Study on the dynamic equilibrium of control system

The steady-state of control system, dynamic equilibrium state and the singular solution of corresponding motion equation, which are three concepts produced in different domain, are considered as different appellation of the one concept in this paper. Based on this consideration, the expression of steady-state output of linear time-invariant system with analytic function input is deduced conveniently, and it is proved that the correspondingly periodical steady-state output exists for the system with the input which can be expanded as Fourier series. Moreover, the above conclusion can be naturally extended to the non-linear system.