Abstract: The absolute stability of 4th order direct control system  （ｄｘ）/（ｄｔ）＝Ａｘ＋ｂｆ（σ），σ＝ＣＴＸ is discussed by means of Popov frequency method.The main results are:（Aｉｊ）４×４ when if Ｒｅ λ（A）＜０，ｃＴ（A－１）２ｂ≤０，ｃＴ（A４－ｔｒ A２·A２）ｂ－１/２ｔｒ（A４－ｔｒ A２·A２）ｃＴｂ≤０，ｃＴｂ·ｔｒ A２－ｃＴA２ｂ≤０，the necessary and sufficient conditions for the absolute stability of the system is that ｃＴｂ≤０，ｃＴA－１ｂ≥０.

Key words: direct control system, absolute stability, necessary and sufficient conditions