Semi-Global Robust Stabilization for a Class of Nonlinear Systems With Uncertain Measurement Functions

Abstract

This paper considers the problem of semi-global stabilization via linear feedback for a class of uncertain nonlinear systems. Different from the existing results, the systems considered here have uncertain measurement functions due to the sensors’ property. By generalizing the notion of homogeneity with monotone degrees to the uncertain case, a measurement feedback controller is recursively constructed to semi-globally asymptotically stabilize the system by appropriately choosing a series of Lyapunov functions as well as the corresponding level sets. The proposed control scheme not only performs in a linear form for better implementation but also leads to robustness to different sensors. Finally, a numerical example is presented to demonstrate the effectiveness of the control law.

Keywords

• Linear controller
• nonlinear systems
• semi-global stabilization
• uncertain measurement functions