On Homogeneity With Respect to a Part of Variables and Accelerated Regulation

This paper addresses the problem of transforming a locally asymptotically stabilizing time-varying control law to a global one with accelerated finite/fixed-time convergence rates. The proposed approach relies on an extension of the theory of homogeneous systems to homogeneity only with respect to a part of the state variables and on the associated partial stability properties. The proposed control design uses the implicit Lyapunov function framework.