Realizing LTI models by identifying characteristic parameters using least squares optimization*

This paper considers the realization of discrete-time linear time-invariant dynamical systems using input-output data. Starting from a generalized state-space representation that accounts for static offsets, a state-independent system representation is derived using the Cayley-Hamilton theorem and characteristic parameters are introduced to describe the system dynamics in an alternative way. Given input-output data, we present two formulations to address model deviations and to identify characteristic parameters by minimizing considered error terms in a least squares sense. The applicability of the proposed subspace identification method is demonstrated with physical data of the identification database DaISy.