observer design using a generalized time scaled block triangular observer form this paper presents an observer design for uncontrolled nonlinear multi output continuous time systems based on a time scaled block triangular observer form tbtof the tbtof generalizes an established block triangular observer form btof by including generalized time scaling functions tsfs which have both state and output dependence introducing these stability preserving tsfs broadens the class of systems which admits a btof based observer design necessary conditions for the tsfs are provided when a tbtof exists an observer can be constructed subsystem at a time sufficient conditions are given to prove estimate error stability a physical example illustrates the tbtof construction and observer design

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

adaptive observers with arbitrary exponential rate of convergence for nonlinear systems concerns the same class of linearly parameterized single output nonlinear systems that the authors previously identified in 1992 in terms of differential geometric conditions when persistency of excitation conditions are satisfied the adaptive observers presented in this note guarantee arbitrarily fast exponential convergence both of parameter and state estimates to actual parameters and states while previous adaptive observers guarantee only exponential not arbitrarily fast convergence this extends earlier results for linear systems

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

morphology of spinodal decomposition the morphology of homogeneous phases during spinodal decomposition i e the scaling of the content shape and connectivity of spatial structures is described by a family of morphological measures known as minkowski functionals besides providing means to determine the characteristic length scale l in a statistically robust and computationally inexpensive way the measures allow also one to define the crossover from the early stage decomposition to the late stage domain growth we observe the scaling behavior l ensuremath sim t ensuremath alpha with ensuremath alpha 1 3 ensuremath alpha 1 2 and ensuremath alpha 2 3 depending on the viscosity when approaching the spinodal ensuremath rho mathrm sp we recover the prediction l ensuremath sim ensuremath rho ensuremath ensuremath rho mathrm sp ensuremath 1 2 for the early time decomposition

a block triangular nonlinear observer normal form abstract the nonlinear observer normal form is generalized to a block triangular observer normal form which can be interpreted as a series connection of subsystems in observer form based on this new form exponential observers can be designed using methods from the linear case necessary and sufficient conditions for the existence of state transformations into this normal form are given

numerical solutions of the spectral problem for arbitrary self adjoint extensions of the one dimensional schrodinger equation a numerical algorithm to solve the spectral problem for arbitrary self adjoint extensions of one dimensional regular schrodinger operators is presented it is shown that the set of all self adjoint extensions of one dimensional regular schrodinger operators is in one to one correspondence with the group of unitary operators on the finite dimensional hilbert space of boundary data and they are characterized by a generalized class of boundary conditions that include the well known dirichlet neumann robin and quasi periodic boundary conditions the numerical algorithm is based on a nonlocal boundary extension of the finite element method and their convergence is proved an appropriate basis of boundary functions must be introduced to deal with arbitrary boundary conditions and the conditioning of its computation is analyzed some significant numerical experiments are also discussed as well as the comparison with some standard algorithms in particular it is shown that appropriate perturbations of stand

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

non linear observer design by observer canonical forms this paper studies the non linear observer design problem by observer canonical forms we present necessary and sufficient conditions in terms of the ranks of matrices for the existence of a non linear state coordinate change under which a time variable system is transformed into an observer canonical form these conditions give the multiple versions of li and tao 1986 for the single output case then a comparison is made with the lie algebraic conditions obtained by krener and respondek 1985 and modified by the authors in a recent paper xia and gao 1987

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

nonlinear observer design by dynamic observer error linearization in this note we address the problem of transforming a nonlinear system into nonlinear observer canonical form in the extended state space with the aid of dynamic system extension and introduction of virtual outputs as an intermediate step for the general problem we consider a restricted structure of dynamic extension which is obtained roughly speaking by adding the chains of integrators to the outputs of original system we propose sufficient conditions which can be verified using the system dynamics expressed in their original coordinates an illustrative example is included that demonstrates the advantage of the proposed method over the conventional method

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

hardy inequalities for robin laplacians abstract in this paper we establish a hardy inequality for laplace operators with robin boundary conditions for convex domains in particular we show explicitly how the corresponding hardy weight depends on the coefficient of the robin boundary conditions we also study several extensions to non convex and unbounded domains

boundary condition varying circle billiards and gratings the dirichlet singularity waves in a two dimensional domain with robin mixed boundary conditions that vary smoothly along the boundary exhibit unexpected phenomena if the variation includes a d point where the boundary condition is dirichlet vanishing wavefunction a variety of arguments indicate that the system is singular for a circle billiard the boundary condition fails to determine a discrete set of levels so the spectrum is continuous for a diffraction grating defined by periodically varying boundary conditions on the edge of a half plane the phase of a diffracted beam amplitude remains undetermined in both cases the wavefunction on the boundary has a singularity at a d point described by the polylogarithm function

