Generalized adaptive output-feedback form with unknown parameters multiplying high output relative-degree states

We propose a global high-gain scaling based observer/controller for systems in the uncertain generalized output-feedback canonical form. Time-varying nonlinear parametric uncertainty is allowed to occur coupled with unmeasured states in the system dynamics. This represents a significant generalization from existing results which allow unknown parameters only in output-dependent terms. This restriction in previous results is mainly owing to the fact that no general solution is known for systems involving bilinear terms in unmeasured states. The design utilizes the dual architecture of a high-gain observer and controller with the underlying state scaling being dynamically output-dependent. The proposed observer/controller structure provides a globally asymptotically stabilizing output-feedback solution for the benchmark open problem proposed in our earlier work with the provision that a magnitude bound on the unknown parameter be given.