We consider valid mathematical transformations of mathematical models
of control systems used in traditional methods of testing stability th
at do nod affect the stability of the system. We show that these trans
formations can lead a system to another environment and, thus, be a so
urce of wrong conclusions about the stability under small variations o
f parameters. Therefore, in the long run, these transformations can ca
use sudden damage to complex systems. Computational methods that preve
nt damage are proposed.