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A universal’ construction of Artstein’s theorem on nonlinear stabilization. (English) Zbl 0684.93063
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:
 93D15 Stabilization of systems by feedback 93D20 Asymptotic stability of control systems 93C10 Nonlinear control systems
Full Text:
##### References:
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