A global high-gain based scaling method for the generalized output-feedback canonical form

We propose various new results and extensions for the global output feedback design for systems in the generalized output-feedback canonical forms. Our investigations also reveal several conceptual and structural connections between high-gain design and the recent results in Krishnamurthy et al. (2001) and Praly (2001). The recognition of these links provides new insight into the stabilization mechanisms of these designs, particularly in the design of the observer. Furthermore, we have extended the results of Praly (2001) to include output dependent upper diagonal terms and we have also shown that the additional scaling proposed in that paper can be removed through a simultaneous stabilization result (i.e., solving a special pair of coupled matrix Lyapunov equations). The removal of this scaling makes the connection between the obtained results and proofs and our earlier results assuming the cascading upper diagonal dominance (CUDD) more transparent. It is shown that the high gain result induces the CUDD structure on the observer error dynamics and global results are obtained by making the high-gain scaling dynamic. Furthermore, we have extended the design techniques to obtain reduced-order observers.