On the Lyapunov indicator of discrete nestings. I

Discrete nestings are considered whose set of designs may, in particular, coincide with that of discrete control systems with vaioous nonlinear characteristics satisfying «sectoral» constraints. The concept of non-singularity of control systems is extended to discrete nestings. For non-singular nestings a norm is proved to exist in an $n$-dimensional Euclidean space, the norm decreasing for all designs of discrete nesting no faster than the exponent with a Lyapunov indicator of this nesting.