Fraction representations, non-additive state feedback, and nonlinear control

Two broad issues in the theory of nonlinear control are discussed, namely, nonlinear static state feedback and the construction of coprime fraction representations. First, a theory of static state feedback, valid for a wide class of nonlinear systems, is developed. The theory yields explicit formulas for the computation of static state feedback functions that internally stabilized a nonlinear system. Next, it is shown that these stabilizing state feedback functions can be used to construct right coprime fraction representations for nonlinear systems, even in cases where the output of the system is not the state. The resulting coprime fraction representations have a particularly simple factorization space