Local stability analysis for large polynomial spline systems

Torbjørn Cunis (1, 2) , Jean-Philippe Condomines (3) , Laurent Burlion (4)

1 DRONES - ENAC - Programme transverse Drones
2 DTIS, ONERA, Université de Toulouse [Toulouse]
3 ENAC - Ecole Nationale de l'Aviation Civile
4 RU - Rutgers, The State University of New Jersey [New Brunswick]

Polynomial switching systems such as multivariate splines provide accurate fitting while retaining an algebraic representation and offering arbitrary degrees of smoothness; yet, application of sum-of-squares techniques for local stability analysis is computationally demanding for a large number of subdomains. This communiqué presents an algorithm for region of attraction estimation that is confined to those subdomains actually covered by the estimate, thereby significantly reducing computation time. Correctness of the results is subsequently proven and the run time is approximated in terms of the number of total and covered subdomains. Application to longitudinal aircraft motion concludes the study.

Mots clés: stability analysis; nonlinear analysis; switching functions; polynomial methods; Lyapunov function

Domaines: Systèmes et contrôle [cs.SY]

Torbjørn Cunis, Jean-Philippe Condomines, Laurent Burlion. Local stability analysis for large polynomial spline systems. Automatica, 2020, 113, pp.108773. ⟨10.1016/j.automatica.2019.108773⟩. ⟨hal-02390130⟩