Global and Semiglobal Stabilizability in Certain Cascade
Nonlinear Systems
Julio H. Braslavsky and Rick H. Middleton
Abstract
This paper addresses the issue of global and semi-global
stabilizability of an important class of nonlinear systems, namely,
a cascade of a linear, controllable system followed by an
asymptotically (even exponentially) stable nonlinear system. Such
structure may arise from the normal form of ``minimum phase''
nonlinear systems that can be rendered input-output linear by
feedback. These systems are known to be stabilizable in a local
sense, and in some cases global stabilizability results have also
been obtained. However, it is also known that when the linear
``connection'' to the nonlinear system is nonminimum phase, then
global or semi-global stabilizability may be impossible. Indeed, it
has been shown that for any given nonminimum phase linear
subsystem, there exists an asymptotically stable nonlinear
subsystem for which the cascade cannot be globally stabilized. We
expand on the understanding of this area by establishing, for a
broader class of systems, conditions under which global or
semi-global stabilization is impossible for linear and nonlinear
feedbacks.
Keywords: Nonlinear systems, Global stabilization,
Cascade systems, Nonminimum phase systems.
21 pages
16 references
125 Kb (gz-compressed)
