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GLOBAL CLF STABILIZATION OF SYSTEMS WITH POINT-DISSIPATIVE FREE DYNAMICS VIA ADMISSIBLE CONTROLS: CHAOS CONTROL OF A CHUA'S SYSTEM

JULIO SOLÍS-DAUN

Departamento de Matemáticas, Universidad Autónoma Metropolitana–Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, Del. Iztapalapa, México, D.F., Apdo. Postal 55-534, C.P. 09340, México

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https://doi.org/10.1142/S0218127413501769Cited by:7 (Source: Crossref)

Abstract

The aim of this paper is to address the global asymptotic stabilization (GAS) of the class of affine control systems which are open-loop point-dissipatives (have compact global attractors), that include some chaotic systems (e.g. Lorenz, Chen, smooth Chua), via admissible (bounded and regular) feedback controls. The existence of the global attractor for the free dynamics, whose overestimation is achieved by a Lyapunov function V(x), allows us to use V(x) as a basis to obtain a control Lyapunov function (CLF) in order to apply our control design method (entailed from Artstein and Sontag's CLF-stabilization approach) developed for the GAS of affine control systems via admissible feedback controls. We illustrate the results with the chaos control of a smooth (cubic) Chua's system via admissible feedback controls.

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