Observer-based control of uncertain systems with non-linear uncertainties

Abstract

Global asymptotic stabilization of nominally linear uncertain systems is considered where uncertain elements in the plant are modelled as cone bounded non-linearities. At first, a linear time-invariant state feedback law ensuring global asymptotic closed-loop stability is obtained. The algorithm which calculates such a feedback law is simple and straightforward. It does not involve repeated solutions of a parameter-dependent algebraic Riccati or any such non-linear equations. Any state feedback law thus developed can then be implemented via an observer specially designed to preserve the global asymptotic stability of the closed-loop system.