Stable Adaptive Observers for Nonlinear Time-Varying Systems

We describe an adaptive observerlidentifier for single input-single output observable nonlinear systems that can be transformed to a certain observable canonical form. We provide sufficient conditions for stability of this observer. These conditions are in terms of the structure of the system and its canonical form, the boundedness of the parameter variations, and the sufficient richness of some signals. We motivate the scope of our canonical form and the use of our observer/ identifier by presenting applications to time-invariant bilinear systems, nonlinear systems in phase-variable form, a biotechnological process, and a robot manipulator. In each case we present he specific stability conditions.