LMI-Based Robust Multivariable Super-Twisting Algorithm Design

• Published in: IEEE transactions on automatic control Vol. 69; no. 7; pp. 4844 - 4850
• Main Authors: Geromel, Jose C., Nunes, Eduardo Vieira Leao, Hsu, Liu
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.07.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Closed loops; Convexity; Disturbance rejection; Feedback control; finite-time convergence; Linear matrix inequalities; LMI-based design; Loop transfer functions; Lyapunov methods; multivariable super-twisting algorithm (MSTA); Optimal control; Performance indices; Robustness (mathematics); Sliding mode control; Stability criteria; State feedback; Symmetric matrices; Transient analysis; Twisting; uncertain input matrix; Uncertainty
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2024.3358235

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 <inline-formula><tex-math notation="LaTeX">{\mathcal H}_\infty</tex-math></inline-formula> norm. An example illustrates the theoretical results reported in this article.