Optimal feedback control stabilisation for fractional output in time-delayed distributed semilinear systems

Abstract

This work focuses on the problem of stabilising the spatial fractional Riemann-Liouville output of order $ \alpha \in [0, 1] $ α∈[0, 1], for a class of distributed semi-linear systems with time delay evolving over the domain Ω. The main objective is to identify efficient feedback control strategies to achieve strong, weak and exponential stabilisdation of the fractional output. Then, we solve a minimisation fractional problem. To illustrate the practical implications of the stabilisation theorems presented, two examples of numerical simulations are provided.