Finite-time stability properties of Lur'e systems with piecewise continuous nonlinearities

Simone Mariano (1) , Romain Postoyan (2) , Luca Zaccarian (3, 4)

1 University of Melbourne
2 CRAN - Centre de Recherche en Automatique de Nancy
3 LAAS - Laboratoire d'analyse et d'architecture des systèmes
4 UNITN - Università degli Studi di Trento = University of Trento

We analyze the stability properties of Lur’e systems with piecewise continuous nonlinearities by exploiting the notion of set-valued Lie derivative for Lur’e-Postnikov Lyapunov functions. We first extend an existing result of the literature to establish the global asymptotic stability of the origin under a more general sector condition. We then present the main results of this work, namely additional conditions under which output and state finite-time stability properties also hold for the considered class of systems. We highlight the relevance of these results by certifying the stability properties of two engineering systems of known interest: mechanical systems affected by friction and cellular neural networks.

Mots clés: Stability; Finite-time stability; Lur'e systems; Neural networks; Nonsmooth analysis

Domaines: Automatique / Robotique

Simone Mariano, Romain Postoyan, Luca Zaccarian. Finite-time stability properties of Lur'e systems with piecewise continuous nonlinearities. IEEE Transactions on Automatic Control, In press, ⟨10.1109/TAC.2024.3383278⟩. ⟨hal-04530198⟩