Control of equilibrium states of normalized bilinear models

The class of so-called normalized bilinear models (NBM), which states and external influences are defined in the cube $[0,1]^n$, and admissible controls – in the cube $[-1,1]^p$, $p<n$, is considered. Assuming that controls and external influences on NBM are constant vectors, and NBM is asymptotically stable, the problem of finding controls that transfer NBM from any initial state to some equilibrium state which is close to some preassigned state is solved. The paper provides the procedures for conditions that are sufficient to solve this problem; such procedures are necessary for correct interpretation of the processes in NBM in accordance with qualitative scales $[0,1]$ and $[-1,1]$. The appendix contains an example illustrating all stages of solving the specified control problem.