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In the paper, H∞ and robust H∞ control for fractional order systems (FOS) with order 0&lt;α&lt;1 are studied. Firstly, necessary and sufficient conditions of H∞ control and state feedback controller design are proposed. Then, robust H∞ control for FOS with uncertainty is studied, and state feedback controller is designed. These conditions are based on linear matrix inequalities (LMI) and can be easily solved by the LMI toolbox. Finally, the effectiveness of these conditions is verified by two numerical examples.

Robust H∞ Control for Fractional Order Systems with Order α (0 < α < 1)