Finite-time fuzzy stabilization for parabolic DPSs via Round-Robin scheduling protocol

In this paper, the problem of finite-time stabilization for a class of nonlinear parabolic distributed parameter systems (DPSs) is addressed, in which a Round-Robin scheduling controller is proposed to input feedback signal. In order to easily design controller, a finite element technique based on Galerkin’s method is applied to DPSs, the approximate finite-dimensional nonlinear systems are obtained. To control the nonlinear DPSs, a Takagi-Sugeno (T-S) fuzzy controller is given based on the finite-dimensional systems. Then, a fuzzy scheduling controller is designed to address the finite-time stability problem under an optimal <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>∞</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> performance level. Finally, a classical chemical model subjected to the Fisher equation is given to show the effectiveness of the proposed control method.