Cybernetics and Systems Analysis

, Volume 55, Issue 2, pp 259–264 | Cite as

Methods of Linear Algebra in the Analysis of Certain Classes of Nonlinear Discretely Transformative Systems. II. Systems with Additively Selected Nonlinearity

  • V. A. StoyanEmail author


Pseudo-solutions of discretely transformative systems are generated; their linear part is complemented with nonlinearities obtained after the Cartesian transformation of input vector or iterative specification of matrix kernel of the transformer. Sets of root-mean-square approximations to inversion of mathematical model of the transformer are analyzed for accuracy and uniqueness. Quadratically nonlinear systems and systems with arbitrary order of nonlinearity are considered.


pseudo-inversion nonlinear discretely transformative systems nonlinear algebraic systems nonlinear iteratively specified systems 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    V. A. Stoyan, “Methods of linear algebra in the analysis of certain classes of nonlinear discretely transformative systems. I. Multiplicative nonlinear systems,” Cybern. Syst. Analysis, Vol. 55, No. 1, 109–116 (2019).Google Scholar
  2. 2.
    N. F. Kirichenko, “Analytical representation of perturbations of pseudoinverse matrices,” Cybern. Syst. Analysis, Vol. 33, No. 2, 230–238 (1997).MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    N. F. Kirichenko, “Pseudo inversion of matrices and their recurrence in modeling and control problems,” Problemy Upravleniya i Informatiki, No. 1, 114–127 (1995).Google Scholar
  4. 4.
    N. F. Kirichenko and V. A. Stoyan, “Analytical representation of matrix and integral linear transformations,” Cybern. Syst. Analysis, Vol. 34, No. 3, 395–408 (1998).Google Scholar
  5. 5.
    V. V. Stoyan, “Pseudoinversion approach to solving one class of nonlinear algebraic equations,” Dopov. Nac. Akad. Nauk Ukrainy, No. 3, 45–49 (2008).Google Scholar
  6. 6.
    V. A. Stoyan, “Mathematical modeling of linear, quasilinear, and nonlinear dynamic systems,” BPTs Kyivs’kyi Universytet, Kyiv (2011).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Taras Shevchenko National University of KyivKyivUkraine

Personalised recommendations