On preservation of the quadratic Lyapunov function of a linear discrete system Under stationary perturbations of the system coefficients

For a discrete system described by a linear pointwise mapping, sufficient conditions on the smallness of perturbations of the system coefficients are obtained, under which the quadratic Lyapunov function constructed for the original system will be a Lyapunov function for the perturbed system as well. The fact of negativity of the first difference in the power of the system is determined by the fact of negativity of the roots of the auxiliary polynomial, whose coefficients depend on the coefficients of the system. Sufficient conditions for preserving the fact of negativity of the roots of the constructed polynomial at finite perturbations of the system coefficients are obtained. One of the methods for determining the coefficients of the quadratic Lyapunov function possessing the given properties is examined: a Lyapunov function satisfying the restriction on the value of its first difference and convenient for use in evaluating the quantitative characteristics of the system.