Subspace identification method incorporated with a priori information characterized in frequency domain

We propose a subspace identification method that involves a priori information of the system characterized in the frequency domain. Some properties of the system over all frequency range are transformed into matrix inequalities that are linear in system matrices, by using the well-known Kalman-Yakubovich-Popov (KYP) lemma. To construct a model that represents the specified frequency characteristics, we formulate a subspace identification problem under the matrix inequality constraints. This constrained problem is in a class of nonlinear optimization problems, then we reduce it to a convex one by applying a proper transformation. Furthermore, the proposed method is extended to that incorporated with a priori information characterized only in a certain frequency range. Finally, we verify the effectiveness of the proposed method in a numerical simulation.