Regional stability and stabilization of a class of linear hyperbolic systems with nonlinear quadratic dynamic boundary conditions

André Caldeira (1) , Christophe Prieur (1) , Daniel Coutinho (2) , Valter J S Leite (3)

1 GIPSA-SYSCO - GIPSA - Systèmes non linéaires et complexité
2 UFSC - Universidade Federal de Santa Catarina = Federal University of Santa Catarina [Florianópolis]
3 CEFET-MG - Centro Federal de Educação Tecnológica de Minas Gerais

This paper addresses the boundary control problem of fluid transport in a Poiseuille flow taking the actuator dynamics into account. More precisely , sufficient stability conditions are derived to guarantee the exponential stability of a linear hyperbolic differential equation system subject to non-linear quadratic dynamic boundary conditions by means of Lyapunov based techniques. Then, convex optimization problems in terms of linear matrix inequality constraints are derived to either estimate the closed-loop stability region or synthesize a robust control law ensuring the local closed-loop stability while estimating an admissible set of initial states. The proposed results are then applied to application-oriented examples to illustrate local stability and stabilization tools.

Mots clés: robust control; LMIs; Poiseuille flow; linear hyperbolic systems; dynamic boundary conditions

Domaines: Automatique / Robotique

André Caldeira, Christophe Prieur, Daniel Coutinho, Valter J S Leite. Regional stability and stabilization of a class of linear hyperbolic systems with nonlinear quadratic dynamic boundary conditions. European Journal of Control, 2018, 43, pp.46-56. ⟨10.1016/j.ejcon.2018.05.003⟩. ⟨hal-01984386⟩