New model transformations for the stability analysis of time-delay systems

Mohammed Safi (1) , Lucie Baudouin (1) , Alexandre Seuret (1)

1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande

This paper deals with the stability analysis of time delay systems based on continuous-time approach. The originality of the present paper relies on the construction of several models for a same time-delay systems using the interconnection of an ordinary differential equation and a transport partial differential equation. The stability analysis is then performed using a Lyapunov functional. These models are constructed in order to first reduce potentially the complexity of the resulting stability conditions. Second several models are build in order to be interpreted as a discretization scheme as the one usually used in the Lyapunov functional. The proposed result can be seen as a generalized (N − M) discretization which consists in both a time-discretization of the delay interval into M sub-intervals, and the projection of the state function within each sub-interval on the Legendre polynomials of degree less than N. The efficiency of this novel approach is illustrated on an academic example.

Mots clés: Time-delay systems; Model transformations; Transport equation; Linear matrix inequalities; Integral inequalities; Lyapunov stability

Domaines: Automatique / Robotique

Mohammed Safi, Lucie Baudouin, Alexandre Seuret. New model transformations for the stability analysis of time-delay systems. IFAC Workshop on Time-Delay Systems (TDS'18), Jun 2018, Budapest, Hungary. 6p. ⟨hal-01799394⟩