Lyapunov-based output-feedback adaptive stabilization of minimum phase second-order systems

We consider output feedback adaptive stabilization for second-order systems in the presence of bounded exogenous disturbances. This case is of particular interest as it has been shown that, in the presence of exogenous disturbances, direct adaptive control schemes for minimum phase plants with relative degree 1 exhibit parameter divergence eventually leading to instability. We present controllers that guarantee convergence of the measured output and boundedness of all controller parameters and signals. The controller has the form of a 7th-order dynamic compensator for the relative-degree 1 case. The proof of convergence is based on a variant of Lyapunov´s method in which the Lyapunov derivative is shown to be asymptotically nonpositive