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Both analog and digital control systems use lead-lag compensators.
A lead-lag compensator consists of a lead compensator cascaded with a lag compensator.
A lead-lag compensator is a component in a control system that improves an undesirable frequency response in a feedback and control system.
Lead-lag compensators influence disciplines as varied as robotics, satellite control, automobile diagnostics, laser frequency stabilization, and many more.
(A loosely related concept is that of lead-lag compensators in control theory, but this is not generally referred to specifically as a "lead-lag effect.")