Smooth stabilization implies coprime factorization
Sontag, E.D.
Dept. of Math., Rutgers Univ., New Brunswick, NJ ;
This paper appears in: Automatic Control, IEEE Transactions on
Publication Date: Apr 1989
Volume: 34,
Issue: 4
On page(s): 435-443
ISSN: 0018-9286
References Cited: 33
CODEN: IETAA9
INSPEC Accession Number: 3383623
Digital Object Identifier: 10.1109/9.28018
Current Version Published: 2002-08-06
Abstract
It is shown that coprime right factorizations exist for the
input-to-state mapping of a continuous-time nonlinear system provided
that the smooth feedback stabilization problem is solvable for this
system. It follows that feedback linearizable systems admit such
fabrications. In order to establish the result, a Lyapunov-theoretic
definition is proposed for bounded-input-bounded-output stability. The
notion of stability studied in the state-space nonlinear control
literature is related to a notion of stability under bounded control
perturbations analogous to those studied in operator-theoretic
approaches to systems; in particular it is proved that smooth
stabilization implies smooth input-to-state stabilization
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