on hearing the shape of a general multi connected vibrating membrane in r2 with piecewise smooth positive functions in the robin boundary conditions the asymptotic expansion of the trace of the heat kernel q t email protected j 1 exp email protected j as t 0 has been derived for a variety of domains where l j are the eigenvalues of the negative laplace email protected email protected i 1 email protected email protected x i 2in the x 1 x 2 plane the dependence of q t on the connectivity of domains and the boundary conditions are analyzed particular attention is given for a general multiply connected bounded domain in r 2 together with a finite number of piecewise robin boundary conditions where the coefficients in the boundary conditions are piecewise smooth positive functions some applications of an ideal gas enclosed in the general multiply connected domain are given

non linear observer design by transformation into a generalized observer canonical form an observer design method for a certain class of non linear single output systems is introduced the characteristic feature of this method consists of the fact that it does not require any linearization in the way that the given non linear system is approximated by a linear one the present paper deals with the derivation of a transformation of the considered non linear system into a generalized observer canonical form gocf which enables a systematic observer design similar to the linear one based on the well known linear observer canonical form to assign conditions for its existence the transformation into the gocf is carried out in two steps via a generalized observability canonical form gobcf in contrast to previous forms used for linear systems the two non linear canonical forms presented here also depend on the time derivatives of the input variables this means that the resulting observer has to be supplied not only with the input and output variables of the given system but also with deri

continuous discrete time observers for a class of mimo nonlinear systems this technical note addresses the observer design problem for a class of continuous time dynamical systems with non uniformly sampled measurements more specifically we propose an observer that runs in continuous time with an output error correction term that is updated in a mixed continuous discrete fashion the proposed observer is actually an impulsive system since it is described by a set of differential equations with instantaneous state impulses corresponding to the measured samples and their estimates nevertheless we shall show that such an impulsive system can be put under the form of a hybrid system composed of a continuous time high gain observer coupled with an inter sample output predictor two design features of the proposed observer are worth emphasizing firstly the observer calibration is achieved through the tuning of a scalar design parameter secondly the exponential convergence to zero of the observation error is established under a well defined condition on the maximum value of the sampling partition diameter simulations results involving a flexible joint robot arm are given in order to highlight the performance of the proposed observer

observer design for nonlinear control systems abstract this paper deals with the observer design problem of a wide class of nonlinear systems subjected to bounded nonlinearities a sufficient liapunovlike condition is provided and the proposed dynamic observer is a direct extension of the one in linear case

remarks on linearization of discrete time autonomous systems and nonlinear observer design abstract this paper presents necessary and sufficient conditions under which a discrete time autonomous system with outputs is locally state equivalent to an observable linear system or a system in the nonlinear observer form krener and isidori 1983 in particular an open problem raised in lee and nam 1991 namely the observer linearization problem is solved for a nonlinear system which may not be invertible i e the mapping f may not be a local diffeomorphism as a consequence the nonlinear observer design problem is solved by means of exact linearization techniques

deadbeat observer construction via sets a geometric generalization of discrete time linear deadbeat observer is presented the proposed method to generate a deadbeat observer for a given nonlinear system is constructive and makes use of sets that can be computed iteratively for demonstration derivations of observer dynamics are provided for two example systems based on the method a simple algorithm that computes the deadbeat gain for a linear system with scalar output is given

on stable solutions of the one and two sided model matching problems an algorithm is introduced to determine proper and stable solutions to the model matching problem it utilizes the theory of inverses and state space algorithms and it guarantees a proper and stable solution to the problem when one exists this approach is also used to determine proper and stable solutions of the two sided matching problem examples are included

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 direct method for the construction of nonlinear discrete time observer with linearizable error dynamics we provide a direct method for the design of nonlinear discrete time observers by a construction of a change of variables an explicit expression of the change of variables is given some simulations for chaotic systems such as lozi system and he spl acute non system are provided to illustrate the proposed method

nonlinear discrete time observer design with linearizable error dynamics a necessary and sufficient condition for the existence of a discrete time nonlinear observer with linearizable error dynamics is provided the result can be applied to any real analytic nonlinear system whose linear part is observable the necessary and sufficient condition is the solvability of a nonlinear functional equation furthermore the well known siegel s theorem on the linearizability of a mapping is naturally reproduced in a corollary the proposed observer design method is constructive and can be applied approximately to any sufficiently smooth linearly observable system yielding a local observer with approximately linear error dynamics

