Separation Results for the Observer-based Stabilization with a Dead-zone High-gain Injection

This article proposes and analyzes the output feed-back stabilization with the separation principle, considering the impact of measurement noise on high-gain observers. To address this issue, a dead-zone injection is introduced into the design, enhancing the performance of the high-gain ob-server in the presence of measurement noise. Based on this observer, a corresponding output feedback control strategy is proposed. This control approach can recover the steady-state performance achieved by state feedback under ideal conditions and ensure bounded convergence of system states in the presence of disturbances and noise. Furthermore, when state feedback guarantees globally consistent asymptotic stability under ideal conditions, our proposed output feedback approach achieves practical convergence with the presence of disturbances and noise, and the effectiveness of our design is illustrated through a numerical example with both of two situations.