Constructing guaranteed control in quasi-linear systems

For a quasi-linear system, the problem of constructing guaranteed control keeping the phase trajectory near to a prescribed family of closed sets $W(t)$ is considered. The deviation of the phase trajectory from the family is estimated with the help of some function. Sufficient conditions that provide keeping the trajectory within the family are obtained. The case when the vectogram of control $U(t)$ and sets $W(t)$ for every $t$ are polyhedrons of a special kind is analyzed in detail. Examples are given.