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Observer‐based H ∞ control of a stochastic Korteweg–de Vries–Burgers equation
Author(s) -
Kang Wen,
Wang XiaoNan,
Wu KaiNing,
Li Qing,
Liu Zhijie
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.5579
Subject(s) - burgers' equation , mathematics , observer (physics) , nonlinear system , exponential stability , lyapunov function , stability (learning theory) , exponential function , computation , control theory (sociology) , differential equation , mathematical analysis , control (management) , computer science , physics , algorithm , quantum mechanics , machine learning , artificial intelligence
This article mainly deals with observer‐based H ∞ control problem for a stochastic Korteweg–de Vries–Burgers equation under point or averaged measurements. Due to the nonlinearity of the stochastic partial differential equations, special emphases are given to computation complexity. By constructing an appropriate Lyapunov functional, we derive sufficient conditions in terms of linear matrix inequalities to guarantee the internal exponential stability and H ∞ performance of the perturbed closed‐loop system by means of the Lyapunov approach. Consistent simulation results that support the proposed theoretical statements are provided. Finally, we have made important instructions for future research directions.