Identi cation of a state - space model set presuming robust performance control

This paper proposes a method of identi cation for a discrete-time state-space model set presuming the existence of robust performance control. The model set is described by a nominal model and a parametric uncertainty bound measured with the Frobenius norm. The identi cation problem considered in this paper is to nd a model set which satis es conditions: (i) the model set is consistent with given observed data and (ii) there exists a controller achieving a prescribed robust performance level for the identi ed model set. We show that we can obtain the solution to the problem by solving matrix inequalities, and propose an identication algorithm.