Identification of affinely parameterized state–space models with unknown inputs

The identification of affinely parameterized state–space system models is quite popular to model practical physical systems or networked systems, and the traditional identification methods require the measurements of both the input and output data. However, in the presence of partial unknown input, the corresponding system identification problem turns out to be challenging and sometimes unidentifiable. This paper provides the identifiability conditions in terms of the structural properties of the state–space model and presents an identification method which successively estimates the system states and the affinely parameterized system matrices. The estimation of the system matrices boils down to solving a bilinear optimization problem, which is reformulated as a difference-of-convex (DC) optimization problem and handled by the sequential convex programming method. The effectiveness of the proposed identification method is demonstrated numerically by comparing with the Gauss–Newton method and the sequential quadratic programming method.