Global Output-Feedback Adaptive Stabilization for Planar Nonlinear Systems with Unknown Growth Rate and Output Function

This paper studies the problem of global output-feedback stabilization by adaptive method for a class of planar nonlinear systems with unmeasurable state dependent growth and unknown output function. It is worth emphasizing that not only the growth rate, but also the upper and lower bounds of the derivative of output function are not required to be known in the paper. To solve the problem, we propose a new adaptive output-feedback control scheme based on only one dynamic high-gain, by skillfully constructing the new Lyapunov function, and flexibly using the ideas of universal control and backstepping. It is shown that the state of the closed-loop system is bounded while global asymptotic stability can be achieved. Two examples including a practical example are given to demonstrate the effectiveness of the theoretical results.