On the Computation of Set-Induced Control Lyapunov Functions for Continuous-Time Systems

Mirko Fiacchini 1 Christophe Prieur 1 Sophie Tarbouriech 2
1 GIPSA-SYSCO - SYSCO
GIPSA-DA - Département Automatique
2 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes
Abstract : The paper presents a computation-oriented method for characterizing and obtaining local control Lyapunov functions induced by particular star-shaped nonconvex sets for continuous-time nonlinear systems with bounded inputs. For a given set, the necessary and sufficient conditions for the induced function to be a nonconvex local control Lyapunov function are provided. The related convex problems for computing the exact region in which the function is decreasing and the optimal control input are presented. The results are applied to the Brockett integrator.
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Mirko Fiacchini, Christophe Prieur, Sophie Tarbouriech. On the Computation of Set-Induced Control Lyapunov Functions for Continuous-Time Systems . SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2015, 53 (3), pp.1305-1327. ⟨hal-01133446⟩

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