Guaranteed cost certification for discrete-time linear switched system with a dwell time

Marc Jungers (1) , Jamal Daafouz (1, 2)

1 CRAN - Centre de Recherche en Automatique de Nancy
2 IUF - Institut universitaire de France

This paper studies the guaranteed cost of a quadratic criterion associated with a linear discrete-time switched system for all the set of admissible switching laws. The admissible switching laws are here the ones exhibiting a dwell time. The approach provided here is to design an upper bound and a parametrized family of lower bounds of the guaranteed cost as close as possible in order to obtain a certification of the guaranteed cost. The upper bound is determined via a switched Lyapunov function and the lower bounds are obtained via the numerical computation of the cost induced by particular periodic switching laws. The features of the proposed approach are illustrated by a numerical example.

Mots clés: Switched systems; performance certification; periodic Lyapunov equations

Domaines: Automatique / Robotique

Marc Jungers, Jamal Daafouz. Guaranteed cost certification for discrete-time linear switched system with a dwell time. IEEE Transactions on Automatic Control, 2013, 58 (3), pp.768-772. ⟨10.1109/TAC.2012.2211441⟩. ⟨hal-00757006⟩