Open AccessRobust H ∞ control for one‐sided Lipschitz non‐linear systems with time‐varying delays and uncertainties
Author(s) -
Huang Ling,
Lin Xiaona,
Zhong Beibei,
Xu Donghao
Publication year - 2020
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2019.1461
Subject(s) - lipschitz continuity , control theory (sociology) , mathematics , observer (physics) , linear matrix inequality , correctness , robust control , controller (irrigation) , matlab , linear system , bounded function , mathematical optimization , control system , computer science , control (management) , mathematical analysis , algorithm , engineering , artificial intelligence , electrical engineering , agronomy , physics , quantum mechanics , biology , operating system
For a class of one‐sided Lipschitz systems with time‐varying delays and parameter uncertainties, the robust control problem of the system based on state observer is elaborated in detail. By constructing Lyapunov–Krasovskii functional for closed‐loop augmented system and combining one‐sided Lipschitz condition and quadratically inner‐bounded condition, the synthesis condition of observer design is derived, which makes the closed‐loop augmented system asymptotically stable and satisfies the H ∞ performance index. Furthermore, bilinear matrix inequalities are transformed into a set of linear matrix inequalities by means of some special derivatives, which can be solved in one step. By using the mature Matlab LMI toolbox, the inequality is solved, thus the gain matrices of the controller and the observer are obtained at the same time. Finally, numerical examples are used to verify the correctness and superiority of the proposed theory.