Separation results for the stabilization of nonlinear systems using different high-gain observer designs

High-gain observers have been used in the design of output feedback controllers due to their ability to robustly estimate the unmeasured states while asymptotically attenuating disturbances. The available techniques for the design of high-gain observers can be classified into three groups: pole-placement algorithms, Riccati equation-based algorithms, and Lyapunov equation-based algorithms. In [1], we presented separation results for globally bounded stabilizing state feedback controllers when the high-gain observer is designed using pole-placement so as to create a closed-loop system with two-time-scale structure. In this paper, we show that the separation results of [1] hold for the other observer designs.