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Improved H ∞ sampled‐data control for semilinear parabolic PDE systems
Author(s) -
Wu HuaiNing,
Wang ZiPeng,
Li HanXiong
Publication year - 2019
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.4464
Subject(s) - parabolic partial differential equation , mathematics , partial differential equation , controller (irrigation) , control theory (sociology) , set (abstract data type) , matrix (chemical analysis) , lyapunov function , control (management) , mathematical analysis , computer science , nonlinear system , physics , materials science , quantum mechanics , artificial intelligence , agronomy , composite material , biology , programming language
Summary In this paper, an H ∞ sampled‐data control problem is addressed for semilinear parabolic partial differential equation (PDE) systems. By using a time‐dependent Lyapunov functional and vector Poincare's inequality, a sampled‐data controller under spatially averaged measurements is developed to stabilize exponentially the PDE system with an H ∞ control performance. The stabilization condition is presented in terms of a set of linear matrix inequalities. Finally, simulation results on the control of the diffusion equation and the FitzHugh‐Nagumo equation are given to illustrate the effectiveness of the proposed design method.