  This paper addresses the problem of robust and optimal control for the class
of nonlinear quadratic systems subject to norm-bounded parametric uncertainties
and disturbances, and in presence of some amplitude constraints on the control
input. By using an approach based on the guaranteed cost control theory, a
technique is proposed to design a state feedback controller ensuring for the
closed-loop system: i) the local exponential stability of the zero equilibrium
point; ii) the inclusion of a given region into the domain of exponential
stability of the equilibrium point; iii) the satisfaction of a guaranteed level
of performance, in terms of boundedness of some optimality indexes. In
particular, a sufficient condition for the existence of a state feedback
controller satisfying a prescribed integral-quadratic index is provided,
followed by a sufficient condition for the existence of a state feedback
controller satisfying a given $\mathcal L_2$-gain disturbance rejection
constraint. By the proposed design procedures, the optimal control problems
dealt with here can be efficiently solved as Linear Matrix Inequality (LMI)
optimization problems.
