Details
Title
The Stability Interval of the Set of Linear SystemJournal title
International Journal of Electronics and TelecommunicationsYearbook
2021Volume
vol. 67Issue
No 2Affiliation
Mazakov, Talgat : Institute of Information and Computational Technologies CS MES RK, Al-Farabi Kazakh National University, Almaty, Kazakhstan ; Wójcik, Waldemar : Lublin Technical University, Poland ; Jomartova, Sholpan : Institute of Information and Computational Technologies CS MES RK, Al-Farabi Kazakh National University, Almaty, Kazakhstan ; Karymsakova, Nurgul : Al-Farabi Kazakh National University, Almaty, Kazakhstan ; Ziyatbekova, Gulzat : Institute of Information and Computational Technologies CS MES RK, Al-Farabi Kazakh National University, Almaty, Kazakhstan ; Tursynbai, Aisulu : Al-Farabi Kazakh National University, Almaty, KazakhstanAuthors
Keywords
automatic control system ; stability ; matrix ; minor ; characteristic polynomial ; Hurwitz criterion ; Lienard-Shipard criterion of interval mathematics ; Lyapunov functionDivisions of PAS
Nauki TechniczneCoverage
155-161Publisher
Polish Academy of Sciences Committee of Electronics and TelecommunicationsBibliography
[1] Y. Y. Aleksankin, A. E. Brzhozovsky, V. A. Zhdanov and others, "Automateddesign of automatic control systems," ed. V. V. Solodovnikov, Moscow: Mashinostroenie, 1990, pp. 1-332.[2] A. A. Voronov and I. A. Orourke, "Analysis and optimal synthesis of computer control systems," Moscow: Nauka, 1984, pp. 1–344.
[3] V. E. Balnokin and P. I. Chinaev, "Analysis and synthesis of automatic control systems on a computer. Algorithms and programs: Reference," Moscow: Radio and communications, 1991, pp 1–256.
[4] P. D. Krutko, A. I. Maximov and L. M. Skvortsov, "Algorithms and programs for designing automatic systems," Moscow: Radio and communications, 1988, 1–306.
[5] G. Davenport, I. Sira and E. Tournier, "Computer algebra," Moscow: Mir, 1991, pp. 1-352. [6] D. M. Klimov, V. M. Rudenko, "Methods of computer algebra in problems of mechanics," Moscow: Nauka, 1989, pp. 1–215.
[7] N. G. Chetayev, "Stability of motion," Moscow: GITL, 1955, pp. 1–207.
[8] V. I. Zubov, "Dynamics of managed systems," High School, 1982, pp. 1– 286.
[9] V. M. Matrosov, "On the theory of motion stability," Applied Mathematics and Mechanics, no 6, pp. 992-1002, 1962.
[10] R. Bellman, "Vector Lyapunov function," J. Soc. Indastr. Appl. Math., vol. 1., no 1, pp. 32-34, 1962.
[11] V. M. Matrosov and S. N. Vasilyev, "Comparison principle for derivation of theorems in mathematical system theory," International Conference on Artificial Intelligence. Moscow: USSR, 1975, pp. 25-34.
[12] V. M. Popov, "On the absolute stability of non-linear automatic control systems," Automatics and Telemechanics, vol. XXII, no. 8., pp. 50-59, 1961.
[13] V. M. Popov, "Hyper-Stability of automatic systems," Moscow: Nauka, 1970, pp. 1–456.
[14] V. Rezvan, "Absolute stability of automatic systems with delay," Moscow: Nauka, 1983, pp. 1–360.
[15] V. V. Rumyantsev and A. S. Oziraner "Stability and stabilization of motion in relation to a part of variables," Moscow: Nauka, 1987, pp. 1– 256.
[16] V. I. Vorotnikov, "Stability of dynamic systems in relation to some variables," Moscow: Nauka, 1991, pp. 1–288.
[17] K. G. Valeev and O. A. Zhautykov, "Infinite systems of differential equations," Alma-ATA: Nauka, 1974, pp. 1–415.
[18] A. K. Bedelbaev, "Stability of nonlinear automatic control systems," Almaty: ed. an KazSSR, 1960, pp. 1–163.
[19] B. J. Magarin, "The Stability and quality of non-linear automatic control systems," Almaty: Science of The Kazakh SSR, 1980. pp. 1–316.
[20] S. A. Aisagaliev, "Analysis and synthesis of autonomous nonlinear automatic control systems," Almaty: Science of The Kazakh SSR, 1980, pp. 1–244.
[21] R. E. Moor, "Interval analysis," New Jersey: Prentice-Hall, 1966, pp. 1- 245. [22] Y. I. Shokin, "Interval analyze," Novosibirsk: Science, 1986, pp. 1–224.
