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The feedback control of automated lane-keeping of passenger cars is analyzed in this paper. The calculations are based on the single-track vehicle model with the consideration of steering system dynamics. A linear feedback controller is used to control the lateral dynamics, while taking into account feedback delay and the effects of the lower-level steering controller. Subcritical Hopf bifurcations are detected along the linear stability limits and the emerging branches of periodic orbits are followed using numerical continuation. It is shown that low amplitude unstable limit cycles exist around the stable equilibrium of straight-line motion for certain parameter ranges. Based on the limit cycle amplitudes, safe and unsafe zones of stabilizing control gains are specified. The unsafe control gain zones within the linearly stable domain are also identified under laboratory conditions using small-scale experiments on a conveyor belt. The theoretical and the practical results show good accordance with respect to the domain of attraction of the straight-line motion. • Linear and nonlinear analyses of a single-track vehicle model with linear feedback control for lane-keeping. • Subcritical Hopf bifurcations and low amplitude unstable limit cycles are detected around the stable equilibrium. • Safe and unsafe zones of stabilizing control gains are specified, based on limit cycle amplitudes. • The safe and unsafe control gain zones are also identified in a series of small-scale laboratory experiments on a conveyor belt. [ABSTRACT FROM AUTHOR]