Continuous-time Model Identification Using Spectrum Analysis with Passivity-preserving Model Reduction

Abstract

This chapter deals with state-space model approximation of linear systems derived from linear regression and spectrum analysis - a problem that can be viewed as a problem of system identification. System identification deals with the problem of fitting mathematical models to time series of input-output data [16]. Important subproblems are the extraction both of a ‘deterministic’ subsystem—i.e., computation of an input-output model—and a ‘stochastic’ subsystem that is usually modeled as a linear time-invariant system with white noise inputs and outputs that represent the misfit between model and data. A pioneering effort in continuous-time model identification was Wiener’s formulation of a Laguerre filter expansion [41]. As for the early literature on continuous-time model identification involving approaches with pseudo-linear regression, correlation and gradient search methods, there are algorithmic contributions [7, 15, 32, 41, 43, 44]; with surveys of Young [44], Unbehauen and Rao [13, 34, 35]; stochastic model estimation aspects [17]; software and algorithmic aspects [11, 40].