Stabilization of coupled delayed nonlinear time fractional reaction diffusion systems using sampled-in-space sensing and actuation

Abstract

This paper is considered with the asymptotic stabilization of coupled delayed nonlinear time fractional reaction diffusion systems (FRDSs) governed by fractional parabolic partial differential equations (PDEs) with space-dependent coefficients under sampled-data in space control. It is assumed that state measurements can be averaged measurements (AMs) or point measurements (PMs), and a finite number of sensing and actuation devices are located in a spaced manner along the spatial domain of the interest. With the proposed sampled-data in space controller, the closed-loop $H^1$ stability is obtained. Tuning rules of system parameters and control parameters are derived using the fractional Halanay's inequality and the fractional Lyapunov method. Subsequently, the dual problem of observer design is formulated. Fractional examples are used to valid the theoretical result. Discussions on the extension of sampled-data boundary feedback stabilization are provided finally.