  This paper proposes a Lyapunov approach to the design of a multivariable
generalized Super-Twisting algorithm (MGSTA), which is able to control a system
with perturbations and uncertain control matrix, both depending on time and the
system states. The presented procedure shows that, under reasonable assumptions
for the uncertainties, it is always possible to find a set of constant gains
for the MGSTA in order to ensure global and robust finite-time stability of the
system's outputs. Simulation results on an omnidirectional mobile robot
illustrate the performance of the MGSTA.
