On the algebraization of nonlinear control

Abstract

An algebraic theory on the stabilization of discrete- and continuous-time nonlinear systems by static state feedback is presented. In both cases, it is shown that the existence of stabilizing feedback controllers can be completely characterized through certain algebraic properties of the functions determining the state representation of the system. The theory includes necessary and sufficient conditions for the existence of stabilizing feedback functions, as well as methods for their computation. An inherent resemblance between the discrete-time and the continuous-time cases is elucidated.<>