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

the wave equation approach for solving inverse eigenvalue problems of a multi connected region in r3 with robin conditions the asymptotic expansion for t of the trace of the wave kernel email protected t email protected u 1exp email protected 1 2 u where m u u 1 are the eigenvalues of the negative laplacian email protected email protected 3 b 1 x b 2 in the x 1 x 2 x 3 space where i 1 and

observer design for nonlinear systems with discrete time measurements this paper focuses on the development of asymptotic observers for nonlinear discrete time systems it is argued that instead of trying to imitate the linear observer theory the problem of constructing a nonlinear observer can be more fruitfully studied in the context of solving simultaneous nonlinear equations in particular it is shown that the discrete newton method properly interpreted yields an asymptotic observer for a large class of discrete time systems while the continuous newton method may be employed to obtain a global observer furthermore it is analyzed how the use of broyden s method in the observer structure affects the observer s performance and its computational complexity an example illustrates some aspects of the proposed methods moreover it serves to show that these methods apply equally well to discrete time systems and to continuous time systems with sampled outputs

on the θ function of a riemannian manifold with boundary let be a compact riemannian manifold of dimension n with smooth boundary let 1 2 be the eigenvalues of the laplace beltrami operator with the boundary condition n 0 the associated function t n 1 exp n t has an asymptotic expansion of the form 4 t n 2 t a 0 a 1 t 1 2 a 2 t a 3 t 3 2 a 4 t 2 the values of a 0 a 1 are well known

theory of a curved planar waveguide with robin boundary conditions a model of a thin straight strip with a uniformly curved section and with boundary requirements zeroing at the edges a linear superposition of the wave function and its normal derivative robin boundary condition is analyzed theoretically within the framework of the linear schrodinger equation and is applied to the study of the processes in the bent magnetic multilayers superconducting films and metallic ferrite filled waveguides in particular subband thresholds of the straight and curved parts of the film are calculated and analyzed as a function of the robin parameter 1 lambda with lambda being an extrapolation length entering robin boundary condition for the arbitrary robin coefficients which are equal on the opposite interfaces of the strip and for all bend parameters the lowest mode energy of the continuously curved duct is always smaller than its straight counterpart accordingly the bound state below the fundamental propagation threshold of the straight arms always exists as a result of the bend in terms of the superconductivity language it means an increased critical temperature of the curved film compared to its straight counterpart localized level dependence on the parameters of the curve is investigated with its energy decreasing with increasing bend angle and decreasing bend radius conditions of the bound state existence for the different robin parameters on the opposite edges are analyzed too in particular it is shown that the bound state below the first transverse threshold of the straight arm always exists if the inner extrapolation length is not larger than the outer one in the opposite case there is a range of the bend parameters where the curved film cannot trap the wave and form the localized mode for example for the fixed bend radius the bound state emerges from the continuum at some nonzero bend angle that depends on the difference of the two lengths lambda at the opposite interfaces various transport properties of the film such as interference blockade of the current flow at some special energies is also discussed with the special attention being paid to the transformation from the dirichlet to the neumann case as the extrapolation length lambda sweeps the positive axis

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

higher dimensional inverse problem of the wave equation for a general multi connected bounded domain with a finite number of smooth mixed boundary conditions the spectral function m t j 1 exp it m j 1 2 where m j j 1 are the eigenvalues of the negative laplacian d 3 u 1 3 x u 2 in the x 1 x 2 x 3 space is studied for small t for a variety of bounded domains where

sampled data observer error linearization the effects of time sampling on the solvability conditions for the observer linearization design methodology are investigated it is shown that the class of systems for which this design method can be applied for an open set of sampling times is quite small in particular when the dimension of the state space is two it consists only of those systems that are state equivalent to a linear system the practical implication is that digital implementations of this methodology will have to be approximate

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

canonical observer forms for multi output systems up to coordinate and output transformations in discrete time in the present paper the problem of equivalence under coordinate changes and output transformations to observer canonical forms is addressed in discrete time for multi output systems necessary and sufficient conditions are given for local equivalence to this form which yields a straightforward observer design with linear error dynamics

an intrinsic observer for a class of lagrangian systems we propose a new design method of asymptotic observers for a class of nonlinear mechanical systems lagrangian systems with configuration position measurements our main contribution is to introduce a state position and velocity observer that is invariant under any changes of the configuration coordinates the observer dynamics equations as the euler lagrange equations are intrinsic the design method uses the riemannian structure defined by the kinetic energy on the configuration manifold the local convergence is proved by showing that the jacobian of the observer dynamics is negative definite contraction for a particular metric defined on the state space a metric derived from the kinetic energy and the observer gains from a practical point of view such intrinsic observers can be approximated when the estimated configuration is close to the true one by an explicit set of differential equations involving the riemannian curvature tensor these equations can be automatically generated via symbolic differentiations of the metric and potential up to order two numerical simulations for the ball and beam system an example where the scalar curvature is always negative show the effectiveness of such approximation when the measured positions are noisy or include high frequency neglected dynamics

