Global and Local Piecewise Fuzzy Control: A Design for Semilinear Time-Fractional Parabolic Partial Differential Equation Systems

This article studies a global and local piecewise fuzzy control for semilinear time-fractional parabolic partial differential equation (PDE) systems. First, the Takagi‒Sugeno (T-S) fuzzy model is used to characterize a semilinear time-fractional parabolic PDE system. Then, on the basis of the T-S fuzzy model, a fuzzy controller is designed to make the resulting closed-loop semilinear time-fractional parabolic PDE system Mittag‒Leffler stable. Meanwhile, the existence condition of the stabilizing fuzzy controller is given in the form of a linear matrix inequality (LMI). Finally, the effectiveness of the proposed scheme is verified by experiment simulation.