Trading the stability of finite zeros for global stabilization of nonlinear cascade systems

• AUTHORS: R. Sepulchre, M. Arcak, A. Teel.
• ABSTRACT: This paper 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.
• KEYWORDS: Stabilization, nonlinear cascades, peaking
• STATUS: IEEE Transactions on Automatic Control, vol.47, no.3, pp. 521-525, 2002.

• A conference version of this paper has appeared in the Proceedings of  the   4th IFAC Symposium

on Nonlinear Control Systems, Enschede, The Netherlands, pp. 624-630, July 1998.
• Final Paper: (Pdf ).