Identifiability conditions for Continuous Time Linear Closed Loop Systems

Abstract

Necessary and sufficient conditions are given for the identifiability of open loop transfer functions for linear continuous time systems operating in closed loop. It is shown that provided certain structural properties are assumed, it is necessary and sufficient that the joint input-output spectral density be block diagonal when evaluated at infinity. With finite data, the spectral density cannot be exactly determined. However, it is shown in the paper, that the errors in the recovered open loop transfer functions will be small provided the estimated spectral density is approximately block diagonal when evaluated at infinity. This latter result leads to a practical test for identifiability of closed loop systems using finite data.