$H_{\infty }$ Sampled-Data Fuzzy Observer Design for Nonlinear Parabolic PDE Systems

Abstract

This article considers the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> sampled-data fuzzy observer (SDFO) design problem for nonlinear parabolic partial differential equation (PDE) systems under spatially local averaged measurements (SLAMs). Initially, the nonlinear PDE system is accurately represented by the Takagi-Sugeno (T-S) fuzzy PDE model. Then, based on the T-S fuzzy PDE model, an SDFO under SLAMs is constructed for the state estimation. To attenuate the effect of the exogenous disturbance and the design disturbance, an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> SDFO design under SLAMs is developed in terms of linear matrix inequalities by utilizing Lyapunov functional and inequality techniques, which can guarantee the exponential stability and satisfy an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance for the estimation error fuzzy PDE system. Finally, simulation results on the state estimation of the FitzHugh-Nagumo equation are given to support the presented H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> SDFO design method.