Fuzzy Observer for 2-D Parabolic Equation With Output Time Delay
Wen Kang, Zhiji Han, Zhijie Liu, Bao‐Zhu Guo
Abstract
This article addresses fuzzy observer design for a nonlinear parabolic equation over an unit square domain <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\Omega$</tex-math></inline-formula> in terms of the time delayed spatially averaged measurement, where the observer is composed of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$m$</tex-math></inline-formula> -chain of subobservers. Due to 2-D domain, special emphases are made to the computational complexity. A Lyapunov argument is utilized to give constructive conditions ensuring the exponential stability of the resulting error system. The method used for the continuous-time fuzzy observer is applicable to the sampled-data implementation. Consistent simulation results that support the proposed theoretical statements are presented.