Trading the Stability of Finite Zeros for Global Stabilization of Nonlinear Cascade Systems

This note analyzes the stabilizability properties of nonlinear
cascades in which a nonminimum phase linear system is interconnected
through its output to a stable nonlinear system. It is shown that the instability
of the zeros of the linear system can be traded with the stability of
the nonlinear system up to a limit fixed by the growth properties of the cascade
interconnection term. Below this limit, global stabilization is achieved
by smooth static-state feedback. Beyond this limit, various examples illustrate
that controllability of the cascade may be lost, making it impossible
to achieve large regions of attractions.