Proving set inclusion via intervals: application to parametric robust stability

Proving that an uncertain parametric model is stable amounts to prove the inclusion of two sets: the set A of all feasible parameters and the set B of all parameters for which the model is stable. In this paper, a new algorithm, able to decide whether or not A is included in B, is presented. The method is based on interval analysis which is a numerical tool able to deal with inequalities in a global and guaranteed way. Convergence properties of the algorithm are provided. The algorithm is then applied to the robust stability of a discrete-time model where the information on the parameters is given through bounded-error data. The behavior of the algorithm with respect to the number of parameters is illustrated on a continuous-time model.