A polynomial approach to nonlinear state feedback stabilization of saturated linear systems

Giorgio Valmorbida (1) , Luca Zaccarian (2, 3) , Isabelle Queinnec (2) , Sophie Tarbouriech (2) , Antonis Papachristodoulou (1)

1 University of Oxford
2 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
3 Dipartimento di Ingegneria Industriale [Trento]

The paper revisits the local exponential stabilization and global asymptotic stabilization problems of saturated linear systems using nonlinear control laws. The proposed approach takes advantage of a rational formulation of the control action in terms of a parameter σ, which is the solution to an implicit equation depending on the state, scheduling the control law. Constructive solutions are then proposed by considering sum-of-squares formulation of the conditions, when imposing a polynomial dependence on parameter σ.

Domaines: Automatique / Robotique

Giorgio Valmorbida, Luca Zaccarian, Isabelle Queinnec, Sophie Tarbouriech, Antonis Papachristodoulou. A polynomial approach to nonlinear state feedback stabilization of saturated linear systems. IEEE 53rd Annual Conference on Decision and Control (CDC 2014), Dec 2014, Los Angeles, United States. pp.6317-6322, ⟨10.1109/CDC.2014.7040379⟩. ⟨hal-01851201⟩