The problem of exponential stability for time‐delay systems with flexible delayed impulse control is investigated. Unlike the conventional Razumikhin‐type inequality, variable parameter based on the flexible impulsive gain is introduced. Sufficient conditions for exponential stability are developed for a class of time‐delay systems, for which the size of delay is not limited by impulsive intervals. A flexible impulse control scheme is developed by utilizing the flexible impulsive gain and time‐varying delays. When the system is disturbed by the impulse interferences, both the impulse gain and impulse delay can be adjusted accordingly to make the system exponential stable. The effectiveness of the present results is illustrated by two numerical examples and an application.

In this paper,the FEM and MD method are used to establish macro and nano cutting model of OFHC copper,and the cutting force, cutting stress and subsurface deformation and phase change are compared and analyzed under the macro cutting depth (0.2mm, 0.3mm, 0.4mm) and nano cutting depth (0.8nm, 1.2nm, 1.6nm). Meanwhile, experiments are used to verify the simulated cutting force. The conclusions are below: The change trends of macro and nano cutting force are similar, and the ratios of the cutting forces in x and y directions at different cutting depths are similar. In addition, there are lateral chip both in the macro and nano cutting processes, showing a high degree of consistency. However, the nano cutting stress reached 25 times of that in the macro state.Then it was found that the area of unrecoverable plastic deformation on the surface increased with the increase of the cutting depth during the macro cutting process, but the existance depth of pure plastic deformation remained unchanged within 0.05mm.While in the nano cutting process, the proportion of FCC crystals converted to HCP crystals remains unchanged as the cutting depth increases,but the existance range is increasing. Finally, the amplitude and change trend of experimental and the simulated cutting force are highly consistent,which verifying the rationality of the macro simulated cutting model.