on the many dirichlet laplacians on a non convex polygon and their approximations by point interactions abstract by birman and skvortsov it is known that if is a planar curvilinear polygon with n non convex corners then the laplace operator with domain h 2 h 0 1 is a closed symmetric operator with deficiency indices n n here we provide a kre n type resolvent formula for any self adjoint extensions of such an operator i e for the set of self adjoint non friedrichs dirichlet laplacians on and show that any element in this set is the norm resolvent limit of a suitable sequence of friedrichs dirichlet laplacians with n point interactions

nonlinear tension observers for web machines precise regulation of span tension in web handling machines is critical to ensure product quality elevated tension causes web fracture during operation depressed or highly variable tension leads to irregular and unacceptable spool web handling machines typically employ costly load cell sensors to measure span tension this work investigates the use of nonlinear estimators or observers to provide cost effective span tension estimates from system measurements after presenting the dynamic equations of a web handling machine their structure is exploited to design a reduced order nonlinear observer with linear time varying error dynamics exponential stability of the error dynamics is demonstrated performance of the estimator is experimentally compared with two competing designs on a real web handling machine

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

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 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

erratum nonlinear observer design in the siegel domain there is an error in the proof of the main result of our paper siam j control optim 41 2002 pp 932 953 an additional assumption is needed for the main result to hold in this erratum we supply a corrected version of the main result

self adjoint extensions of the laplace beltrami operator and unitaries at the boundary abstract we construct in this article a class of closed semi bounded quadratic forms on the space of square integrable functions over a smooth riemannian manifold with smooth compact boundary each of these quadratic forms specifies a semi bounded self adjoint extension of the laplace beltrami operator these quadratic forms are based on the lagrange boundary form on the manifold and a family of domains parametrized by a suitable class of unitary operators on the boundary that will be called admissible the corresponding quadratic forms are semi bounded below and closable finally the representing operators correspond to semi bounded self adjoint extensions of the laplace beltrami operator this family of extensions is compared with results existing in the literature and various examples and applications are discussed

morphometry of spatial patterns abstract minkowski functionals constitute a family of order parameters which discriminate spatial patterns according to size shape and connectivity here we point out that these scalar descriptors can be complemented by vector valued curvature measures also known as quermas vectors using examples of galaxy clusters we demonstrate that the quermas vectors provide additional morphological information on directional features and symmetries displayed by spatial data

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

morphological characterization of patterns in reaction diffusion systems received 24 october 1995 morphological measures for spatial patterns occuring as dissipative structures in systems driven far from equilibrium are introduced they characterize the geometry and topology of the patterns and are capable to distinguish irregular structures with respect to the morphology in particular we analyze turbulent and regular patterns turing patterns in chemical reaction diffusion systems observed in a two dimensional open gel reactor with a chlorite iodide malonic acid reaction introducing the concept of level contours the measures turn out to be polynomials of low order cubic and fourth degree in the grey scale level of the images thus the dependence on the experimental conditions is reflected only in a finite number of coefficients which can be used as order parameters for the morphology of patterns we observe a symmetry breaking of the polynomials when the type of the pattern changes from hexagons to turbulence or stripes therefore it is possible to describe the pattern transitions quantitatively and it may be possible to classify them in a similar way like thermodynamic phase transitions

semi global observer for multi output nonlinear systems abstract we present an explicit form of nonlinear observers for a class of multi input multi output systems observer construction for multi output nonlinear systems is not a trivial extension of single output case especially when the global error convergence is of interest in this paper we consider a class of systems in which the subsystem for each output has a triangular dependence on the states of that subsystem itself and the overall system has a block triangular form for each subsystem hence the contribution is to extend the results existing in the literature in that interconnections between the subsystems are allowed the construction is based on the saturation of some estimates which is originated by khalil and esfandiari for the use of semi global output feedback control

nonlinear observer design in the siegel domain we extend the method of kazantzis and kravaris systems control lett 34 1998 pp 241 247 for the design of an observer to a larger class of nonlinear systems the extended method is applicable to any real analytic observable nonlinear system it is based on the solution of a first order singular nonlinear pde this solution yields a change of state coordinates which linearizes the error dynamics under very general conditions the existence and uniqueness of the solution is proved lyapunov s auxiliary theorem and siegel s theorem are obtained as corollaries the technique is constructive and yields a method for constructing approximate solutions