A global model structure is developed for parametrization and identification of a general class of Linear Parameter-Varying (LPV) systems. By using a fixed orthonormal basis function (OBF) structure, a linearly parametrized model structure follows for which the coefficients are dependent on a scheduling signal. An optimal set of OBFs for this model structure is selected on the basis of local li...

In this paper we propose a new modeling technique for LTI multivariable systems using the generalized Orthonormal basis functions with ordinary poles. Once the model structure is built we proceed to update the membership set of the resulting model parameters through the execution of unknown but bounded error identification algorithms. This updating aims to synthesize a robust control strategy. ...

It is a well known fact that any orthonormal basis in L 2 can produce a \random density". If fng is an orthonormal basis and fang is a sequence of random variables such that a 2 n = 1 a.s., then f(x) = jann(x)j 2 is a random density. In this note we deene a random density via orthogonal bases of wavelets and explore some of its basic properties.

This paper examines the use of general orthonormal bases for system identification from frequency domain data. This idea has been studied in great depth for the particular case of the orthonormal trigonometric basis. Here we show that the accuracy of the estimate can be significantly improved by rejecting the trigonometric basis in favour of a more general orthogonal basis that is able to be ad...

In the present work a newer type of black box nonlinear model in Hammerstein structure is proposed. The model has Wavelet Network coupled with Orthonormal Basis Functions which is capable of modeling a class of non-linear systems with acceptable accuracy. Wavelet basis functions have the property of localization in both the time and frequency domains which enables wavelet networks to approximat...

This paper provides an overview of system identification using orthonormal basis function models, such as those based on Laguerre, Kautz, and generalised orthonormal basis functions. The paper is separated in two parts. In this first part, the mathematical foundations of these models as well as their advantages and limitations are discussed within the context of linear and robust system identif...

This discussion sparse representations of signals in R. The sparsity of a signal is quantified by the number of nonzero components in its representation. Such representations of signals are useful in signal processing, lossy source coding, image processing, etc. We first speak of an uncertainty principle regarding the sparsity of any two different orthonormal basis representations of a signal S...

In a complex vector space of dimension N , by a full set of mutually unbiased bases (MUB’s) we mean a set of N+1 orthonormal bases such that the modulus square of the scalar product of any member of one basis with any member of any other basis is equal to 1/N . If we take e to denote the k vector in the α orthonormal basis, then having a full set of MUB’s amounts to having a collection e ; α = ...