identification of systems containing linear dynamic and static nonlinear elements identification of nonlinear systems which can be represented by combinations of linear dynamic and static nonlinear elements are considered previous results by the authors based on correlation analysis are combined to provide a unified treatment for this class of systems it is shown that systems composed of cascade feedforward feedback and multiplicative connections of linear dynamic and zero memory nonlinear elements can be identified in terms of the individual component subsystems from measurements of the system input and output only

controllability and stabilizability of a class of continuous piecewise affine dynamical systems this paper studies controllability and stabilizability of continuous piecewise affine dynamical systems which can be considered as a collection of ordinary finite dimensional linear input state output systems together with a partition of the product of the state space and input space into full dimensional polyhedral regions each of these regions is associated with one particular linear system from the collection the main results of the paper are popov belevitch hautus type necessary and sufficient conditions for both controllability and stabilizability of such systems

a prediction error and stepwise regression estimation algorithm for non linear systems the identification of non linear systems based on a narmax non linear autoregressive moving average model with exogenous inputs model representation is considered and a combined stepwise regression prediction error estimation algorithm is derived the stepwise regression routine determines the model structure by detecting significant terms in the model while the prediction error algorithm provides optimal estimates of the final model parameters implementation of the algorithms is discussed in detail and several simulated examples and industrial applications are included to illustrate that parsimonious models of non linear systems can be identified using the algorithm

a parallel divide and conquer algorithm for the symmetric eigenvalue problem on distributed memory architectures we present a new parallel implementation of a divide and conquer algorithm for computing the spectral decomposition of a symmetric tridiagonal matrix on distributed memory architectures the implementation we develop differs from other implementations in that we use a two dimensional block cyclic distribution of the data we use the lowner theorem approach to compute orthogonal eigenvectors and we introduce permutations before the back transformation of each rank one update in order to make good use of deflation this algorithm yields the first scalable portable and numerically stable parallel divide and conquer eigensolver numerical results confirm the effectiveness of our algorithm we compare performance of the algorithm with that of the qr algorithm and of bisection followed by inverse iteration on an ibm sp2 and a cluster of pentium piis

dead beat control of simple hammerstein models dead beat controllers for simple hammerstein systems are investigated several designs for nonminimum time state dead beat controllers are given for certain classes of simple hammerstein systems a general minimum time state dead beat controller is presented for a class of simple hammerstein systems a design for a family of minimum time control laws is provided this enables to a certain extent shaping of transient response via choosing an appropriate control law finally the authors design an output dead beat controller for a class of hammerstein systems that are not necessarily state dead beat controllable

outer functions and cyclic elements in bergman spaces abstract the notion of an outer function in a bergman space l p a d is introduced and shown to be necessary for cyclicity in l p a d and sufficient for cyclicity in a

output dead beat control for a class of planar polynomial systems output dead beat control for a class of nonlinear discrete time systems which are described by a single input output i o polynomial difference equation is considered the class of systems considered is restricted to systems with a two dimensional state space description it is assumed that the highest degree with which the present input appears in the equation is odd necessary and sufficient conditions for the existence of output dead beat control and for the stability of the zero output constrained dynamics are presented we also design a minimum time output dead beat control algorithm feedback controller which yields stable zero dynamics whenever this is feasible a number of interesting phenomena are discussed and illustrated with examples

model structure selection by cross validation two criteria for choosing between different model structures are proposed their derivation is within a natural cross validatory assessment context and is fairly assumption free in particular the two criteria can be used for discriminating between non nested model structures and more importantly the true system is not required to belong to the considered set of models should the true system belong to the model set the two proposed criteria will asymptotically reduce to some well known structure selection criteria this is believed to be a desirable feature of our proposals on the other hand it provides a nice cross validation interpretation of some well known model structure selection rules also the cross validation interpretation helps one to choose which criteria to use in a given application the paper also has a second purpose somewhat decoupled from that mentioned above it contains an extensive survey of the literature that is useful in its own right

algebraic necessary and sufficient conditions for the controllability of conewise linear systems the problem of checking certain controllability properties of even very simple piecewise linear systems is known to be undecidable this paper focuses on conewise linear systems i e systems for which the state space is partitioned into conical regions and a linear dynamics is active on each of these regions for this class of systems we present algebraic necessary and sufficient conditions for controllability we also show that the classical results of controllability of linear systems and input constrained linear systems can be recovered from our main result our treatment employs tools both from geometric control theory and mathematical programming

