A dual high gain controller for the uncertain generalized output-feedback canonical form with appended dynamics driven by all states

In this paper, we propose a global high gain scaling based observer/controller for nonlinear systems with appended input-to-state stable (ISS) dynamics which are allowed to have finite nonlinear gains from all system states. This represents a significant generalization from existing results which require the appended dynamics to be ISS with respect to the output i.e., require the gains from other states to be zero. The restriction on the appended ISS dynamics imposed in previous results is due to the form of the Lyapunov functions generated in the backstepping design utilized which prevents gains from states of appended dynamics to system states other than the output to be effectively assigned. The proposed 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. Furthermore, time varying nonlinear parametric uncertainty is allowed to occur coupled with unmeasured states in the system dynamics.