Deterministic Subspace Identification

This chapter focuses on the foundation of the system identification problem for state‐space systems that leads to subspace identification techniques. The original basis has evolved from systems theory and the work of Kalman for control system design. The fundamental problem is called the “realization problem". The basic paper by Ho and Kalman has been cited as the seminal publication showing how to extract the state‐space model. The chapter discusses this problem for two distinct data sets: impulse sequences of an infinite length (number of samples) data leading to the realization problem and input/output data leading to the subspace identification problem. Subspace identification techniques enable the capability to extract a large number of parameters compared to the prediction error methods that are quite time‐consuming and not practical for large parametric problems coupled with the need for potential real‐time applications.