Input-dependent stability analysis of systems with saturation in feedback

Alexander Pogromsky (1) , A.S. Matveev (2) , Antoine Chaillet (3) , Björn Rüffer (4)

1 Department of Mechanical Engineering [Eindhoven]
2 The Mathematics and Mechanics Faculty
3 L2S - Laboratoire des signaux et systèmes
4 Signal and System Theory Group

The paper deals with global stability analysis of linear control systems with saturation in feedback driven by an external input. Various new criteria based on non- quadratic Lyapunov functions are proposed, that unlike many previous results, offer better account for the role of the external excitation by providing input-dependent conditions for stability of solutions. For example, it is shown that even if the system fails to satisfy the incremental version of the circle criterion, the stability is guaranteed whenever the uniform root mean square value of the input signal is less than a computable threshold. The general theoretical results are illustrated in the case of the double integrator closed by a saturated linear feedback with an external excitation.

Mots clés: averaging function; saturated feedback; Lyapunov stability

Domaines: Automatique / Robotique

Alexander Pogromsky, A.S. Matveev, Antoine Chaillet, Björn Rüffer. Input-dependent stability analysis of systems with saturation in feedback. 52nd IEEE Conference on Decision and Control CDC 2013, Dec 2013, Florence, Italy. pp.1-6, ⟨10.1109/cdc.2013.6760820⟩. ⟨hal-00927730⟩