert spaces of analytic functions this will lead us to the most intriguing general question namely whether or not the feichtinger conjecture holds true for systems of reproducing kernels in such spaces we begin by assuming that we are given an infinite sequence of distinct points n in c and a corresponding sequence of positive numbers v vn both indexed by the

extended output depending normal form this paper concerns the design of a nonlinear observer through a transformation of a nonlinear system into an observer form that supports a high gain observer sufficient geometrical condition is deduced to guarantee the existence of change of coordinates allowing the transformation of a nonlinear system into the proposed normal form the result is highlighted by studying the susceptible exposed infected and recovered seir model

a note on observers for lipschitz nonlinear systems this note deals with the design of reduced order observers for lipschitz nonlinear systems it shows that the conditions under which a full order observer exists also guarantee the existence of a reduced order observer a design method of the reduced order observer that is dependent on the solution of the riccati equation is then presented and an example is given to illustrate effects of the design method

digital filter bank design quadratic constrained formulation formulate the filter bank design problem as an quadratic constrained least squares minimization problem the solution of the minimization problem converges very quickly since the cost function as well as the constraints are quadratic functions with respect to the unknown parameters the formulations of the perfect reconstruction cosine modulated filter bank of the near perfect reconstruction pseudo qmf bank and of the two channel biorthogonal linear phase filter bank are derived using the proposed approach compared with other design methods the proposed technique yields pr filter banks with much higher stopband attenuation the proposed technique can also be extended to design multidimensional filter banks

observability through delayed measurements a new approach to state observers design an original approach for the construction of state observers for dynamic systems is presented in this article new notions of observability delay observability and delay drift observability useful for the development of the observer equations and for the convergence proof are introduced and compared with other standard observability concepts in particular it is shown that delay drift observability is an extension of the well known drift observability property the construction of the proposed observer is straightforward and does not require any coordinate transformation of the system into a canonical form which is a common feature of many other approaches a numerical example is reported where a system that is not drift observable is considered in this case the proposed observer is easily constructed and performs well

the theory and design of arbitrary length cosine modulated filter banks and wavelets satisfying perfect reconstruction it is well known that fir filter banks that satisfy the perfect reconstruction pr property can be obtained by cosine modulation of a linear phase prototype filter of length n 2mm where m is the number of channels in this paper we present a pr cosine modulated filter bank where the length of the prototype filter is arbitrary the design is formulated as a quadratic constrained least squares optimization problem where the optimized parameters are the prototype filter coefficients additional regularity conditions are imposed on the filter bank to obtain the cosine modulated orthonormal bases of compactly supported wavelets design examples are given

global tracking via output feedback for nonlinear mimo systems in this note we present a constructive method for the design of global asymptotic tracking control for a class of mimo nonlinear systems by output feedback the class of systems considered is a special case of those in nonlinear observer form and coincides with the output feedback form when there is only one input and one output this approach generalizes a siso method which uses filtered transformations and backstepping the technique presented here may be useful in accommodating subsystem coupling in other mimo design contexts we demonstrate our method by example and observe several interesting features that distinguish it from the siso case

generalised observer design for dissipative lipschitz nonlinear systems in the presence of measurement noise this paper presents two novel observer concepts first it develops a globally exponentially stable nonlinear observer for noise free dissipative nonlinear systems second for a dissipative nonlinear system with measurement noise the paper develops an observer to guarantee a desired performance namely an upper limit on the ratio of the square of the weighted l2 norm of the error to the square of the weighted l2 norm of the measurement noise the necessary and sufficient conditions for both observers are reformulated as algebraic riccati equations ares so that standard solvers can be utilised in addition the paper presents necessary and sufficient conditions to be satisfied by the nonlinear system in order to ensure that the are and hence the observer design problem has a solution the use of the methodology developed in this paper is demonstrated through illustrative examples in literature there is no previous observer for dissipative system that provides both necessary and sufficient condition

fault detection observers for continuous non linear polynomial systems of general degree this paper proposes a robust fault detection observer rfdo for a continuous non linear system with polynomial non linearities up to any finite degree the observer error and residual are robust with respect to unknown inputs sufficient conditions are given in an efficient algebraic compact form for a rfdo observer and residual to exist useable results on detectablility conditions are proved numerical prodedures for the design of a rfdo and a sub optimal rfdo sorfdo are given the theory is illustrated with an application to a benchmark three tank system one linear and three non linear models are considered with corresponding rdfos including a sub optimal rfdo and the performances of the corresponding residuals are compared under two initial conditions for a scenario consisting of a leak fault and a disturbance

failure detection and identification using the geometric concept of an unobservability subspace a solution is given to the problem of detecting and identifying control system component failures in linear time invariant systems conditions are developed for the existence of a causal linear time invariant processor that can detect and uniquely identify a component failure first for the case where components can fail simultaneously and then for the case where they fail only one at a time explicit design algorithms are provided when these conditions are satisfied in addition to time domain solvability conditions frequency domain interpretations of the results are given and connections are drawn with results already available in the literature