*(English)*Zbl 1012.93053

The paper addresses the problem of the global stabilization by means of continuous feedback of a class of nonlinear (possibly non-affine and nonsmooth) systems which in general cannot be stabilized by smooth (i.e., at least ${C}^{1}$) feedback. The basic result concerns systems which can be represented as a chain of power integrators perturbed by a vector field in triangular form

where the ${p}_{i}$’s are odd, the ${d}_{i}\left(t\right)$ are unknown but constrained to a bounded interval, and

(${x}_{n+1}$ stands for $u$). The functions ${a}_{ij}$ are subject to some other technical assumptions. The proof is based on an iterative procedure and exploits the theory of homogeneous systems. It uses the method of adding a power integrator in order to explicitly construct a continuous feedback and generate a ${C}^{1}$ Lyapunov function. The paper contains also some extensions of the basic result and a rich variety of interesting examples.

##### MSC:

93D15 | Stabilization of systems by feedback |

93D30 | Scalar and vector Lyapunov functions |

93C10 | Nonlinear control systems |