State feedback H ∞ control of commensurate fractional-order systems

This article focuses on the state feedback H ∞ control problem for commensurate fractional-order systems with a prescribed H ∞ performance. For linear time-invariant fractional-order systems, a sufficient condition to guarantee stability with H ∞ performance is firstly presented. Then, by introducing a new flexible real matrix variable, the feedback gain is decoupled with complex matrix variables and further parametrised by the new flexible matrix. Moreover, iterative linear matrix inequality algorithms with initial optimisation are developed to solve the state feedback H ∞ suboptimal control problem for fractional-order systems. Finally, illustrative examples are given to show the effectiveness of the proposed approaches.

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