on the orthogonality of eigenvectors computed by divide and conquer techniques a detailed analysis on the accuracy issues in calculating the eigensystems of rank 1 perturbed diagonal systems is presented such calculations are the core of the divide and conquer technique prop

restricted rank modification of the symmetric eigenvalue problem theoretical considerations the problem is considered how to obtain the eigenvalues and vectors of a matrix a vvt where a is a symmetric matrix with known spectral decomposition and vvt is a positive semidefinite matrix of low rank it is shown that the eigenvalues of a vvt can easily be located to any desired accuracy by means of the inertia of the matrix i vt a 1v the problem of determining the eigenvalues of a restricted to r v can be treated likewise

on determining the structure of a non linear system abstract a method is presented for constructing a model of a non linear system from the input output data the structure of the system is assembled from a library of nonlinear terms that are possible suspects for inclusion in the model while each possible model structure is represented by a node in a tree it is shown that searching the tree for the optimal n term model structure can be done in n stages using an algorithm based on conjugate direction ideas the essential feature of the technique is that it generates a sequence of projection matrices such that the original vector valued functions become conjugate directions this leaves the original non linear terms intact and allows the structure for the optimal n term model to be assembled in n selections from the library examples are presented from regression analysis and non linear dynamic systems

large bergman spaces invertibility cyclicity and subspaces of arbitrary index in a wide class of weighted bergman spaces we construct invertible non cyclic elements these are then used to produce z invariant subspaces of index higher than one in addition these elements generate non trivial bilaterally invariant subspaces in anti symmetrically weighted hilbert spaces of sequences

output deadbeat control of nonlinear discrete time systems with one dimensional zero dynamics global stability conditions output deadbeat control in one step is considered for a class of discrete time systems described by a nonlinear single input single output recursive representation global stability conditions are established for the particular subclass of systems with one dimensional zero dynamics the results are illustrated with applications to polynomial and neural dynamical systems

model selection and validation methods for non linear systems the theory of hypothesis testing is used to select a model with the correct structure and the relation of such a method to the aic and fpe criteria is investigated parametric validation and correlation validation methods are developed for non non linear difference equation models several shortcomings of traditional methods especially when applied to non linear systems are described

on controllability of discrete time bilinear systems by near controllability abstract in this paper controllability of discrete time bilinear systems is studied by applying a recent result on near controllability a new sufficient condition for controllability of the systems is presented where controllability is proved by approximation with near controllability the new condition is algebraically verifiable and is hence easy to apply compared with a classical result on controllability of discrete time bilinear systems which can be effective even when the classical result does not work furthermore the control inputs to achieve the transition of the systems between any given pair of states are approximately computable according to near controllability therefore near controllability can be used to not only better characterize the system properties but also prove controllability with computable control inputs the new condition is then generalized to derive similar results on controllability and near controllability of the systems finally examples are given to illustrate the results of this paper

on small controllability and controllability of a class of nonlinear systems in this paper small controllability and controllability of a class of nonlinear systems are studied both the discrete time case and continuous time case are considered by proposing an implicit function approach sufficient conditions for the systems respectively to be small controllable and controllable are obtained examples are also provided to illustrate the results of the paper

stabilizability and dead beat controllers for two classes of wiener hammerstein models two classes of block oriented models of the wiener hammerstein type are considered we prove that a generic condition is sufficient for a null controllable discrete time system of this form to have a stabilizing minimum time dead beat controller when the condition is violated we show how to design a nonminimum time stabilizing dynamic dead beat controller the result is used to obtain stabilizability conditions for these systems

input output parametric models for non linear systems part ii stochastic non linear systems recursive input output models for non linear multivariate discrete time systems are derived and sufficient conditions for their existence are defined the paper is divided into two parts the first part introduces and defines concepts such as nerode realization multistructural forms and results from differential geometry which are then used to derive a recursive input output model for multivariable deterministic non linear systems the second part introduces several examples compares the derived model with other representations and extends the results to create prediction error or innovation input output models for non linear stochastic systems these latter models are the generalization of the multivariable arm ax models for linear systems and are referred to as narmax or non linear autoregressive moving average models with exogenous inputs

computing approximate eigenpairs of symmetric block tridiagonal matrices a divide and conquer method for computing approximate eigenvalues and eigenvectors of a block tridiagonal matrix is presented in contrast to a method described earlier w n gansterer r c ward and r p muller acm trans math software 28 2002 pp 45 58 the off diagonal blocks can have arbitrary ranks it is shown that lower rank approximations of the off diagonal blocks as well as relaxation of deflation criteria permit the computation of approximate eigenpairs with prescribed accuracy at significantly reduced computational cost compared to standard methods such as for example implemented in lapack

