Nonlinear observers and output tracking control of nonlinear systems via output feedback

A state observer and an output feedback tracking controller for single-input/single-output (SISO) nonlinear systems are presented. The main contribution of this paper is to establish the following three new results: 1) if a nonlinear system satisfies the generalized observability rank condition, then there exists a local state observer for the given nonlinear system; 2) if a nonlinear system has exponentially stable zero dynamics and if there exists a state observer for the given nonlinear system, then there exists an output feedback stabilizing controller; and 3) if a nonlinear system satisfies the generalized observability rank condition and its associated zero dynamics are exponentially stable, then an explicit output feedback control law is presented, which guarantees the tracking error to be less than the prescribed bound ε and the whole state remains bounded