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Output‐feedback Lyapunov redesign of uncertain systems with delayed measurements
Author(s) -
Xu Jing,
Fridman Leonid M.,
Fridman Emilia,
Niu Yugang
Publication year - 2021
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.5464
Subject(s) - control theory (sociology) , differentiator , lyapunov function , observer (physics) , estimator , trajectory , mathematics , lyapunov redesign , lyapunov equation , computer science , nonlinear system , control (management) , filter (signal processing) , physics , quantum mechanics , artificial intelligence , statistics , astronomy , computer vision
This paper presents an output‐feedback Lyapunov redesign for uncertain systems with the delayed measurements, which recasts the state estimation and robust control into a unified framework. Instead of the traditional observer/differentiator‐based output‐feedback design, a static state estimator is constructed by the Taylor expansion of delayed measurements with the integral remainders. Then, a sliding variable is constructed according to the nominal Lyapunov function. A Lyapunov redesign approach is used to keep the system trajectory in predefined vicinity of origin, even subject to approximation errors and exogenous disturbances. The maximum value of the allowable delays for the closed‐loop stability is found via linear matrix inequalities. Finally, the effectiveness of the proposed method is verified in the magnetic suspension system.