Exponential stabilization of nonlinear parabolic PDE systems via sampled-data fuzzy control approach

Abstract

This paper investigates the exponential stabilization problem of nonlinear parabolic partial differential equation (PDE) systems via sampled-data fuzzy control approach. Initially, the nonlinear PDE system is accurately represented by the Takagi-Sugeno (T-S) fuzzy PDE model. Then, based on the fuzzy PDE model, a novel time-dependent Lyapunov functional is used to design a sampled-data fuzzy controller such that the closed-loop fuzzy PDE system is exponentially stable with a given decay rate. The stabilization condition is presented in terms of a set of linear matrix inequalities (LMIs). Finally, simulation results on the temperature profile of a catalytic rod show that the proposed design method is effective.