Finite-time attractive ellipsoid method: implicit Lyapunov function approach

ABSTRACT

A finite-time version, based on implicit Lyapunov functions (ILFs), for the attractive ellipsoid method (AEM) is developed. Based on this, a robust control scheme is presented to ensure finite-time convergence of the solutions of a chain of integrators with bounded output perturbations to a minimal ellipsoidal set. The control parameters are obtained by solving a minimisation problem of the ‘size’ of the ellipsoid subject to a set of linear matrix inequalities (LMIs) constraints, and by applying the implicit function theorem. A numerical example is presented to support the implementability of these theoretical results.

KEYWORDS:

• Robust control
• ellipsoid methods
• finite time
• implicit Lyapunov functions

Acknowledgements

The first author acknowledges the CONACyT postdoctoral grant [230105] for supporting this work.

Disclosure statement

No potential conflict of interest was reported by the authors.