Optimal feedback stabilization of fractional output in semilinear distributed systems

Abstract

This study explores the stabilization of state–space fractional derivatives in semilinear distributed systems, using the Riemann–Liouville derivative of order α, where α lies within the interval 0,1. The main objective is to develop effective feedback control strategies that ensure both strong and weak stabilization of fractional outputs. Additionally, we tackle a fractional minimization problem to enhance the system’s performance. A numerical simulation example is provided to demonstrate the practical significance of the proposed stabilization theorems.

Keywords

• Distributed semilinear systems
• Fractional spatial derivative
• Weak stabilization
• Strong stabilization
• Feedback optimal control