Synthesis of nonlinear observers via structural analysis and numerical differentiation

Recent work in nonlinear observer design has sought to bring together the structural (or transformation based) approach found in [8, 5, 1, 11] and the numerical differentiation approach found in [4]. The goal is to achieve higher flexibility and wider applicability than is possible with either approach alone. In this paper, it is noted that any observable, autonomous system admitting an equilibrium point can be expressed as a state-affine system parameterized by the output and its derivatives. A class of (single-output) systems is identified that admit parameterizations with fewer than n - 1 derivatives, where n is the dimension of the state.