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H ∞ Control for Continuous‐Time Mean‐Field Stochastic Systems
Author(s) -
Ma Limin,
Zhang Tianliang,
Zhang Weihai
Publication year - 2016
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1290
Subject(s) - stochastic differential equation , mathematics , bounded function , lemma (botany) , nonlinear system , control theory (sociology) , controller (irrigation) , stochastic control , mean field theory , field (mathematics) , state (computer science) , noise (video) , control (management) , mathematical analysis , computer science , pure mathematics , mathematical optimization , optimal control , physics , algorithm , ecology , poaceae , quantum mechanics , artificial intelligence , agronomy , image (mathematics) , biology
An H ∞ ‐type control is considered for mean‐field stochastic differential equations (SDEs) in this paper. A stochastic bounded real lemma (SBRL) is proved for mean‐field stochastic continuous‐time systems with state‐ and disturbance‐dependent noise. Based on SBRL, a sufficient condition is given for the existence of a stabilizing H ∞ controller in terms of coupled nonlinear matrix inequalities.