This paper is aimed to describe the regions in the controller parameter space such that the given single-input or single-output plant is stable and the H-infinity norm of a related transfer function is less than a prescribed level. The approach is focused on structurally simple controllers (PI, PID, first-order). Particularly, we consider the family of linear control systems, comprising also plant with PID controller and show that for such systems the problem can be easily tackled with the analysis of non-homogeneous quadratic forms in the parameters space.