Boundary state feedback control for semilinear fractional-order reaction diffusion systems

Abstract

This paper investigates the stabilization results for a semilinear time fractional-order reaction diffusion partial differential equations using backstepping method. The parabolic system is addressed with time fractional-order of (0, 1) in the Caputo sense. More general type of actuation setup which can be expressed as Dirichlet, Neumann and Robin type boundary actuation's is considered. The main aim is to achieve the stabilization of the considered system using an invertible transformation through the stability of target system which is verified by Mittag-Leffler stability based on (Q, S, R) dissipativity theory and linear matrix inequality (LMI) technique. The explicit solutions of kernel functions are found by method of successive approximation and to be design the boundary control law for the closed loop system. Finally, the proposed results are validated through numerical examples.