The stabilizing composite control in a weakly nonlinear singularly perturbed control system

We investigated an approach to a stabilizing nonlinear regulator construction in weakly nonlinear singularly perturbed control system. The control design had two stages. First of all control system was decomposed into the two linear subsystems with reduced dimensions and appropriate composite linear control was constructed. Then nonlinear correction of composite linear control was made. The proposed approach was based on a formal asymptotic expansion of the solution of the corresponding algebraic state-dependent Riccati equation (SDRE).