output feedback stabilization of a class of wiener systems a globally stabilizing output feedback controller is designed for a class of continuous time wiener systems the wiener systems we consider consist of a linear dynamical block and an output polynomial nonlinearity connected in series the hybrid controller consists of three modes of operation which are periodically applied to the system the controller achieves a dead beat response of the closed loop system

a note on observability tests for general polynomial and simple wiener hammerstein systems we propose an algorithm based on symbolic computation packages for testing observability conditions of general polynomial systems which were formulated in sontag siam j control optim 17 1979 139 151 computational complexity of the observability test can be reduced and the test simplified for classes of polynomial systems we illustrate this by considering the class of simple wiener hammerstein systems which consist of a series of two linear dynamic blocks between which a static nonlinearity is sandwiched we consider the case when the nonlinearity is a monomial n q q 1 simple necessary and sufficient conditions for observability are given and they resemble but are subtly different from the well known result on observability for the series connection of two linear systems c 1998 elsevier science b v all rights reserved

hilbert spaces of analytic functions with a contractive backward shift abstract we consider hilbert spaces of analytic functions in the disk with a normalized reproducing kernel and such that the backward shift f z f z f 0 z is a contraction on the space we present a model for this operator and use it to prove the surprising result that functions which extend continuously to the closure of the disk are dense in the space this has several applications for example we can answer a question regarding reverse carleson embeddings for these spaces we also identify a large class of spaces which are similar to the de branges rovnyak spaces and prove some results which are new even in the classical case

dead beat controllability of polynomial systems symbolic computation approaches state and output dead beat controllability tests for a very large class of polynomial systems with rational coefficients may be based on the quantifier elimination by partial cylindrical algebraic decomposition qepcad symbolic computation program the method is unified for a very large class of systems and can handle one or two sided control constraints families of minimum time state output dead beat controllers are obtained the computational complexity of the test is prohibitive for general polynomial systems but by constraining the structure of the system we may beat the curse of complexity a computationally less expensive algebraic test for output dead beat controllability for a class of odd polynomial systems is presented necessary and sufficient conditions are given they are still very difficult to check therefore a number of easier to check sufficient conditions are also provided the latter are based on the grobner basis method and qepcad it is shown on a subclass of odd polynomial systems how it is possible to further reduce the computational complexity by exploiting the structure of the system

controllability for a class of simple wiener hammerstein systems abstract controllability for a class of simple wiener hammerstein systems is considered necessary and sufficient conditions for dead beat and complete controllability for these systems are presented the controllability tests consist of two easy to check tests for the subsystems

state deadbeat control of nonlinear systems construction via sets a geometric generalization of the discrete time linear deadbeat control problem is studied the proposed method to generate a deadbeat tracker for a given nonlinear system is constructive and makes use of sets that can be computed iteratively for demonstration derivations of the deadbeat feedback law and tracker dynamics are provided for an example system based on the method a simple algorithm that computes the deadbeat gain for a linear system with scalar input is given

popov belevitch hautus type controllability tests for linear complementarity systems it is well known that checking certain controllability properties of very simple piecewise linear systems are undecidable problems this paper deals with the controllability problem of a class of piecewise linear systems known as linear complementarity systems by exploiting the underlying structure and employing the results on the controllability of the so called conewise linear systems we present a set of inequalitytype conditions as necessary and sufficient conditions for controllability of linear complementarity systems the presented conditions are of popov belevitch hautus type in nature 2006 elsevier b v all rights reserved

weighted integrability of polyharmonic functions abstract to address the uniqueness issues associated with the dirichlet problem for the n harmonic equation on the unit disk d in the plane we investigate the l p integrability of n harmonic functions with respect to the standard weights 1 z 2 the question at hand is the following if u solves n u 0 in d where stands for the laplacian and d u z p 1 z 2 d a z must then u z 0 here n is a positive integer is real and 0 p d a is the usual area element the answer will generally speaking depend on the triple n p the most interesting case is 0 p 1 for a given n we find an explicit critical curve p n p a piecewise affine function such that for n p there exist nontrivial functions u with n u 0 of the given integrability while for n p only u z 0 is possible we also investigate the obstruction to uniqueness for the dirichlet problem that is we study the structure of the functions in ph n p d when this space is nontrivial we find a new structural decomposition of the polyharmonic functions the cellular decomposition which decomposes the polyharmonic weighted l p space in a canonical fashion corresponding to the cellular expansion is a tiling of part of the p plane into cells the above uniqueness for the dirichlet problem may be considered for any elliptic operator of order 2n however the above mentioned critical integrability curve will depend rather strongly on the given elliptic operator even in the constant coefficient case for n 1

