Prescribed-Time Observer Design for Nonlinear Triangular Systems With Delayed Measurements

In this article, we propose a prescribed-time observer for nonlinear triangular systems with delayed outputs. The proposed observer is endowed with prescribed-time stability and relies on a scaling function and Lyapunov–Razumikhin-based conditions. We establish that the observer design derives a delay-independent stability condition in terms of linear matrix inequalities that guarantees prescribed-time convergence to zero of the estimation error. Additionally, we derive an explicit relation between the maximum bound of the delay and the prescribed-time convergence. We extend the proposed prescribed-time observer to systems with multiple nonlinearities. Finally, we provide a first illustrative example where we analyze the disturbance attenuation feature of the prescribed-time observer to vanishing measurement noise and a second application for estimating the water level in the coupled-tank systems to demonstrate the applicability and performance of the observer.