Generalized Orthonormal Basis Functions in System y Identification

Over the last years a general theory has been developed for the consttuction and analysis of rational ofihonormal basis functions, often called Generalized Orthonormal Basis Functions (GOBF) in the engineeing literature. These investigations motivate the interest in the examination of the approximation properties of the rational orthonormal systems generated by a given set of poles. These basis can be viewed as an ertension of the tigonomet' ic system on the unit circle, that coresponds to the special choice when all of the poles are located at the orign. This poper provides a generalization of certain classical Lo norm convergence and summation theorems of the paftial sums of Fouier seies ttsing GOBF expansions. Using the so called Hambo-domain techniques the paper considers the construction of minimal state space models of linear time-invaiant (LTI) systems on the basis of systems representations in terms of GOBF expansions.

[1]  Zoltán Szabó,et al.  Minimal partial realization from generalized orthonormal basis function expansions , 2002, Autom..

[2]  Jozsef Bokor,et al.  Approximate Identification in Laguerre and Kautz Bases , 1998, Autom..

[3]  Jie Chen,et al.  Optimal nonparametric identification from arbitrary corrupt finite time series , 1995, IEEE Trans. Autom. Control..

[4]  R. G. Hakvoort,et al.  Worst-case system identification in l/sub 1/: error bounds, optimal models and model reduction , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[5]  K. Pan.  On characterization theorems for measures associated with orthogonal systems of rational functions on the unit circle , 1992 .

[6]  Guoxiang Gu,et al.  A class of algorithms for identification in H∞ , 1992, Autom..

[7]  J. Partington.  Robust identification and interpolation in H , 1991 .

[8]  J. Willems,et al.  On the solution of the minimal rational interpolation problem , 1990 .

[9]  A. Helmicki,et al.  Identification in H∞: a robustly convergent, nonlinear algorithm , 1990, 1990 American Control Conference.

[10]  R. Tempo,et al.  Optimal algorithms theory for robust estimation and prediction , 1985 .

[11]  Georg Heinig,et al.  Algebraic Methods for Toeplitz-like Matrices and Operators , 1984 .

[12]  Michael A. Arbib,et al.  Topics in Mathematical System Theory , 1969 .

[13]  N. Aronszajn.  Theory of Reproducing Kernels. , 1950 .

[14]  Zoltán Szabó,et al.  Identification of rational approximate models in H/sup /spl infin// using generalized orthonormal basis , 1999 .

[15]  Yongjian Hu,et al.  Inversion of a generalized block Loewner matrix, the minimal partial realization, and matrix rational interpolation problem , 1999 .

[16]  Michel Gevers,et al.  Towards a Joint Design of Identification and Control , 1993 .

[17]  Karl Johan Åström,et al.  Matching Criteria for Control and Identification , 1993 .

[18]  Β. L. HO,et al.  Editorial: Effective construction of linear state-variable models from input/output functions , 1966 .

[19]  K. Hoffman.  Banach Spaces of Analytic Functions , 1962 .