Bounding the parameters of linear systems with stability constraints

Identification of linear systems, a priori known to be stable, from input output measurements corrupted by bounded noise is considered in the paper. A formal definition of the feasible parameter set is provided, taking explicitly into account prior information on system stability. On the basis of a detailed analysis of the geometrical structure of the feasible set, convex relaxation techniques are presented to solve nonconvex optimization problems arising in the computation of parameters uncertainty intervals. Properties of the computed relaxed bounds are discussed. A simulated example is presented to show the effectiveness of the proposed technique.