Abstract
A method for system identification with Linear Matrix Inequalities (LMIs) is proposed in this report. We show that system identification problems for various types of systems, e.g., an identification problem of LTI discrete time systems, continuous time systems and time varying systems etc., can be formulated as an LMI optimization problem. With the present problem formulation we can easily incorporate inequality constraints on identified parameters, e.g., a constraint on the upper and the lower bounds and/or quadratic constraints, etc.. This property helps us to get the mathematical model that is physically valid, such as the damping and the stiffness matrix of mechanical systems generally take positive value. Furthermore, the proposed LMI formulation for system identification can be applied to a framework of iterative system identification and controller design. The effectiveness the present identification methodology is experimentally examined with a system identification for a 3-story benchmark building of NCREE, Taiwan.
