Global high-gain-based observer and backstepping controller for generalized output-feedback canonical form

We provide results and extensions for global output feedback design for systems in the generalized output-feedback canonical form. Our investigations reveal several conceptual and structural connections between high-gain design and two recent results on the generalized output-feedback canonical form. The recognition of these links provides new insight into the stabilization mechanisms of these designs, particularly in the observer design. Furthermore, we have extended the results to include output dependent upper diagonal terms and also shown that the additional scaling proposed in a recent paper can be removed through a simultaneous stabilization result (i.e., solving a special pair of coupled matrix Lyapunov equations). We provide necessary and sufficient conditions for solvability of these coupled Lyapunov equations. The removal of the additional scaling makes the connection between the obtained results and proofs and our earlier results assuming cascading upper diagonal dominance (CUDD) more transparent. Moreover, removing the additional scaling (and possibly introducing a negative scaling) provides a better guaranteed convergence of the observer errors and allows smaller controller gains. It is shown that the high gain scaling induces the CUDD structure on the observer error dynamics. Finally, the design utilizes a reduced-order observer.