Non-invasive chaos control based on 2-contraction stabilizability
File(s)
Published version
Author(s)
Angeli, David
Martini, Davide
Innocenti, Giacomo
Tesi, Alberto
Type
Journal Article
Abstract
In this paper a non-invasive approach to chaos control based on k-Contraction Theory is developed.
Specifically, some recent results on 2-contractive nonlinear systems are suitably extended to design a
feedback controller capable to remove attractors with positive Lyapunov exponents of the open loop
system, without altering the equilibrium points. First, 2-contraction stabilizability of linear control
systems is discussed, showing that it can be checked by solving some linear matrix inequalities. Then,
a novel technique based on 2-contraction stabilizability is devised for computing the gain matrix of a
derivative feedback controller ensuring that the controlled system has the same equilibrium points of
the uncontrolled one but no longer displays attractors with positive Lyapunov exponents. Finally, the
classical Lorenz system is employed to illustrate the features of the proposed technique.
Specifically, some recent results on 2-contractive nonlinear systems are suitably extended to design a
feedback controller capable to remove attractors with positive Lyapunov exponents of the open loop
system, without altering the equilibrium points. First, 2-contraction stabilizability of linear control
systems is discussed, showing that it can be checked by solving some linear matrix inequalities. Then,
a novel technique based on 2-contraction stabilizability is devised for computing the gain matrix of a
derivative feedback controller ensuring that the controlled system has the same equilibrium points of
the uncontrolled one but no longer displays attractors with positive Lyapunov exponents. Finally, the
classical Lorenz system is employed to illustrate the features of the proposed technique.
Date Issued
2026-03-01
Date Acceptance
2025-11-02
Citation
Automatica, 2026, 185
ISSN
0005-1098
Publisher
Elsevier BV
Journal / Book Title
Automatica
Volume
185
Copyright Statement
© 2025 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
License URL
Publication Status
Published
Article Number
112778
Date Publish Online
2025-12-19