necessary and sufficient conditions for state equivalence to a nonlinear discrete time observer canonical form in this technical note we obtain necessary and sufficient conditions for a multi input multi output discrete time nonlinear system to be state equivalent to a nonlinear observer form and for an uncontrolled multi output system to be state equivalent to a linear observer form we adopt a geometric approach and the proofs are constructive with respect to the required coordinate change

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

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

further results on the observer design problem abstract in this paper the observer design problem for nonlinear systems is considered sufficient lyapunov like conditions are presented for the existence of a nonlinear observer the theory we develop considerably improves and extends the results of our recent work 14

hearing the shape of a general convex domain abstract the spectral function t j 1 exp t j where j j 1 are the eigenvalues of the laplace operator i 1 2 x i 2 in the x 1 x 2 plane is studied for a general convex domain together with an impedance condition on a part of its boundary and another impedance condition on the remaining part of that boundary

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

an inverse problem for a general annular bounded domain in r2 with mixed boundary conditions and its physical applications this paper deals with the very interesting problem about the influence of the boundary conditions on the distribution of the eigenvalues of the negative laplacian in r 2 the asymptotic expansion of the trace of the heat kernel q t u 1 exp t m n where m n n 1 are the eigenvalues of the negative laplacian d 2 k 1 2 x k 2 in the x 1 x 2 plane is studied for short time t of a general annular bounded domain w in r 2 together with its smooth inner boundary w 1 and its smooth outer boundary w 2 where a finite number of dirichlet neumann and robin boundary conditions on the piecewise smooth components c i i 1 m of w 1 and on the piecewise smooth components c i i m 1 n of w 2 such that w 1 i 1 m c i and w 2 i m 1 n c i are considered in this paper one may extract information on the geometry of w by analyzing the asymptotic expansions of q t for short time t some applications of q t for an ideal gas enclosed in w are given thermodynamic quantities of an ideal gas enclosed in w are examined we use an asymptotic expansion for high temperatures to obtain the partition function of an ideal gas showing the leading corrections to the internal energy due to a finite container we show that the ideal gas cannot feel the shape of its container although it can feel some geometrical properties of it

the extended luenberger observer for nonlinear systems abstract for nonlinear single input single output systems dot x f x u y h x u the relationships for a state transformation into the nonlinear observer canonical form are developed it is possible to dimension a nonlinear observer by an eigenvalue assignment without solving the nonlinear partial differential equations for the transformation if the transformed nonlinearities are linearized about the reconstructed state with reference to the extended kalman filter algorithm this nonlinear observer design is called the extended luenberger observer

observers for discrete time nonlinear systems abstract the problem of observers for discrete time nonlinear systems has been considered and a simple easy to implement algorithm is given whose convergence properties are guaranteed for autonomous and forced systems some numerical examples show the effectiveness of the proposed observer

on hearing the shape of rectilinear regions from complete knowledge of the eigenvalues of the negative laplacian on a bounded domain one may extract information on the geometry and the boundary conditions by analyzing the asymptotic expansion of a spectral function explicit calculations are performed for an equilateral triangular domain with dirichlet or neumann boundary conditions yielding in particular the corner angle terms in three dimensions some applications to eigenvalue problems for an equilateral triangular prism are dealt with including the solid vertex terms

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

an inverse problem of the wave equation for a general doubly connected region in r2 with a finite number of piecewise smooth robin boundary conditions the spectral distribution m t w 1 exp ite w 1 2 where e w w 1 are the eigenvalues of the negative laplacian d k 1 2 x k 2in the x 1 x 2 plane is studied for a variety of domains where 0

canonical form observer design for non linear time variable systems an observer of canonical phase variable form for non linear time variable systems is introduced the development of this non linear time variable form requires regularity of the non linear time variable observability matrix of the system from the relationships derived during the development it follows that a non linear time variable observer can be dimensioned by an eigenvalue assignment with respect to the canonical state coordinates if a linearization of system non linearities about the reconstructed state trajectories is permissible this is an assumption similar to that of the extended kalman filter based on a linearization about the current estimate

