Work

Finite-time stabilization of affine nonlinear systems

Year: 2026

Type: article

Abstract: The finite-time stabilization problem deals with the enforcement of a quantitative bound on the state trajectory of a dynamical system along a finite-time horizon. Sufficient conditions have been provided to solve this problem for different classes of nonlinear systems. However, by implying a certain degree of conservatism, these conditions are only sufficient. This work contributes to fill this gap, by giving a necessary and sufficient condition for the finite-time stabilization of affine nonlinear systems. First a necessary and sufficient condition available in literature to check finite-time stability (FTS) of nonlinear systems is extended to the case of continuously differentiable Lyapunov-like functions. Thanks to the obtained smoothness of the Lyapunov function and by a proper definition of a FTS Control Lyapunov Function, we show that it is possible to apply the Sontag’s universal formula to derive a necessary and sufficient condition to solve the stabilization problem for affine nonlinear systems.

Source: International Journal of Dynamics and Control

DOI: 10.1007/s40435-026-02177-z

Authors: Gianmaria De Tommasi, Federico Fiorenza, Adriano Mele, Alfredo Pironti

Institutions: University of Naples Federico II, École Polytechnique Fédérale de Lausanne

Language: English

Topic: Control and Stability of Dynamical Systems

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funder: Ministero dell'Università e della Ricerca