The kernel of nonlinear system analysis is the solving of system state equation. Therefore, for a general
nonlinear control system, the concept of general time-state space comprising of state variables, control variable, and time
?? is introduced. In order to solve the state equation of nonlinear control systems, at the operation point (????, ??(??), ??(??)) of
general time-state space, the right side of the state equation can be expanded as Taylor series about (?? − ????). Then the series
solution of the nonlinear control state equation, for which the solution is expression in (?? − ????) series, can be obtained by
using direct-integrating approach. Finally, the convergence of the solution is proved.