Global adaptive observers and output-feedback stabilization for a class of nonlinear systems

Abstract

We address the problem of determining global adaptive observers for a class of single-output nonlinear systems which are linear with respect to an unknown constant parameter vector. Sufficient conditions are given for the construction of a global adaptive observer of an equivalent state, without persistency of excitation. Under additional geometric conditions the original (physical) state can be asymptotically observed as well. The results obtained are based on nonlinear changes of coordinates driven by auxiliary filters (filtered transformations). When only a single in put is allowed and it is assumed to enter linearly in the state equations, we determine via geometric conditions a more restricted class of nonlinear single-input, single-output systems which can be globally stabilized by a dynamic (adaptive) observer-based output feedback control. Linear minimum-phase systems with unknown poles and zeroes, known sign of the high-frequency gain and known relative degree belong to such a class of systems. Systems which are not feedback linearizable may belong to such a class as well.