Smooth output feedback stabilization of planar systems without controllable/observable linearization

This note considers the problem of global stabilization by output feedback for a family of planar systems whose Jacobian linearization is neither controllable nor observable. The problem cannot be dealt with by existing output feedback design methods-most of them are based on the separation principle. Under appropriate growth conditions, we propose an output feedback control scheme that does not rely on the separation principle and achieves global asymptotic stabilization. The novelty of our control scheme lies in the explicit design of a dynamic output compensator, which combines a nonlinear-gain observer design and the technique of adding a power integrator. As a consequence, an interesting global stabilization result by output feedback can be obtained for feedback linearizable systems in a triangular form, which turns out to be new even in the two-dimensional case.