The Carlina hypertelescope is a planned sparse aperture 100 m telescope with pupil densification. The telescope has a spherical primary with segments located in a valley between mountains, and additional optical elements in a gondola suspended in eight cables some 100 m above the primary mirror. The resolution is about 1.2×10-3 arcsec. It is imperative that the position and attitude of the gondola be maintained within tight tolerances during observation and star tracking. The present design has servo-controlled winches on the ground for control of the gondola via the cables. An integrated model of the system, including optics, cables, gondola, position and attitude control system, and wind disturbances has been set up. The structural and control models are linear. Calculations in the frequency domain and simulations in the time domain show that the performance of the telescope with the present design seems adequate for short exposures. However, for long-exposure operation, the gondola stability should be improved by about two orders of magnitude. Recommendations are given on possible approaches for performance improvement.