Robust Finite-time stability of homogeneous systems with respect to multiplicative disturbances

This paper studies the robustness properties of homogeneous finite-time stable systems with respect to multiplicative perturbation for sufficiently small inputs. Robust stability conditions are presented for the systems admitting homogeneous approximation at the origin and at infinity. The utility of the obtained results is illustrated via robustness analysis of homogeneous observer with time-varying gains.