About absolute stability of a class of nonlinear sampled-data systems

frequency criterion for the absolute stability of sampled-data automatic control systems with nonlinear characteristics belonging to $r,k$-sector and possesing a restricted derivative is proposed.
The proof of this criterion based on the certain generalization of the approach described in [1, 4] is easier than the proofs proposed in [5, 6] for $r=0$.
Conditions of the expediency of using the general frequency criterion instead of previously described one [1] for the case of the nonlinear element characteristic derivative without restriction are determined.