On Multivariable Super-Twisting Algorithm Reaching Time Assessment

This paper provides an LMI-based procedure for reaching time estimation of the multivariable supertwisting algorithm (MSTA) dealing with convex bounded parameter uncertainty and exogenous disturbances with norm-bounded time-derivative. For a class of Lyapunov functions, we are able to determine the optimal reaching time estimation that emerges from the solution of a surprisingly simple mathematical programming problem. As far as the reaching time estimation and validation are concerned the worst input disturbance, related to the considered class of Lyapunov function, is fully characterized. The impact of the theoretical results is discussed by means of illustrative examples borrowed from the literature.