PERFORMANCE ANALYSIS OF N4SID STATE-SPACE SYSTEM IDENTIFICATION

PERFORMANCE ANALYSIS OF N4SID STATE-SPACE SYSTEM IDENTIFICATION

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Proceedings of the American Control Conference Philadelphia, Pennsylvania - June 1998 PERFORMANCE ANALYSIS OF N4SID STATE-SPACE SYSTEM IDENTIFICATION Thomas W Flint and Richard J. Vaccaro Department of Electrical Engineering, University of Rhode Island, Kingston, RI 02881 USA ([email protected]) ABSTRACT This paper describes a statistical performance analysis method for multi-variate subspace system identification algorithms. The analysis is based on a recently developed perturbation expansion of the singular value decomposition. We demon- strate the technique by analyzing the numerical state-space subspace system identification algorithm N4SID. An ex- pression for the variance of the identified eigenvalues based on a finite record of inputloutput data is derived and verified using MATLAB simulations. 1. INTRODUCTION Nearly all subspace system identification methods depend on the singular value decomposition (SVD) to estimate a low-order observability subspace corresponding to a state- space model from a higher order noisy data matrix [ 13 [2]. The non-linearity of the SVD has been the limiting factor in previous attempts at performance analysis which have been limited to asymptotic analysis or generalizations based on simulation. Recently, a perturbation expansion of the SVD was derived in [3]. This expansion describes how the sin- gular sub-spaces of a nominal matrix are changed when a small noise matrix is added and makes possible a complete analysis of a subspace algorithm for the finite data case. 2, N4SID The problem addressed by N4SID is to identify the param- eters of an m-input Z-output linear time-invariant nth order state space system given only s samples of the (noise free) inputs uk and (noisy) outputs Yk.
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PERFORMANCE ANALYSIS OF N4SID STATE-SPACE SYSTEM IDENTIFICATION

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