Active vibration control for fractional order systems based on multiple region eigenvalue assignment

This work addresses active vibration control for fractional-order systems based on a multiple region eigenvalue assignment. First, we propose the selection criteria of fractional-order multiple stability regions and define multiple stability regions by generalized linear matrix inequality. Based on the inverse eigenvalue problem theory, we give the sufficient condition for solving the feedback control matrix under multiple region eigenvalue assignment and present the expression of the feedback control matrix. Then, we propose a numerical algorithm for solving this problem, which improves the control performance. Finally, we verify the feasibility and effectiveness of the proposed method through numerical examples of fractional-order simulation and actual physical systems.