A multi-index coordinated control method based nonlinear differential algebraic model for single machine infinite bus power system with thyristor controlled braking resistor (TCBR) is proposed. By means of Hartman-Grobman theorem, differential algebraic system multi-index nonlinear control (DASMINC) design method can reassign the closed-loop system eigenvalues of linear approximate system to the nonlinear differential algebraic system via appropriately selecting output function parameter matrix. Therefore, the system can access to good control performance and strong anti-interference ability. Simulation results show that TCBR and generator excitation system controlled by this proposed method can significantly improve power system transient stability limitation and effectively coordinate the dynamic and the steady-state performances of the system.