LMI-Based Robust Multivariable Super-Twisting Algorithm Design
José C. Geromel, Eduardo V. L. Nunes, Liu Hsu
Abstract
The aim of this paper is to provide a new 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\cal H}_\infty$</tex-math></inline-formula> norm. An example illustrates the theoretical results reported in the paper.