On the Properties of the Solvability Set for a Linear Systemwith Uncertainty

The work is devoted to the problem of verifying the fact that the state of a linear controlled system of differential equations hits the target set over a finite time interval despite the uncertainty (noise). Some geometric, pointwise convex constraints on uncertainties are imposed. In the case of a two-dimensional state space a method is proposed for constructing the solvability set without the calculation of the convex hulls of the functions necessary to construct a support function of the geometric difference of the sets. A Hamilton–Jacobi–Bellman type equation is obtained that is satisfied by the distance function to the solvability set.