Feedback control of nonlinear systems by extended linearization

For single-input, multiple-output, nonlinear systems, we consider a design method based on the family of linearizations of the system, parameterized by constant operating points. Nonlinear state feedback control laws and observer/state feedback control laws are designed such that the eigenvalues of the family of linearized closed-loop systems are placed at specified values that are locally invariant with respect to the closed-loop operating point. The method is illustrated by application to the problem of automatically balancing an inverted pendulum.