The　control　method　based　on　the　equivalent-input-disturbance　(EID)　estimator　and　the　Luenberger　state　observer　has　received　much　attention　in　recent　years.　However,　the　property　of　EID-based　control　systems　is　still　not　well　investigated.　A　number　of　design　procedures　were　proposed　but　lacked　sufficient　theoretic　justification.　In　this　article,　the　two-degree-of-freedom　nature　of　an　EID-based　control　system　is　revealed.　Specifically,　the　reference-tracking　is　determined　by　an　outer　loop,　while　the　disturbance　rejection　and　robustness　is　determined　by　an　inner　loop　consisting　of　the　EID　estimator　and　state　observer.　The　bandwidth　constraints　on　the　inner　loop　are　analyzed　for　plants　having　zeros　or　poles　in　the　open　right-half　plane　by　using　the　Bode　and　the　Poisson　integral　formulas.　These　analyses　provide　a　theoretic　justification　for　conventional　design　procedures.　Further,　a　coordinated　design　algorithm　is　provided　for　the　EID-based　uncertain　control　systems.　In　addition,　a　comprehensive　comparison　of　the　EID-based　and　the　disturbance　observer　(DOB)　based　control　systems　is　conducted　in　the　system　design　aspect.　Lastly,　comparative　studies　of　the　EID-based　and　DOB-based　control　methods　are　given　for　various　types　of　plants　to　validate　the　developed　design　algorithm.