Achieving Almost Feedback-Linearization via Low-Power Extended Observer

Freidovich and Khalil have shown that a nonlinear system having relative degree $n$ 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 $n+1$. 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.