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Zbl 0684.93063
Sontag, Eduardo D.
A `universal' construction of Artstein's theorem on nonlinear stabilization. (English)
[J] Syst. Control Lett. 13, No.2, 117-123 (1989). ISSN 0167-6911

Summary: This note presents an explicit proof of the theorem - due to {\it Z. {\it Artstein}} [Nonlinear Anal., Theory Methods Appl. 7, 1163-1173 (1983; Zbl 0525.93053)] - which states that the existence of a smooth control- Lyapunov function implies smooth stabilizability. Moreover, the result is extended to the real-analytic and rational cases as well. The proof uses a `universal' formula given by an algebraic function of Lie derivatives; this formula originates in the solution of a simple Riccati equation.

MSC 2000:: *93D15 Stabilization of systems by feedback
93D20 Asymptotic stability of control systems
93C10 Nonlinear control systems

Keywords: Artstein; smooth control-Lyapunov function; smooth stabilizability

Citations: Zbl 0525.93053

Cited in: Zbl 0723.93053 Zbl 0704.93056

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