GLOBAL AND SEMIGLOBAL STABILIZABILITY IN CERTAIN CASCADE NONLINEAR-SYSTEMS

This paper addresses the issue of global and semi-global stabilizabili ty of an important class of nonlinear systems, namely, a cascade of a linear, controllable system followed by an asymptotically (even expone ntially) stable nonlinear system, Such structure may arise from the no rmal form of ''minimum phase'' nonlinear systems that can be rendered input-output linear by feedback. These systems are known to be stabili zable in a local sense, and, in some cases, global stabilizability res ults have also been obtained, It is also known, however, that when the linear ''connection'' to the nonlinear system is nonminimum phase, i. e., it has zeros with positive real part, then global or semi-global s tabilizability may be impossible. Indeed, it has been shown that for a ny given nonminimum phase linear subsystem, there exists an asymptotic ally stable nonlinear subsystem for which the cascade cannot be global ly stabilized. We expand on the understanding of this area by establis hing, for a broader class of systems, conditions under which global or semiglobal stabilization is impossible for linear and nonlinear feedb acks.