Algebraic observer design for a class of uniformly-observable nonlinear systems: Application to 2-link robotic manipulator

We propose a globally convergent observer for three-state nonlinear systems verifying the uniform complete observability condition. By constructing a time-varying differentiator, we are then able to reproduce the first and the second derivatives of the system output without imposing the boundedness of the states or the output. By exploiting the algebraic observability of the system, we show that the unmeasured states can be reproduced as nonlinear outputs of the time-varying differentiator. This new technique has several advantages over classical observer design methodologies that are basically related to the form of the system nonlinearities. It will be shown that the complete uniform observability implies the existence of globally convergent observer without major restriction on the system nonlinearities. Illustrative example is provided to demonstrates the efficiency of the proposed design.