Hybrid feedback stabilization of quasilinear systems in the plane

Abstract

We apply Artstein's hybrid feedback algorithm to stabilize quasilinear dynamical systems with complex multipliers in the plane. We study only the case of incomplete observation when ordinary feedback controls do not work. The main results of the paper state that Artstein's procedure provides an arbitrary rate of asymptotic convergence/divergence of solutions. In other words, we prove the complete controllability from below of the upper Lyapunov exponent and the uniform upper Lyapunov exponent for the quasilinear systems in question. (E. Litsyn), yuvn2@yandex.ru (Y. Nepomnyashchikh), arkadi@nlh.no (A. Ponosov).