State estimation and output feedback stabilization of a class of upper-triangular systems using a homogeneous observer

This paper considers the problem of state estimation and output feedback control of a class of upper-triangular systems with unmeasurable states. Due to the presence of the high-order nonlinearities, most of the existing state estimation methods can only yield local results. In this paper, we will show that the newly developed homogeneous observers can be used to estimate the states of some nonlinear systems in larger regions than a small neighborhood of the origin. When the initial error is small, we can design an asymptotically convergent high-order observer for the upper-triangular system. The observer is also combined with the output feedback controller and Least Square Estimation method to stabilize the upper-triangular systems.