Determine the robustness of a controller
Using classical methods (non state-space) for a SISO system, I suggest take a look on frequency response methods (bode plot), where the goal is to reach specified phase and margin gains for the open-loop transfer function (before close the loop). With the increase of the frequency, the magnitude must cross unity gain before the phase be -180 degrees. By default Matlab tuning algorithms are designed for a 60 degree phase margin. In other hand, true robust control is concerned with \$S\$ functions (sensitivity) with respect to varying parameters affecting the system. Simulation tools are helpful here (eg Sisotool).