Asymptotic stabilization via output feedback for lower triangular systems with output dependent incremental rate

We study the global asymptotic stabilization by output feedback for systems whose dynamics are in a feedback form and where the nonlinear terms admit an incremental rate depending only on the measured output. The output feedback we consider is of the observer-controller type where, the design of the controller follows from standard robust backstepping. The novelty is in the observer which is high-gain such as with a gain coming from a Riccatti equation.