Non-smooth feedback stabilizer for strict-feedback nonlinear systems not even linearizable at the origin

We present a continuous feedback stabilizer for nonlinear systems in the strict-feedback form, whose chained integrator part has the power of positive odd rational numbers. Since the power is not restricted to be larger than or equal to one, the linearization of the system at the origin may fail. Nevertheless, we show that the closed-loop system is globally strongly stable with the proposed continuous (but, possibly not differentiable) feedback. We formulate a condition that enables our design by characterizing the powers of the given system. The condition also shows that our result is an extension of (Qian and Lin, Systems and Control Letters, 2001) where the power of odd positive integers has been considered.