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Smooth Stabilization Implies Coprime Factorization (1989)
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@MISC{Sontag89smoothstabilization,
author = {Eduardo D. Sontag},
title = {Smooth Stabilization Implies Coprime Factorization},
year = {1989}
}
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Abstract
This paper shows that coprime right factorizations exist for the input to state mapping of a continuous time nonlinear system provided that the smooth feedback stabilization problem be solvable for this system. In particular, it follows that feedback linearizable systems admit such factorizations. In order to establish the result a Lyapunov-theoretic definition is proposed for "bounded input bounded output" stability. The main technical fact proved relates the notion of stabilizability studied in the state space nonlinear control literature to a notion of stability under bounded control perturbations analogous to those studied in operator theoretic approaches to systems; it states that smooth stabilization implies smooth input-to-state stabilization. 1 Introduction Constructions of coprime factorizations for nonlinear systems have been obtained of late in the literature ([10], [12], [8]). The potential significance of such fraction representations to the theory of nonlinear control ha...
Keyphrases
smooth stabilization implies coprime factorization operator theoretic approach lyapunov-theoretic definition smooth feedback stabilization problem state space nonlinear control literature fraction representation coprime factorization coprime right factorization continuous time nonlinear system input-to-state stabilization nonlinear system introduction construction main technical fact smooth stabilization implies feedback linearizable system output stability potential significance state mapping control perturbation nonlinear control ha
