Non-invasive chaos control based on 2-contraction stabilizability

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.