We consider in this paper the estimation problems for both orders and coefficients of linear feedback control systems, described by ARMAX models. The estimation algorithms are inspired by the Hannan-Rissanen method used for the estimation of stationary ARMA models, while the convergence analyses are based on limit theorems for both double array martingales and nonnegative supermartingales, and on techniques of stochastic Lyapunov functions. Traditionally used assumptions, such as the strictly positive real condition and the requirement of known upper bounds for true orders, are not imposed here.
"Estimation of Nonstationary Armax Models Based on the Hannan-Rissanen Method." Ann. Statist. 18 (4) 1729 - 1756, December, 1990. https://doi.org/10.1214/aos/1176347875