This paper presents a method of synthesizing controllers for excitation system of synchronous generator with saturating input that guarantees a given set of admissible initial states and the dynamic characteristics of closed-loop system. The novel design method based on extended state observer (ESO) and linear matrix inequalities (LMI) optimization shows excellent control performance, especially including disturbance rejection, local asymptotic stability of the saturating input system and Dstability. Simulation results demonstrate that the proposed control is better than conventional automatic voltage regulator (AVR) and power system stabilizer (PSS) control.Index Terms-extended state observer, feedback linearization, saturating input, linear matrix inequalities, excitation system I.