Stability analysis of time-varying delay systems in quadratic separation framework

Yassine Ariba (1) , Frédéric Gouaisbaut (1) , Dimitri Peaucelle (1)

1 LAAS - Laboratoire d'analyse et d'architecture des systèmes

This paper deals with the stability analysis of linear time-delay sys- tems. The time-delay is assumed to be a time-varying C1 function be- longing to an interval and has a bounded derivative. Considering stable delay-free system, the quadratic separation framework is used to assess the maximal allowable value of the delay that preserves stability. To take into account the time-varying nature of the delay, the quadratic separation principle has been extended to cope with the general case of uncertain op- erators (instead of just uncertain matrices). Then, separation conditions lead to linear matrix inequality (LMI) which can be efficiently solved with Semi Definite Programming solvers in Matlab. The paper concludes with an illustrative academic example.

Mots clés: Time-delay systems stability; robust control; quadratic separation

Domaines: Automatique / Robotique

Yassine Ariba, Frédéric Gouaisbaut, Dimitri Peaucelle. Stability analysis of time-varying delay systems in quadratic separation framework. ICNPAA- 2008: Mathematical Problems in Engineering, Aerospace and Sciences, Jun 2008, Genoa, Italy. ⟨hal-00357766v3⟩