- Код статьи
- S30345030S0374064125080085-1
- DOI
- 10.7868/S3034503025080085
- Тип публикации
- Статья
- Статус публикации
- Опубликовано
- Авторы
- Том/ Выпуск
- Том 61 / Номер выпуска 8
- Страницы
- 1094-1116
- Аннотация
- Рассмотрены нестационарные линейные и нелинейные дескрипторные системы наблюдения с дискретным временем. В линейном случае получены критерии наблюдаемости на конечном горизонте, а также найдены условия робастной наблюдаемости. Доказаны теоремы двойственности, связывающие свойства управляемости и наблюдаемости. Для нелинейных систем с использованием линейного приближения получены условия локальной наблюдаемости на конечном горизонте.
- Ключевые слова
- дискретная дескрипторная система нестационарная система нелинейная система наблюдаемость двойственность
- Дата публикации
- 07.12.2025
- Год выхода
- 2025
- Всего подписок
- 0
- Всего просмотров
- 45
Библиография
- 1. Luenberger, D., Dynamic equations in descriptor form, IEEE Trans. Automat. Control, 1977, vol. 22, no. 3, pp. 312–321.
- 2. Mills, J.K. and Goldenberg, A.A., Force and position control of manipulators during constrained motion task, IEEE Trans. Robot. Automat., 1989, vol. 5, pp. 30–46.
- 3. Bauer, I., Bock, H.G., Leineweber, D.B., and Schl¨oder, J.P., Direct Multiple Shooting Methods for Control and Optimization of DAE in Chemical Engineering. Scientific Computing in Chemical Engineering. II, Springer, 1999.
- 4. Rabier, P.J. and Rheinbolt, W.C., Nonholonomic Motion of Rigid Mechanical Systems from a DAE Viewpoint, SIAM, 2000.
- 5. Scott, B., Power system dynamic response calculations, Proc. IEEE, 1979, vol. 67, pp. 219–247.
- 6. Riaza, R., Differential-Algebraic Systems: Analytical Aspects and Circuit Applications, World Scientific, 2008.
- 7. Br¨ull, T., Explicit solutions of regular linear descriptor systems with constant coefficients, Electronic J. of Linear Algebra, 2009, vol. 18, no. 1, pp. 317–338.
- 8. Hemami, H. and Wyman, B.F., Modeling and control of constrained dynamic systems with application to biped locomotion in the frontal plane, IEEE Trans. Automat. Control, 1979, vol. 24, pp. 526–535.
- 9. Chen, T. and Francis, B.A., Input-output stability of sampled-data systems, IEEE Trans. Automat. Control, 1991, vol. 36, no. 1, pp. 50–58.
- 10. Stevens, B.L. and Lewis, F.L., Aircraft Modelling, Dynamics and Control, New York: John Wiley & Sons, 1991.
- 11. Verghese, G., L´evy, B., and Kailath, T., A generalized state-space for singular systems, IEEE Trans. Automat. Control, 1981, vol. 4, pp. 811–831.
- 12. Bender, D., Lyapunov-like equations and reachability-observability Gramians for descriptor systems, IEEE Trans. Automat. Control, 1987, vol. 32, no. 4, pp. 343–348.
- 13. Lewis, F. and Mertzios, B., On the analysis of discrete linear time-invariant singular systems, IEEE Trans. Automat. Control, 1990, vol. 35, no. 4, pp. 506–511.
- 14. Dai, L., Singular Control System, New York: Springer-Verlag, 1989.
- 15. Dai, L., Observer for discrete singular systems, IEEE Trans. Automat. Control, 1988, vol. 33, pp. 187–191.
- 16. Coll, C., Fullana, M.J., and S´anchez, E., Some invariants of discrete-time descriptor systems, Appl. Math. Comput., 2002, vol. 127, no. 2, 3, pp. 277–287.
- 17. Moysis, L., Karampetakis, N., and Antoniou, E.N., Observability of linear discrete-time systems of algebraic and difference equations, Int. J. Control, 2017, vol. 92, no. 2, pp. 1–25.
- 18. Karampetakis, N. and Vologiannidis, S., On the fundamental matrix of the inverse of a polynomial matrix and applications to ARMA representations, Linear Algebra Appl., 2009, vol. 431, no. 11, pp. 2261–2276.
- 19. Kaczorek, T., Positive 1D and 2D Systems, London: Springer, 2002.
- 20. Dassios, I. and Kalogeropoulos, G., On a non-homogeneous signal linear discrete-time system with a singular matrix pencil, Circuits Syst. Signal Process, 2013, vol. 32, no. 4, pp. 1615–1635.
- 21. Koumboulis, F. and Mertzios, B., On Kalman's controllability and observability criteria for singular systems, Circuits Syst. Signal Process, 1999, vol. 18, no. 3, pp. 269–290.
- 22. Duan, G.R., Analysis and Design of Descriptor Linear Systems, New York: Springer, 2010.
- 23. Berger, T., Reis, T., and Trenn, S., Observability of linear differential-algebraic systems: a survey, in: Surveys in Differential-Algebraic Equations. IV, Cham: Springer, 2017, pp. 161–219.
- 24. Losse, P. and Mehrmann, V., Controllability and observability of second order descriptor systems, SIAM J. Control Optim., 2008, vol. 47, no. 3, pp. 1351–1379.
- 25. Shcheglova, A.A., The stability by linear approximation of discrete-time nonlinear singular systems, Siberian Math. J., 2024, vol. 65, no. 2, pp. 407–427.
- 26. Gaˆıshun, I.V., Sistemy s diskretnym vremenem (Systems with Discrete Time), Minsk: Inst. Mat. NAN Belarus, 2001.
- 27. Shilov, G.E., Matematicheskiy analiz. Funktsii neskol’kikh veshchestvennykh peremennykh (Mathematical Anal-isys. Functions of Several Real Variables), Moscow: Nauka, 1972.