On Multivariable Super-Twisting Algorithm Reaching Time Assessment

• 成果类型: Article
• 署名作者: Geromel, J. C.; Hsu, L.; Nunes, E. V. L.
• 署名单位: Universidade Estadual de Campinas; Universidade Federal do Rio de Janeiro
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3407018
• 发表日期: 2024
• 页码: 7972-7979
• 关键词: estimation; Lyapunov methods; Symmetric matrices; Upper bound; Closed loop systems; uncertainty; Eigenvalues and eigenfunctions; Finite-time convergence; multivariable super twisting algorithm (MSTA); reaching time estimation; Robustness

摘要

This article provides an linear matrix inequality (LMI)-based procedure for reaching time estimation of the multivariable super-twisting algorithm 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.