Identification of a State-space Model Set Taking Stabilizing State Feedback into Consideration

Abstract

In this paper, we propose a method of identification for a discrete-time state-space model set. The identification problem is to determine the parameter set which characterizes the model set such that the model set is consistent with given input/output data in the time-domain. In addition, it is required that there exists a stabilizing feedback controller for the model set. These consistency and existing conditions are derived in terms of linear matrix inequalities. The proposed algorithm iteratively solves these LMI's to obtain the model set and the controller. A remarkable result shows that there is no difference between the Frobenius norm and spectral norm which measures the bound of parametric uncertainty of the model set in the context of identification and control in this paper.