We study the stabilization of linear nonstationary dynamical systems by introducing a linear nonstationary feedback with delay. We obtain sufficient stabilization conditions for the systems and propose a method for constructing stabilizing matrices.
Similar content being viewed by others
References
R. A. Brockett, “A stabilization problem,” In: Open Problems in Mathematical Systems and Control Theory, pp. 75–78, Springer, London (1999).
G. A. Leonov and M. M. Shumafov, Problems of Stabilization of Linear Controlled Systems, St. Petersbg. Univ. Press, St. Petersbg. (2002)
M. M. Shumafov, “Stabilization of linear control systems and pole assignment problem: a survey,” Vestn. St. Petersbg. Univ., Math. 52, No. 4, 349–367 (2019).
I. V. Boykov, “The Brockett stabilization problem,” Autom. Remote Control 66, No. 5, 746–751 (2005).
G. A. Leonov and M. M. Shumafov, Stabilization Methods for Linear Controlled Systems, St. Petersbg. Univ. Press, St. Petersbg. (2005)
G. A. Leonov, “The Brockett problem for linear discrete control systems,” Autom. Remote Control 63, No. 5, 777–781 (2002).
I. V. Boykov, Stability of Solutions to Differential Equations [in Russian], Penza State Univ. Press, Penza (2008).
K. Pyragas, “Continuous control of chaos by selfcontrolling feedback,” Phys. Lett. A 170, 421–428 (1992).
G. A. Leonov and M. M. Shumafov, “Pyragas stabilizability of unstable equilibria by nonstationary time-delayed feedback,” Autom. Remote Control 79, No. 6, 1029–1039 (2018).
G. A. Leonov, “Pyragas stabilizability via delayed feedback with periodic control gain,” Syst. Control Lett. 69, 34–37 (2014).
M. M. Shumafov, “Stabilization of the second-order linear time-invariant control systems by a delayed feedback,” Russ. Math. 54. No. 12, 76–78 (2010).
V. Lakshmikantam, S. Lila, and A. A. Martynyuk, Stability of Motion: Comparison Method [in Russian], Naukova Dumka, Kiev (1991).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Problemy Matematicheskogo Analiza 109, 2021, pp. 27-37.
Rights and permissions
About this article
Cite this article
Boykov, I.V., Krivulin, N.P. Methods for Control of Dynamical Systems with Delayed Feedback. J Math Sci 255, 561–573 (2021). https://doi.org/10.1007/s10958-021-05393-4
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-021-05393-4