The Strong Stabilization of the State Fractional Derivative for Semi-Linear Systems

Abstract

The purpose of this work is to study the strong stabilization of the state fractional spatial derivative of order $q\in (0,1),$ for a class of semi-linear dynamical systems. First of all, we establish the existence and the uniqueness of the global solution for such a class of systems. Also, we develop sufficient conditions for the strong stabilization with decay estimate of the state fractional spatial derivative. Moreover, under weaker conditions, we determine an alternative feedback control that ensures the strong stabilization of the considered output. Furthermore, we investigate the fractional output stabilization by considering the minimization of a suitably chosen functional cost. Finally, we present a numerical example to illustrate the applicability of our obtained results.

Keywords:

• Decay estimate
• minimization control problem
• output feedback stabilization
• Riemann–Liouville derivative
• semi-linear systems

2010 Mathematics Subject Classification Codes:

• 93C10
• 93D15
• 26A33
• 93C20