Achieving Almost Feedback-Linearization via Low-Power Extended Observer

Freidovich and Khalil have shown that a nonlinear system having relative degree <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> can be controlled, by means of an extended high-gain observer, so as to recover – up to any arbitrarily fixed degree of accuracy – the performance that would have been obtained by means of the classical feedback-linearization design. This observer involves a gain parameter that grows up to power <inline-formula> <tex-math notation="LaTeX">$n+1$ </tex-math></inline-formula>. In this letter we show that the same result can be obtained by means of a controller employing an extension of the “low power” high-gain observer of Astolfi and Marconi, in which the gain parameter grows up only to power 2.