Further results on global stabilization of uncertain nonlinear systems by output feedback

Abstract

For a family of uncertain nonlinear systems dominated by a triangular system that satisfies linear growth condition with an output dependent growth rate, we prove that global robust stabilization can be achieved by smooth output feedback. This conclusion has incorporated and generalized the recent output feedback stabilization results, for instance, the work (IEEE Trans. Automat. Control 2002; 47:2068-2073) where the same conclusion was already shown to be true for planar systems, and the work (Proceedings of the 42nd IEEE, CDC, 2003; 1544-1549) where the growth rate is required to be a polynomial function of the system output. There are two key ingredients in the present contribution. One of them is the introduction of a rescaling transformation with a dynamic factor that is tuned on-line through a Riccati-like differential equation, which turns out to be extremely effective in dealing with the system uncertainty. The other one is the development of a recursive observer design algorithm making it possible to assign the robust observer gains in a step-by-step fashion. Both a smooth state feedback controller and a robust observer are explicitly constructed for the rescaled system using only the knowledge of the bounding system. Copyright © 2005 John Wiley & Sons, Ltd.