Funnel-Precompensated Disturbance Observer for Uncertain Minimum-Phase SISO Linear Systems of Arbitrary Relative Degree

Disturbance observers (DOBs) recover nominal behavior, but fast filters risk peaking. We propose a funnel-precompensated DOB for uncertain minimum-phase single-input single-output linear systems of known relative degree. A stable-factor residual yields a minimum-phase channel. At relative degree two, gain conditions require positive plant high-frequency gains and one positive common design gain; for higher degrees, the common-design result also uses a plant-gain interval and mismatch condition. Global boundedness, practical nominal-output recovery, and open-funnel initialization are established.