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Stabilization of Nonlinear Systems in the Plane

By Matthias Kawski

Abstract

. It is shown that every small-time locally controllable system in the plane can (locally) be asymptotically stabilized by employing locally H\u7folder continuous feedback laws, as essentially was conjectured by E. Sontag. An explicit algorithm for the construction of such feedback laws is given. Keywords: Stabilization, controllability, nonlinear control, H\u7folder continuous feedback, Lyapunov function. 1 Introduction This paper presents some recent advances in the design of nonlinear state-feedback stabilization schemes. For the clarity of the underlying arguments we restrict our considerations to single-input systems in the plane of the form _ x = f(x) + ug(x) f(0) = 0; g(0) 6= 0 (1) with f and g smooth (real analytic) vector elds on R 2 and the control an integrable function with values in R. While over the past few years a tremendous progress has been made towards the understanding of (small-time) local controllability (STLC) of such systems on general n- dimensional space (e...

Year: 1989
OAI identifier: oai:CiteSeerX.psu:10.1.1.41.4339
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