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Boundary control of stochastic reaction‐diffusion systems with Markovian switching
Author(s) -
Han XinXin,
Wu KaiNing,
Ding Xiaohua,
Yang Baoqing
Publication year - 2020
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.4992
Subject(s) - boundary (topology) , weighting , mathematics , parametric statistics , markov process , control theory (sociology) , diffusion , exponential stability , lyapunov function , stability (learning theory) , markov chain , control (management) , computer science , mathematical analysis , physics , nonlinear system , statistics , quantum mechanics , artificial intelligence , machine learning , acoustics , thermodynamics
Summary This article focuses on the boundary control of stochastic Markovian reaction‐diffusion systems (SMRDSs). Both the cases of completely known and partially unknown transition probabilities are taken into account. By using the Lyapunov functional method, a sufficient condition is obtained under the designed boundary controllers to guarantee the asymptotic mean square stability for SMRDSs with completely known transition probabilities. For the case of partially unknown transition probabilities, we introduce free‐connection weighting matrices to handle the boundary control problem. When external disturbance enters the system, a sufficient criterion of H‐infinity boundary control is developed. Furthermore, robust stabilization is investigated for parametric uncertain SMRDSs in both cases. Two examples are presented to demonstrate the efficiency of the proposed approaches.