Resonance control of nonlinear dynamical systems

An efficient method for the design of nonlinear feedback control to ensure local asymptotic stability of critical dynamical systems which produces bifurcations is addressed. This procedure is a resonance control method. It is shown that the method is feasible for a very broad class of dynamical systems, including systems with nonsmooth and discontinuous nonlinearity. The method makes it possible both to find an efficient stabilizing nonlinear feedback control and to estimate the basin of attraction. The GNF (generalized normal form) gives the invariants which make it possible to shape local stability conditions in a most simple and accurate way. The GNF method has been implemented in computer software, which becomes a convenient tool for both qualitative and numerical analysis. The GNF method is applied to design a resonance stabilization feedback control for a critical nonlinear system