Reliable exponential stabilisation for fractional-order semilinear parabolic distributed parameter systems: an LMI approach.

This paper investigates the problem of exponential stabilisation for fractional-order semilinear parabolic distributed parameter systems with actuator faults, and a reliable state feedback controller is proposed. First, the considered nonlinear fractional-order distributed parameter systems are reconstructed by Takagi-Sugeno (T-S) fuzzy partial differential equation (PDE) model, where a finite number of actuators are active only at some specified points of the spatial domain. Then, based on the obtained fractional-order T-S fuzzy PDE model, a fractional-order Lyapunov technique is used to analyse the closed-loop exponential stability. By using the vector-valued Wirtinger's inequality, a reliable state feedback controller that can guarantee locally exponential stabilisation of the fractional-order semilinear PDE systems is presented in terms of linear matrix inequalities. Finally, a numerical simulation is provided to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]