Automation and Remote Control

, Volume 79, Issue 5, pp 775–792 | Cite as

Construction of Controls Providing the Desired Output of the Linear Stationary Dynamic System

  • S. P. ZubovaEmail author
  • E. V. Raetskaya
Linear Systems


The problem of getting the given output vector-function by program control was solved for the uniform linear stationary dynamic system. Cascaded decomposition revealed the minimal amount of the components of the vector-function which suffices for solution of the formulated problem. The control and state functions were constructed. Solution of the problem without constructing the projectors and semi-inverse matrices was demonstrated by way of example.


dynamic system given output “free” elements of control cascade splitting method 


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  1. 1.
    Utkin, V.A., The Method of Separation of Movement in the Problems of Observation, Autom. Remote Control, 1990, vol. 51, no. 3, pp. 300–308.zbMATHGoogle Scholar
  2. 2.
    Zubova, S.P. and Chernyshov, K.I., On Linear Differential Equation with Fredholm Operator at the Derivaive, Differ. Uravn. Primen., Vil’nyus: Inst. Fiz. Mat. AN Litovskoi SSR, 1976, vol. 14, pp. 21–39.zbMATHGoogle Scholar
  3. 3.
    Zubova, S.P., Raetskaya, E.V., and Le Hai Trung, On Polynomial Solutions of the Linear Stationary Control System, Autom. Remote Control, 2008, vol. 69, no. 11, pp. 1852–1858.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Zubova, S.P. and Tran Thanh Tuan, Development of a Fast Decreasing Solution of the Nonuniform system in the Presence of Check Points and Conditions for Control, Autom. Remote Control, 2010, vol. 71, no. 11, pp. 2283–2290.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Zubova, S.P., On Full Controllability Criteria of a Descriptor System. The Polynomial Solution of a Control Problem with Checkpoints, Autom. Remote Control, 2011, vol. 72, no. 1, pp. 3–37.MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Raetskaya, E.V., On a Problem of Observation of Perturbed System, in Mathematical Methods and Applications, Proc. X Mathem. Readings of MGSU, Moscow, 2003, pp. 80–85.Google Scholar
  7. 7.
    Raetskaya, E.V., Conditional Controllability and Observability of Linear Systems, Cand. Sc. (Phys.- Math.) Dissertation, Voronezh: VGU, 2004.Google Scholar
  8. 8.
    Krasnova, S.A. and Utkin, V.A., Cascaded Design of State Observers of the Dynamic System, Moscow: Nauka, 2006.Google Scholar
  9. 9.
    Gantmakher, F.R., Teoriya matrits (Theory of Matrices), Moscow: Nauka, 1988. Translated into English under the title Theory of Matrices, New York: Chelsea, 1959.zbMATHGoogle Scholar
  10. 10.
    D’Angelo, G., Lineinye sistemy s peremennyni parametrami. Analiz i sisntez (Linear Systems with Variable Parameters. Analysis and Design), Moscow: Mashinostroenie, 1974.Google Scholar
  11. 11.
    Andreev, Yu.N., Upravlenie konechnomernymi lineinymi ob”ektami (Control of Finite-Dimensional Linear Plants). Moskow: Nauka, 1976.zbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Voronezh State UniversityVoronezhRussia
  2. 2.Voronezh State Forestry University n.a. G.F. MorozovVoronezhRussia

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