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

a spectral approach for sifting process in empirical mode decomposition in this paper we propose an alternative to the algorithmic definition of the sifting process used in the original huang s empirical mode decomposition emd method although it has been proven to be particularly effective in many applications emd method has several drawbacks the major problem with emd is the lack of theoretical framework which leads to difficulties for the characterization and evaluation this approach on top of the mathematical model there are other concerns with mode mixing and transient phenomena such as intermittency or pure tones separation this paper follows a previous published nonlinear diffusion based filtering to solve the mean envelope estimation in sifting process the major improvements made in this present work are a non iterative resolution scheme for the previously proposed partial differential equation pde a new definition of the stopping function used in the pde framework and finally an automatic regularization process based on inverse problem theory to deal with mode mixing or transient detection problem obtained results confirm good properties of the new version of the pde based sifting process and its usefulness for decomposition of various kinds of data the efficiency of the method is illustrated on some examples using informative and pathological signals for which standard emd algorithm fails

nonlinear observers with approximately linear error dynamics the multivariable case exact error linearization uses nonlinear input output injection to design observers with linear error dynamics in certain coordinates this approach can only be applied nongenerically we propose an observer for a wider class of multivariable systems which uniformly minimizes the nonlinear part of the system that cannot be canceled by nonlinear input output injection our approach is numerical constructive and provides locally exponentially stable error dynamics an example compares our design with a high gain method

the empirical mode decomposition and the hilbert spectrum for nonlinear and non stationary time series analysis a new method for analysing nonlinear and non stationary data has been developed the key part of the method is the empirical mode decomposition method with which any complicated data set can be dec

monotonicity preserving c2 rational cubic spline for monotone data abstract designers in industries need to generate splines which can interpolate the data points in such a way that they preserve the inherited shape characteristics positivity monotonicity convexity of data among the properties that the spline for curves and surfaces need to satisfy smoothness and shape preservation of given data are mostly needed by all the designers in this paper a rational cubic function with three shape parameters has been developed data dependent sufficient constraints are derived for one of these shape parameters to preserve the inherited shape feature like monotonicity of data remaining two shape parameters are left free for designer to refine the shape of the monotone curve as desired numerical examples and interpolation error analysis show that the interpolant is not only c 2 local computationally economical and visually pleasant but also smooth the error of rational cubic function is also calculated when the arbitrary function being interpolated is c 3 in an interpolating interval the order of approximation of interpolant is o h i 3

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

exponential sums and newton polyhedra cohomology and estimates the basic objects of this study are exponential sums on a variety defined over a finite field fq q pa p char fq as we have remarked in some earlier articles 1 2 we find it more natural to begin with exponential sums on the torus gm n extend via the usual toric decomposition of an to exponential sums on affine n space and finally proceed via a standard character argument 4 to exponential sums on an affine variety defined over fq while this is the natural order of the work what we do in fact in the first part of this article is to combine the first two steps and deal with exponential sums on varieties v of the form v gm r x as r s n let f e fq xl xn xl xr be an arbitrary regular function on v then f is a sum of monomials and as such has a well defined newton polyhedron a ff at infinity this is the convex closure in rn of the lattice points which occur as exponents of the terms of f together with the origin we have indicated in our previous work 1 2 the description of some of the invariants of the associated l function in terms of properties of this polyhedron for example in 1 we showed how bounds for the degree and total degree of the l function associated with a general exponential sum on v can be expressed in terms of the volumes of a f and the intersections of a f and the various coordinate spaces in the present article assuming f is nondegenerate and commode with respect to af f we show these estimates are sharp our methods are p adic and are based on the work of dwork 11 12 our main accomplishment from which our other results follow is the extension of dwork s cohomology theory from smooth projective hypersurfaces in characteristic p to a general class of exponential sums given f regular on v we construct a complex of p adic banach spaces on which frobenius acts the alternating product of characteristic polynomials of frobenius describes the associated l function in fact when f is nondegenerate and commode with respect to a f the complex is acyclic in dimensions other than 0 and the characteristic

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

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

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

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

estimates for coefficients of l functions iii in this sequence of papers we investigate dirichlet series rm a s x sum limits 1 infty a n x n n 3 1 having euler products and compatible functional equations with the aim of estimating the coefficients a n it was shown in 2 3 by different techniques that if the analytic continuation and the functional equations hold for sufficiently many characters then a suitable upper bound for a n is true which is considerably better than that resulting from the absolute convergence of the series in this installment we combine both techniques to give new results and improve on those of 3 when a s x has an euler product of degree 3

a nonsplit sum of coefficients of modular forms we introduce and study certain truncated sums of hecke eigenvalues of gl2 automorphic forms along quadratic polynomials a power saving estimate is established and new applications to moments of critical l values associated to quadratic fields are derived an application to the asymptotic behavior of the height of heegner points and singular moduli is discussed in detail

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 improved emd method with modified envelope algorithm based on c2 piecewise rational cubic spline interpolation for emi signal decomposition abstract in this paper we propose an improved empirical mode decomposition emd method termed iemd with modified envelope algorithm based on c2 piecewise rational and c2 monotone piecewise rational cubic spline interpolations for the decomposition of nonlinear and non stationary emi signals in the sifting procedure we first construct the upper and lower envelopes employing c2 piecewise rational cubic spline interpolation prcsi technique considering the existence of undershoots we further modify the original envelopes iteratively with c2 monotone piecewise rational cubic spline interpolation mprcsi technique for the elimination of undershoots as accurate as possible experiments on synthetic and real signals compared with three improved versions of emd three for ensemble emd eemd and tl svd demonstrate that the proposed method is more valid and flexible when applied to the decomposition of synthesis harmonic signals and real eeg signals signifying it also can be applied to the decomposition of emi signals which are known to be extremely nonlinear and non stationary

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