a luenberger like observer for nonlinear systems a state observer is proposed for nonlinear continuous time systems which extends the well known luenberger observer in particular on the basis of simple assumptions on the regularity of the system equations observability and the global holder condition for suitable functions which are generally satisfied for physically meaningful dynamic systems the global asymptotic convergence of the estimated state towards the true state is shown finally some examples of applications are also reported showing the effectiveness of the proposed observer

discrete time nonlinear observer design using functional equations abstract the present research work proposes a new approach to the discrete time nonlinear observer design problem based on the early ideas that influenced the development of the linear luenberger observer the proposed approach develops a nonlinear analogue the formulation of the discrete time nonlinear observer design problem is realized via a system of first order linear nonhomogeneous functional equations and a rather general set of necessary and sufficient conditions for solvability is derived using results from functional equations theory the solution to the above system of functional equations can be proven to be locally analytic and this enables the development of a series solution method that is easily programmable with the aid of a symbolic software package

on the observer problem for discrete time control systems this paper studies the construction of observers for nonlinear time varying discrete time systems in a general context where a certain function of the states must be estimated appropriate notions of robust complete observability are proposed under which a constructive proof of existence of an observer is developed moreover a transitive observer property is proven according to which a state observer can be generated as the series connection of two observers the analysis and the results are developed in general normed linear spaces to cover both finite dimensional and infinite dimensional systems

an inverse eigenvalue problem for a general convex domain the underlying problem is to deduce the precise shape of a membrane from the complete knowledge of the eigenvalues i for the lapace operator a cf a ax in the x1x2 plane let d g r be a simply connected bounded domain with a smooth boundary ad let us suppose that the a are the eigenvalues of the impedance problem au k o in d

an inverse problem for a general vibrating annular membrane in r3 with its physical applications further results this paper deals with the very interesting problem about the influence of the boundary conditions on the distribution of the eigenvalues of the negative laplacian in r 3 the trace of the heat semigroup q t email protected v 1 exp email protected v where m v v 1 are the eigenvalues of the negative laplacian email protected email protected b 1 email protected x b 2 in the x 1 x 2 x 3 space is studied for short time t for a general vibrating annular membrane w in r 3 together with its smooth inner bounding surface s 1 and its smooth outer bounding surface s 2 where a finite number of dirichlet neumann and robin boundary conditions on the piecewise smooth components s i i 1 m of s 1 and on the piecewise smooth components s i i m 1 n of s 2 is considered such that s email protected i 1 ms i and s email protected i m 1 ns i in this paper one may extract information on the geometry of w by analyzing the asymptotic expansions of q t for short time t some applications of q t for an ideal gas enclosed in the general vibrating annular membrane w are given we show that the asymptotic expansion of q t for short time t plays an important role in investigating the influence of the annular region w on the thermodynamic quantities of an ideal gas some applications of q t for an ideal gas enclosed in a compact n dimensional riemannian manifold are also given we show that the ideal gas cannot feel the shape of its container although it can feel some geometrical properties of it

an inverse problem for the three dimensional multi connected vibrating membrane with robin boundary conditions this paper deals with the very interesting problem about the influence of the boundary conditions on the distribution of the eigenvalues of the negative laplacian in r 3 the trace of the heat semigroup q t n 1exp t m n where m n n 1 are the eigenvalues of the negative laplacian 2 3 b 1 x b 2 in the x 1 x 2 x 3 space is studied for a general multiply connected bounded domain w in r 3 surrounded by simply connected bounded domains w j with smooth bounding surfaces s j j 1 n where a finite number of piecewise smooth robin boundary conditions on the piecewise smooth components s i i 1 k j 1 k j of the bounding surfaces s j are considered such that s j k j i 1 k j 1s i where k 0 0 some applications of q t for an ideal gas enclosed in the multiply connected bounded container w with robin boundary conditions are given we show that the asymptotic expansion of q t for short time t plays an important role in investigating the influence of the finite container w on the thermodynamic quantities of an ideal gas

an inverse eigenvalue problem of the wave equation for a multi connected region in r2 together with three different types of boundary conditions the trace of the wave kernel m t email protected w 1exp ite 1 2 w where e w w 1 are the eigenvalues of the negative laplacian email protected email protected 2 k 1 email protected x k 2 in the x 1 x 2 plane is studied for a variety of bounded domains where

