Abstract: In this paper we consider a nonlinear control design for
nonlinear systems by using two-stage formal linearization and twotype
LQ controls. The ordinary LQ control is designed on almost
linear region around the steady state point. On the other region,
another control is derived as follows. This derivation is based on
coordinate transformation twice with respect to linearization functions
which are defined by polynomials. The linearized systems can be
made up by using Taylor expansion considered up to the higher order.
To the resulting formal linear system, the LQ control theory is applied
to obtain another LQ control. Finally these two-type LQ controls
are smoothly united to form a single nonlinear control. Numerical
experiments indicate that this control show remarkable performances
for a nonlinear system.