A Separation Principle for a Class of Non−Uniformly Completely Observable System

This paper introduces a new approach to output feedback stabilization of SISO systems which, unlike other techniques found in the literature, does not use quasi-linear high-gain observers and control input saturation to achieve separation between the state feedback and observer designs. Rather, we show that by using nonlinear high-gain observers working in state coordinates, together with a dynamic projection algorithm, the same kind of separation principle is achieved for a larger class of systems which are not uniformly completely observable. By working in state coordinates, this approach avoids using knowledge of the inverse of the observability mapping to estimate the state of the plant, which is otherwise needed when using high-gain observers to estimate the output time derivatives