LMI-Based Robust Multivariable Super-Twisting Algorithm Design

The aim of this article is to provide a new linear matrix inequality (LMI)-based robust multivariable super-twisting algorithm design able to deal with convex bounded model uncertainties in the input matrix and exogenous disturbances with norm-bounded time derivative. The final state feedback gain is calculated from a convex programming problem, expressed by LMIs with respect to all involved variables, that optimizes a guaranteed (worst case) performance index associated to the closed-loop system. As far as the nominal system is concerned, the existence of a solution to the control design problem is given in terms of a certain closed-loop transfer function
${\mathcal H}_\infty$
norm. An example illustrates the theoretical results reported in this article.