Subspace Identification of Linear Systems with Partial Eigenvalue Constraints

For subspace identification methods with eigenvalue constraints, the constraints are enforced by means of an optimization problem subject to LMI constraints. First principals or step response tests could be used as a source of auxiliary information in order to build LMI regions. In these cases, all the eigenvalues of the identified state space model are subject to the same constraints. However, it often happens that the non-dominant eigenvalues have larger real part or larger natural frequencies. In this paper, we propose a two-step method in order to constrain the dominant dynamics of SISO models into LMI regions. In virtue of this result, in addition, the model eigenvalues could be constrained into disjoint LMI regions. Numerical examples illustrate the e effectiveness of our proposed method.