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Finite spectrum assignment problem for linear neutral-type systems in the class of differential-difference output-feedback controllers

https://doi.org/10.67268/1812-5093-2026-34-1s-155-166

EDN: JHUQCK

Abstract

We investigate the finite spectrum assignment problem for linear autonomous neutral-type systems using output-feedback controllers with lumped delays. We establish a connection between the solvability of this problem in the class of state feedback controllers and in the class of output feedback controllers. Finally, we consider an observer-based controller and validate the separation principle within the framework of the finite spectrum assignment problem.

About the Authors

V. E. Khartovskii
Yanka Kupala State University of Grodno
Belarus

Grodno



O. M. Kiturko
Yanka Kupala State University of Grodno
Belarus

Grodno



References

1. Wonham W. M. Linear Multivariable Control. New York, Springer, 1974. https://doi.org/10.1007/978-3-662-22673-5

2. Marchenko V. M. Control of systems with aftereffect in scales of linear controllers with respect to the type of feedback. Differential Equations, 2011, vol. 47, no. 7, pp. 1014–1028. https://doi.org/10.1134/s0012266111070111

3. Marchenko V. M., Yakimenko A. A. Modal control of multi-input systems of neutral type with retarded argument. Differential Equations, 2008, vol. 44, no. 11, pp. 1595–1604. https://doi.org/10.1134/S0012266108110116

4. Metel’skii A. V., Khartovskii V. E. Criteria for modal controllability of linear systems of neutral type. Differential Equations, 2016, vol. 52, no. 11, pp. 1506–1521 (in Russian). https://doi.org/10.1134/S0012266116110070

5. Khartovskii V. E. Modal controllability of linear systems of neutral type in classes of difference-differential controllers. Automation and Remote Control, 2017, no. 11, pp. 3–19 (in Russian). https://doi.org/10.1134/S0005117917110017

6. Metel’skii A. V. Modal controllability of a differential system with delay with respect to incomplete output. Differential Equations, 2018, vol. 54, no. 11, pp. 1508–1517 (in Russian). https://doi.org/10.1134/S0012266118110095

7. Manitius A. Z., Olbrot A. W. Finite spectrum assignment problem for systems with delays. IEEE Transactions on Automatic Control, 1979, vol. 24, no. 4, pp. 541–552. https://doi.org/10.1109/TAC.1979.1102124

8. Watanabe K. Finite spectrum assignment and observer for multivariable systems with commensurate delays. IEEE Trans. Autom. Control, 1986, vol. AC-31, no. 6, pp. 543–550. https://doi.org/10.1109/TAC.1986.1104336

9. Wang Q. G., Lee T. H., Tan K. K. Finite Spectrum Assignment Controllers for Time Delay Systems. London, Springer, 1995.

10. Bhat K., Koivo H. Model characterizations of controllability and observability in time delay systems. IEEE Trans. Automatic Control, 1976, vol. 21, no. 2, pp. 292–293.

11. Pandolfi L. Stabilization of neutral functional differential equations. J. Optim. Theory Appl., 1976, vol. 20, no. 2, pp. 191–204. https://doi.org/10.1007/BF01767451

12. Hao Z., Hu G.-D., Li H. Controller based on spectral decomposition for neutral delay systems. Acta Automat. Sinica, 2010, vol. 36, no. 4, pp. 615–619.

13. Khartovskii V. E. Finite stabilization and finite spectrum assignment by a single controller with incomplete measurements for linear systems of neutral type. Differential Equations, 2024, vol. 60, no. 5, pp. 686–706 (in Russian). https://doi.org/10.1134/S0012266124050093

14. Khartovskii V. E. Control of Linear Systems of Neutral Type: Qualitative Analysis and Implementation of Feedback. Grodno, GrSU, 2022. 500 p. (in Russian).

15. Mirkin L. On the approximation of distributed-delay control laws. Systems & Control Letters, 2004, vol. 51, no. 5, pp. 331–342. https://doi.org/10.1016/j.sysconle.2003.09.010

16. Mondie´ S., Michiels W. Finite spectrum assignment of unstable time-delay systems with a safe implementation. IEEE Transactions on Automatic Control, 2003, vol. 48, no. 12, pp. 2207–2212. https://doi.org/10.1109/TAC.2003.820147

17. Lu H., Di Loreto M., Eberard D., Simon J. P. Approximation of distributed delays. Systems & Control Letters, 2014, vol. 66, pp. 16–21. https://doi.org/10.1016/j.sysconle.2014.01.001

18. Khartovskii V. E. Finite stabilization based on incomplete measurements for not fully controllable systems of neutral type. Differential Equations, 2025, vol. 61, no. 10, pp. 1624–1647. https://doi.org/10.1134/S0012266125100118

19. Hu G.-D. An observer-based stabilizing controller for linear neutral delay systems. Siberian Mathematical Journal, 2022, vol. 63, no. 4, pp. 789–800. https://doi.org/10.1134/S003744662204019X


Review

For citations:


Khartovskii V.E., Kiturko O.M. Finite spectrum assignment problem for linear neutral-type systems in the class of differential-difference output-feedback controllers. Proceedings of the Institute of Mathematics of the NAS of Belarus. 2026;34(1s):155-166. (In Russ.) https://doi.org/10.67268/1812-5093-2026-34-1s-155-166. EDN: JHUQCK

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ISSN 1812-5093 (Print)