ARMARKOV Least-Squares Identi cation

In recent work, ARMARKOV representations have been proposed as an extension of ARMA representations of nite-dimensional linear time-invariant systems. ARMARKOV representations have the same form as ARMA representations, but explicitly involve Markov parameters. This paper generalizes ARMA least-squares time-domain identi cation to ARMARKOV representations. The ARMARKOV/least-squares identi cation algorithm is used to estimate the Markov parameters of a linear time-invariant system from measurements of the inputs and outputs. The eigensystem realization algorithm is then used to construct a minimal realization. A numerical example involving a second-order lightly damped system illustrates the decreased sensitivity of the eigenvalues to the Markov parameters of a perturbed ARMARKOV representation compared to the Markov parameters of a perturbed ARMA representation. Finally, using experimental data, the dynamics of an acoustic duct are identi ed using the ARMA/least-squares identi cation algorithm to obtain a transfer function representation and the ARMARKOV/least-squares identi cation algorithm with ERA to obtain a minimal realization.