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Summary: This paper aims to introduce a new approach to optimize the tunable controller parameters of linear parameterizable controllers. The presented approach is frequency‐domain based and can therefore directly be used to tune, among others, proportional integral derivative controllers, low/high‐pass filters, and notch filters, using a Frequency Response Function of the plant. The approach taken in this paper is to extract the tunable controller parameters into a diagonal matrix gain and absorb the remainder of the controller in the plant. Then, the generalized Nyquist stability criterion is exploited so as to impose stability and  H ∞ performance specifications on the closed‐loop system. It is shown that the approach results in a convex feasibility problem for certain controller cases and can be reformulated such that it can also be used for grey‐box system identification. Simulation and experimental examples demonstrate the efficacy of the approach. © 2016 The Authors. International Journal of Robust and Nonlinear Control published by John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]