<p>The large-scale inverse eigenvalue problem arising from the fractional order control system presents mathematical and computational challenges due to its expensive computational costs and nonconvex nature. Considering that a smaller feedback control force implies less energy consumption and lower noise influence in control applications of the actual system, we transform the large-scale inverse eigenvalue problem into a matrix-based nonconvex optimization problem, which transcends the limitations of the vector-based optimization problem. To solve this nonconvex optimization problem, we propose an effective probability criterion and present a matrix-based randomized gradient descent method. The proposed method operates directly on the matrix form without vectorization and only needs to update a single row of the parameter matrix per iteration in practice, which makes it more suitable for the computation of large-scale nonconvex optimization problem. Then, we prove the smoothness of the objective function and further analyze the convergence of the proposed method. Finally, numerical experiments demonstrate the validity of our approach against traditional optimization-based methods and confirm the effectiveness of our approach in solving large-scale inverse eigenvalue problem arising from the fractional order control system.</p>