Stabilization of a class of nonlinear systems with incomplete state information

A controller design incorporating a nonlinear state reconstructor is considered for a class of unstable non-linear plants of the form &x = Ax + f(x) + Du where the state x is an n-vector, the control u is a p-vector, and A is an unstable matrix. It is assumed that f(??) is such that (1) yields a unique solution starting from any initial state x(o) and that f(x) contains only terms of second-order or greater. Measurements of the form y = Hx where H is an mxn matrix are assumed to be available as the input to the controller. The objective of the controller design is to yield an asymptotically stable closed loop system.