the discrete linear time invariant time optimal control problem an overview a review of two decades of investigation into one of the fundamental problems of control theory the discrete linear time invariant time optimal control problem is presented two classes of multi input time optimal controller one based on system controllability and the other on eigenvalue assignment are considered in some detail also discussed are the dual state reconstruction problem the deadbeat control of linear systems with inaccessible state and other extensions the exposition is a unifying one and involves only that matrix algebra commonly encountered in control theory

a note on dead beat controllability of generalised hammerstein systems necessary and sufficient conditions for dead beat and complete controllability for a class of generalised hammerstein systems are presented since the system s structure is very close to linear only linear algebra is used for the controllability test the test is very simple and easy to use a closed loop minimum time dead beat controller can be designed for a subclass of generalised hammerstein systems using the grobner basis method

beurling type density theorems in the unit disk we consider two equivalent density concepts for the unit disk that provide a complete description of sampling and interpolation ina n the banach space of functionsf analytic in the unit disk with 1 z 2 n f z bounded this study reveals a nyquist density a sequence of points is roughly speaking a set of sampling if and only if its density in every part of the disk is strictly larger thann and it is a set of interpolation if and only if its density in every part of the disk is strictly smaller thann similar density theorems are also obtained for weighted bergman spaces

structure identification of nonlinear dynamic systems a survey on input output approaches abstract in the past several methods have been elaborated for the identification of nonlinear dynamic systems most of the methods assume that the structure of the system is given a priori therefore they are in reality parameter estimation algorithms and structure identification is thus usually performed by repeated parameter estimation however in nonlinear system theory several methods are known to determine the structure of a system in this paper structure identification of block oriented especially cascade models of semi linear dynamic models with signal dependent parameters and of nonlinear dynamic models being linear in the parameters will be considered different structure selection methods are summarized based on step and impulse tests frequency response measurements correlation analysis repeated reproducible tests and normal operating data

output dead beat control for nonlinear systems with one zero at infinity the problem of output dead beat control i e one step zeroing of the output is considered for nonlinear systems with discrete time controllers the nonlinear system is assumed to have one zero at infinity conditions for the existence of the dead beat control for small sampling intervals are derived the closed loop system is shown to be stable in the sense that all states converge to the origin if the controlled system is minimum phase

harmonic functions of maximal growth invertibility and cyclicity in bergman spaces in the theory of commutative banach algebras with unit an el ement generates a dense ideal if and only if it is invertible in which case its gelfand transform has no zeros and the ideal it generates is the whole algebra with varying degrees of success efforts have been made to extend the validity of this result beyond the context of banach algebras for instance for the hardy space h2 on the unit disk it is known that all invertible elements are cyclic an element is cyclic if its polynomial multiples are dense but cyclic elements need not be invertible in this paper we supply examples of func tions in the bergman and uniform bergman spaces on the unit disk which are invertible but not cyclic this answers in the negative questions raised by shapiro nikolsk i shields korenblum brown and frankfurt department of mathematics university of bordeaux i 351 cours de la liberation 33405 talence france e mail address borichev math u bordeaux fr department of mathematics lund university box 118 22100 lund sweden e mail address haakan maths lth se

zero dynamics of sampled nonlinear systems abstract the behaviour of the zero dynamics of a discrete time system obtained when sampling a continuous time nonlinear system is studied we give a result which generalizes the known behaviour of the zeros of a sampled linear system for small time intervals

computing eigenvectors of block tridiagonal matrices based on twisted block factorizations new methods for computing eigenvectors of symmetric block tridiagonal matrices based on twisted block factorizations are explored the relation of the block where two twisted factorizations meet to an eigenvector of the block tridiagonal matrix is reviewed based on this several new algorithmic strategies for computing the eigenvector efficiently are motivated and designed the underlying idea is to determine a good starting vector for an inverse iteration process from the twisted block factorizations such that a good eigenvector approximation can be computed with a single step of inverse iteration an implementation of the new algorithms is presented and experimental data for runtime behaviour and numerical accuracy based on a wide range of test cases are summarized compared with competing state of the art tridiagonalization based methods the algorithms proposed here show strong reductions in runtime especially for very large matrices and or small bandwidths the residuals of the computed eigenvectors are in general comparable with state of the art methods in some cases especially for strongly clustered eigenvalues a loss in orthogonality of some eigenvectors is observed this is not surprising and future work will focus on investigating ways for improving these cases