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Zbl 0682.93045
Sontag, Eduardo D.
Smooth stabilization implies coprime factorization. (English)
[J] IEEE Trans. Autom. Control 34, No.4, 435-443 (1989). ISSN 0018-9286

The main theorem states that if a nonlinear system $\dot x=f(x)+G(x)u$ can be made globally asymptotically stable by a smooth feedback $u=K(x)$, then there also exists a smooth feedback $u=K'(x)+v$ such that the feedback modified system is input-to-state stable. The construction of $K'(x)$ is given explicitly for feedback linearizable systems, which are trivially smoothly stabilizable. Based upon this main result it is also shown that smoothly stabilizable systems admit coprime factorizations. Finally some results about input-to-output stability are given.
[A.van der Schaft]

MSC 2000:: *93D15 Stabilization of systems by feedback
93B28 Operator-theoretic methods in systems theory
47A68 Factorization theory of linear operators
93C10 Nonlinear control systems
93D25 Input-output approaches to stability of control systems

Keywords: globally asymptotically stable; input-to-state stable; smoothly stabilizable; coprime factorizations

Cited in: Zbl 1157.93503 Zbl 0843.93060 Zbl 0704.93056

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