[23] T. I. Nazarenko and L. V. Marchenko, "Introduction to interval methods of computational mathematics, " Irkutsk: Publishing house of Irkutsk University, 1982, pp. 1–108.
[24] S. A. Kalmykov, Y. I. Shokin and Z. H. Yuldashev, "Methods of interval analyze. – Novosibirsk: Science, 1986. – 224 p.
[25] Yu. M. Gusev, V. N. Efanov, V. G. Krymsky and V. Yu. Rutkovsky, "Analysis and synthesis of linear interval dynamic systems (state of the problem)," RAN. Technical cybernetics, no. 1, 1991, pp. 3-30.
[26] E. M. Smagina, A. N. Moiseev and S. P. Moiseeva, "Methods for calculating the IHP coefficients of interval matrices," Computational Technologies, vol. 2, no.1. 1997, pp. 52-61.
[27] V. A. Pochukaev and I. M. Svetlov, "Analytical method of constructing Hurwitz interval polynomials," Automatics and Telemechanics, no. 2, 1996, pp. 89-100.
[28] N. A. Bobylev, S. V. Emelyanov and S. K. Korovin, "On positive definiteness of interval families of symmetric matrices," Automatics and Telemechanics, no. 8, 2000, pp. 5-10.
[29] S. B. Partushev, "Improving the accuracy of interval estimates of voltage deviations in General-purpose electrical networks," Computational Technology, no. 1, 1997, pp. 45-51.
[30] I. V. Svyd, A. I. Obod, G. E. Zavolodko, I. M. Melnychuk, W. Wójcik, S. Orazalieva and G. Ziyatbekova, "Assessment of information support quality by “friend or foe” identification systems," Przegląd Elektrotechniczny, vol. 95, no. 4, 2019, pp. 127-131.
[31] T. Zh. Mazakov, Sh. A. Jomartova, T. S. Shormanov, G. Z. Ziyatbekova, B. S. Amirkhanov and P. Kisala, "The image processing algorithms for biometric identification by fingerprints," News of the National Academy of Sciences of the Republic of Kazakhstan. Series of Geology and Technical Sciences, vol. 1, no 439. 2020, pp. 14-22.
[32] V. M. Belov, V. A. Sukhanov, E. V. Lagutina, "Interval approach for solving problems of kinetics of simple chemical reactions," Technol, no. 1, 1997, pp. 10-18.
[33] A. Kydyrbekova, M. Othman, O. Mamyrbayev, A. Akhmediyarova and Z. Bagashar, "Identification and authentication of user voice using DNN features and i-vector," Cogent Engineering, vol. 7, 2020, pp. 1-22.
[34] I. Nurdaulet, M. Talgat, M. Orken, G. Ziyatbekova, "Application of fuzzy and interval analysis to the study of the prediction and control model of the epidemiologic situation," Journal of Theoretical and Applied Information Technology, Pakistan, vol. 96, no. 14, 2018, pp. 4358-4368.
[35] V. N., Podlesny and V. G. Rubanov, "A simple frequency criterion for robust stability of a class of linear interval dynamic systems with delay," Automatics and Telemechanics, no. 9, 1996, pp. 131-139.
[36] A. P. Molchanov and M. V. Morozov, "Sufficient conditions for robust stability 5f linear non-stationary control systems with periodic interval restrictions," Automatics and Telemechanics, no. 1, 1997, pp. 100-107.
[37] A. M. Letov, "Stability of nonlinear control systems, " Moscow: Fizmatgiz, 1962, pp. 1–312.
[38] N. S. Bakhvalov, "Numerical methods," Moscow: Nauka, 1973. pp. 1–632.
[39] A. I. Lurie , "Some nonlinear problems of the automatic control theory," Moscow: GITL, 1951, pp. 1–216.
[40] K. I. Babenko, "Fundamentals of numerical analysis," Moscow: Nauka, 1986. pp. 1–744.
[41] B. P. Demidovich, I. A. Maron and E. Z. Shuvalova, "Numerical methods of analysis. Approximation of functions, differential and integral equations," Moscow: Nauka, 1967, pp. 1–368 p.
[42] V. N. Afanasiev, V. B. Kolmanovsky and V. R. Nosov, "Mathematical theory of designing control systems," Moscow: Higher. SHK., 1989, pp. 1–447.
[43] G.A. Amirkhanova, A. I. Golikov and Yu.G. Evtushenko, "On an inverse linear programming problem," Proceedings of the Steklov Institute of Mathematics, vol. 295. no. 1, 2016, pp. S21-S27.