Further results on almost disturbance decoupling with global asymptotic stability for nonlinear systems

As a complement to some new breakthroughs on global almost disturbance decoupling problems with stability for nonlinear systems, in a recent note, we identified a class of unstable zero dynamics that are allowed to be affected by disturbances. The class of unstable zero dynamics identified in that note is linear and has all the poles at the origin. In this paper, we enlarge such a class of zero dynamics to include any linear system with all its poles in the closed left-half plane. This enlargement is due to a new scaling technique that views each pair of jw axis zeros as a "generalized integrator" and transforms the zero dynamics into a number of chains of "generalized integrators.