Robust <i>H</i>_∞ Control of Fractional-Order Switched Systems with Order 0 < <i>α</i> < 1 and Uncertainty

Abstract

In this paper, robust H∞ control for fractional-order switched systems (FOSSs) with uncertainty is studied. Firstly, the fractional-order switching law for FOSSs is proposed. Then, H∞ control for FOSSs is proven based on the switching law and linear matrix inequalities (LMIs). Moreover, H∞ control for FOSSs with a state feedback controller is extended. Furthermore, the LMI-based condition of robust H∞ control for FOSSs with uncertainty is proven. Furthermore, the condition of robust H∞ control is proposed to design the state feedback controller. Finally, four simulation examples verified the effectiveness of the proposed methods.

Keywords

• robust H∞ control
• fractional-order switched systems
• fractional-order switching law
• linear matrix inequalities (LMIs)
• state feedback controller