Robust stability and stabilization of LTI fractional-order systems with poly-topic and two-norm bounded uncertainties

Abstract

Abstract This paper investigates the problems of robust stability and stabilization of LTI fractional-order systems with poly-topic and two-norm bounded uncertainties. Firstly, some sufficient conditions of the robust asymptotical stable for such fractional-order uncertain systems are derived. Secondly, the robust stabilizing state-feedback controller is designed. All the results are obtained in terms of linear matrix inequalities (LMIs). Lastly, three numerical examples are provided to demonstrate the correctness and effectiveness of the proposed approaches.

Keywords

• LTI fractional-order system
• Poly-topic uncertainty
• Two-norm bounded uncertainty
• Robust stability
• Linear matrix inequality