The author studies the following Lotka-Volterra type competitive system with feedback control
where represents the density of the th species at time , respectively, , and is the control variable, . , , are continuous functions defined on . Given a function defined on , let It is assumed in (1) that and .
Some average conditions for the permanence of system (1) and sufficient conditions for the global attractivity of positive solutions of system (1) are derived, respectively. The results developed by J. Zhao, J. Jiang and A. C. Lazer [Nonlinear Anal., Real World Appl. 5, 265–276 (2004; Zbl 1085.34040)] are generalized.