Proving set inclusion via intervals: application to robust stability

Luc Jaulin (1, 2, 3) , Jacques Burger (1)

1 LISA - Laboratoire d'Ingéniérie des Systèmes Automatisés
2 STIC - Département STIC [Brest]
3 Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance

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 base 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.

Domaines: Sciences de l'ingénieur [physics]

Luc Jaulin, Jacques Burger. Proving set inclusion via intervals: application to robust stability. Automatica, 1999, 35 (4), pp.627-632. ⟨hal-00844570⟩