On performance improvement of an output feedback control for non-uniformly observable nonlinear systems

We enhance the recently proposed output feedback stabilization scheme by the authors. One of the major contributions of the previous work is the presentation of a constructive way to relax the uniform observability condition, which has been frequently used in order to establish nonlinear semi-global separation principle, by assuming the existence of a specific input signal (universal input) that guarantees observability. Based on this input signal, the control input alternates periodically between a stabilizing feedback and the universal input. Meanwhile, this may cause unnecessary digression of input from the stabilizing action, which in turn may leads to performance degradation when the stabilizing input in fact does not hurt observability. This paper therefore considers the reduction of the necessity of unnecessary input digression by introducing a set of universal inputs. The set is also enlarged by making it depend on the knowledge of the output and its derivatives. To incorporate this enhanced condition of observability, a new output feedback scheme is proposed and analyzed