higher dimensional inverse problem for a multi connected bounded domain with piecewise smooth robin boundary conditions and its physical applications the asymptotic expansions of the trace of the heat kernel q t email protected j 1 exp email protected j for short time t have been derived for a variety of bounded domains where l j j 1 are the eigenvalues of the negative laplace operator email protected email protected i 1 3 x i 2 in the x 1 x 2 x 3 space the dependence of q t on the connectivity of bounded domains and the boundary conditions is analyzed particular attention is given for an arbitrary multiply connected bounded domain w in r 3 together with piecewise smooth robin boundary conditions where the coefficients in these conditions are assumed to be piecewise smooth positive functions some applications of an ideal gas enclosed in the multiply connected bounded domain w are given we show that the ideal gas cannot feel the shape of its container although it can feel some geometrical properties of it

nonlinear observer design via an extended observer canonical form based on the theory of designing unknown input observers an extended nonlinear observer canonical form is introduced observers can easily be constructed for those systems which can be transformed into this canonical form necessary and sufficient conditions for the existence of such transformation are derived and furthermore an algorithm for calculating this transformation in given

nonlinear observer design using lyapunov s auxiliary theorem abstract the present work proposes a new approach to the nonlinear observer design problem based on the early ideas that influenced the development of the linear luenberger observer theory the proposed approach develops a nonlinear analogue the formulation of the observer design problem is realized via a system of singular first order linear pdes and a rather general set of necessary and sufficient conditions for solvability is derived by using lyapunov s auxiliary theorem the solution to the above system of pdes is locally analytic and this enables the development of a series solution method that is easily programmable with the aid of a symbolic software package

the wave equation approach to an inverse problem for a general multi connected domain in r2 with mixed boundary conditions the spectral function email protected t email protected j 1 exp email protected j 1 2 where m j j 1 are the eigenvalues of the negative laplacian email protected email protected u 1 email protected x u 2 in r 2 is studied for small t for a variety of domains where

a reduced order observer for non linear discrete time systems abstract in this note a simple and useful reduced order observer for a large class of non linear discrete time systems is presented neither detectability of the linear part nor resolution of the sylvester constraint is required from the stability analysis we show that the proposed state observer has strong tracking properties under very general conditions and generalizes results in m boutayeb et al ieee trans automat control 42 4 1997 581 586 high performances from the design and implementation point of view will be shown through three numerical examples of physical processes largely used in industrial applications

a dual pair of optimization based formulations for estimation and control a finite horizon optimal estimation problem for discrete time linear systems is formulated and solved the formulation is a natural extension of that which yields a deadbeat observer the resultant observer is the dual of the controller produced by the finite horizon minimum energy control problem with terminal equality constraint nonlinear extensions of this dual pair are also considered and sufficient conditions are provided for stability and convergence

nonlinear observer design in the presence of delayed output measurements the present work proposes a new approach to the nonlinear observer design problem in the presence of delayed output measurements the proposed nonlinear observer possesses a state dependent gain which is computed from the solution of a system of first order singular partial differential equations and in particular consists of a chain of state observation algorithms that reconstruct the unmeasurable state vector at different delayed time instants within the time delay window introduced by the available output measurements therefore the proposed nonlinear observer exhibits a chain like structure that explicitly reflects and takes into account the magnitude of the output delay furthermore a set of conditions is derived under which convergence of the estimation error to zero is established finally the performance of the proposed observer and its convergence properties are evaluated in an illustrative biological reactor example

from continuous time design to sampled data design of observers in this work a sampled data nonlinear observer is designed using a continuous time design coupled with an inter sample output predictor the proposed sampled data observer is a hybrid system it is shown that under certain conditions the robustness properties of the continuous time design are inherited by the sampled data design as long as the sampling period is not too large the approach is applied to linear systems and to triangular globally lipschitz systems

brief paper robust h observer design for sampled data lipschitz nonlinear systems with exact and euler approximate models an lmi approach is proposed for the design of robust h observers for a class of lipschitz nonlinear systems two type of systems are considered lipschitz nonlinear discrete time systems and lipschitz nonlinear sampled data systems with euler approximate discrete time models observer convergence when the exact discrete time model of the system is available is shown then practical convergence of the proposed observer is proved using the euler approximate discrete time model as an additional feature maximizing the admissible lipschitz constant the solution of the proposed lmi optimization problem guaranties robustness against some nonlinear uncertainties the robust h observer synthesis problem is solved for both cases the maximum disturbance attenuation level is achieved through lmi optimization

on the existence and uniqueness of locally analytic invertible solutions of a system of nonlinear functional equations in the present research work a set of necessary and sufficient conditions is derived under which a rather broad class of nonlinear functional equations admits a unique locally analytic and invertible solution which can be easily computed with the aid of a symbolic software package the main results naturally reproduce the solution of the linear problem where the system of functional equations to be solved becomes equivalent to a lyapunov matrix equation