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Discrete Dynamics in Nature and Society
Volume 2015, Article ID 658048, 5 pages
Research Article

Controlling the Stochastic Sensitivity in Nonlinear Discrete-Time Systems with Incomplete Information

Ural Federal University, Lenina, 51, Ekaterinburg 620000, Russia

Received 19 April 2015; Revised 13 September 2015; Accepted 16 September 2015

Academic Editor: Zhan Zhou

Copyright © 2015 Lev Ryashko and Irina Bashkirtseva. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For stochastic nonlinear discrete-time system with incomplete information, a problem of the stabilization of equilibrium is considered. Our approach uses a regulator which synthesizes the required stochastic sensitivity. Mathematically, this problem is reduced to the solution of some quadratic matrix equations. A description of attainability sets and algorithms for regulators design is given. The general results are applied to the suppression of unwanted large-amplitude oscillations around the equilibria of the stochastically forced Verhulst model with noisy observations.