Linear regressive realizations of LTI state space models

Abstract

In this paper, linear regressive model structures are deduced from single input -single output (SISO) deterministic LTI systems in state space form. The resulting linear regression and predictor are exact representations of a discrete-time LTI state space model Σ d belonging to a certain class S. As an illustrative example, a process with first-order reaction and advective transport is approximated by a discrete-time state space model Σ d , where the one-dimensional space is divided into n compartments and is reparametrized such that Σ d ⊆ S. The system output can then be explicitly predicted by y(t) = θ T φ(t−1)−γ(t−1) as a function of the number of compartments n, the sensor position j * , the parameter vector θ = ξ(ϑ) with ϑ a vector with original (physical) parameters, and input-output data. The method is attractive for experimental design, direct parameter estimation and prediction when prior (physical) parameter knowledge is to be preserved.