A BTOF observer backstepping-based output feedback law for nonlinear systems

We present an observer-backstepping based approach to designing an output feedback law on the basis of a BTOF (block triangular observer form) observer for multi-variable nonlinear systems. The BTOF observer is a recently developed extension to the nonlinear observer used in an established approach to demonstrate observer backstepping. We illustrate our design on a model of a physical system-the magnetically levitated ball.

I INTRODUCTION

Research on the problems of the nonlinear separation principle and non-local OFB (output feedback) for nonlinear systems has been widely pursued over the last few decades. Many seminal results including [1], [2], [3], [4], and [5] have elaborated the central issues and limitations involved in designing algorithms that are guaranteed to stabilize a nonlinear system, or have it perform tracking over more than a local region of its state space. For linear systems the separation principle ensures that any stabilizing state feedback employing exponentially convergent state estimates is guaranteed to globally exponentially stabilize the entire observer-controller-plant interconnection. However it is well known that this certainty equivalence approach is generally not effective for nonlinear systems due to the so-called peaking phenomenon [1]. That is, for some nonlinear systems even an exponentially convergent observer error may cause a finite escape time in closed loop for some initial conditions.