Summary: This paper proposes a plant/controller design integration method for \({\mathcal H}_\infty\) loop-shaping design based on symbolic-numeric hybrid optimization. This approach firstly employs parametric polynoinial spectral factorization to accomplish parametric optimization and derive an expression for the optimal cost. Owing to the obtained expression, sensitivity analysis of the achievable performance level with respect to plant parameters is amenable, which allows numerical optimization methods to seek the optimal set of parameter values.