The choice of a Lyapunov function class for close approximation of the set of linear stabilization

Linear control systems closed by saturated linear feedback are widely known in control theory. When studying the region of attraction of such a system the problem arises of estimating some positive invariant its subset within which the closed-loop system does not encounter control constraints. The problem under consideration is characteristic for a Lyapunov function approach, it consists in choosing the class of Lyapunov functions providing the complete solution for the problem of approximating this subset.