93
Views
3
CrossRef citations to date
0
Altmetric
Articles

Structurally variable control of Lurie systems

, , &
Pages 2960-2972 | Received 23 Jun 2018, Accepted 04 Jan 2019, Published online: 28 Jan 2019

References

  • Azar, A. T., & Zhu, Q. (2015). Advances and applications in sliding mode control systems. Berlin: Springer.
  • Bandyopadhyay, B., Janardhanan, S., & Spurgeon, S. K. (Eds.). (2013). Advances in sliding mode control: Concept, theory and implementation (1st ed.). Berlin: Springer-Verlag.
  • Bartolini, G., Fridman, L., Pisano, A., & Usai, E. (Eds.). (2008). Modern sliding mode control theory: New perspectives and applications (1st ed.). Berlin: Springer-Verlag.
  • Emelianov, S. (1976). Structurally variable automatic control systems. Moscow: Nauka.
  • Gan, Z., & Han, J. (2003). Lyapunov function of general Lurie systems with multiple nonlinearities. Applied Mathematics Letters, 16(1), 119–126. doi:10.1016/S0893-9659(02)00153-2.
  • Gao, J., Su, H., Ji, X., & Chu, J. (2008). Robust absolute stability for general neutral type Lurie indirect control systems. Asian Journal of Control, 10, doi:10.1002/asjc.70.
  • Ge, S. S., Lee, T. H., & Ren, S. X. (2001). Adaptive friction compensation of servo mechanisms. International Journal of Systems Science, 32(4), 523–532. doi:10.1080/00207720119378.
  • Grujić, L. (1977). Un lemme matriciel reciproque, application a la stabilite absolute. Comptes Rendus de l'Académie des Sciences, Series A, t.284.
  • Grujić, L. (1978a). Solutions for the Lurie-Postnikov and Aizerman problems. International Journal of Systems Science, 9(12), 1359–1372. doi: 10.1080/00207727808941783
  • Grujić, L. (1980). Necessary and sufficient Liapunov like conditions for absolute stability and Aizerman conjecture. Matematicheskaja Fizika, 28, 7–20.
  • Grujić, L. (1981a). Lyapunov-like solutions for stability problems of the most general stationary Lurie-Postnikov systems. International Journal of Systems Science, 12(7), 813–833. doi: 10.1080/00207728108963785
  • Grujić, L. T. (1978b). Absolute stability of non-stationary systems: Resolutions and applications. In Joint automatic control conference (pp. 327–338).
  • Grujić, L. T. (1981b). On absolute stability and the Aizerman conjecture. Automatica, 17(2), 335–349. doi: 10.1016/0005-1098(81)90051-0
  • Grujić, L. T., Borne, P., & Gentina, J. (1979). Matrix approaches to the absolute stability of time-varying Lurie-Postnikov systems. International Journal of Control, 30(6), 967–980. doi: 10.1080/00207177908922827
  • Gruyitch, L. (1997). Consistent Lyapunov methodology for time-invariant nonlinear systems. Avtomatika i Telemekhanika, 12, 35–73.
  • Gruyitch, L. (2013). Tracking control of linear systems. BocaRaton, FL: CRC Press.
  • Gruyitch, L., Ribar, Z., Bučevac, Z., & Jovanović, R. (2017). Structurally variable control of time-varying Lurie systems. International Journal of Control, 90(2), 186–200. doi:10.1080/00207179.2016.1173229.
  • Jie, Y., Qing-Lin, W., & Yuan, L. (2012, July). Sliding mode variable structure control theory: A survey. In Proceedings of the 31st Chinese control conference (pp. 3197–3202).
  • Kao, C. (2005). Surveys of discrete-time variable structure control. In IEEE ICSS2005 international conference on systems & signals (pp. 573–577). Kaohsiung.
  • Liberzon, M. R. (2006, October). Essays on the absolute stability theory. Automation and Remote Control, 67, doi:10.1134/s0005117906100043.
  • Liu, J., & Wang, X. (2012). Advanced sliding mode control for mechanical systems: Design, analysis and matlab simulation. Beijing: Tsinghua University Press.
  • Lurie, A., & Postnikov, V. (1944). Concerning the theory of stability of regulating systems. Prikladnaya Matematika i Mekhanika, 8, 246–248.
  • Perruquetti, W., & Jean-Pierre, B. (2002). Sliding mode control in engineering. New York, NY: Marcel Dekker, Inc.
  • Pisano, A., & Usai, E. (2011). Sliding mode control: A survey with applications in math. Mathematics and Computers in Simulation, 81(5), 954–979. Important aspects on structural dynamical systems and their numerical computation. doi:10.1016/j.matcom.2010.10.003.
  • Popov, V. (1961). On absolute stability of non-linear automatic control systems. Avtomatika i Telemekhanika, 12, 961–979.
  • Popov, V. (1962). Concerning a critical case of absolute stability. Avtomatika i Telemekhanika, 23(1), 3–24.
  • Popov, V. (1964). On a certain problem in theory of absolute stability of controlled systems. Avtomatika i Telemekhanika, 25, 1257–1262.
  • Popov, V. (1973). Hyperstability of control systems. Berlin: Springer-Verlag.
  • Sabanovic, A. (2011, May). Variable structure systems with sliding modes in motion control-a survey. IEEE Transactions on Industrial Informatics, 7, doi:10.1109/TII.2011.2123907.
  • Sabanovic, A., Fridman, L. M., & Spurgeon, S. K. (2004). Variable structure systems: From principles to implementation (Vol. 66). London: The Institution of the Electrical Engineers.
  • Shi, K., Tang, Y., Liu, X., & Zhong, S. (2017). Non-fragile sampled-data robust synchronization of uncertain delayed chaotic Lurie systems with randomly occurring controller gain fluctuation. ISA Transactions, 66, 185–199. doi:10.1016/j.isatra.2016.11.002.
  • Shi, K., Tang, Y., Zhong, S., Yin, C., Huang, X., & Wang, W. (no date). Nonfragile asynchronous control for uncertain chaotic Lurie network systems with Bernoulli stochastic process. International Journal of Robust and Nonlinear Control, 28(5), 1693–1714. doi:10.1002/rnc.3980.
  • Shtessel, Y., Edwards, C., Fridman, L., & Levant, A. (2014). Sliding mode control and observation. New York, NY: Springer.
  • Utkin, V. (1977). Variable structure systems with sliding modes. IEEE Transactions on Automatic Control, 22, 212–222. doi: 10.1109/TAC.1977.1101446
  • Utkin, V. (1981). Sliding regimes in optimization and control problems. Moscow: Nauka.
  • Utkin, V., Guldner, J., & Shi, J. (2009). Sliding mode control in electro-mechanical systems (Vol. 34). Boca Raton, FL: CRC Press.
  • Utkin, V., & Jang, K. (1978). Methods for constructing the sliding surface of multivariable structurally variable systems. Avtomatika i Telemehanika, 10, 72–77.
  • Wang, J., Shi, K., Huang, Q., Zhong, S., & Zhang, D. (2018). Stochastic switched sampled-data control for synchronization of delayed chaotic neural networks with packet dropout. Applied Mathematics and Computation, 335, 211–230. doi:10.1016/j.amc.2018.04.038.
  • Xin, G. Z., & Gao, G. W. (2001, October). Absolute stability of general Lurie control systems with multi-nonlinear feedback terms. Acta Mathematica Sinica, English Series (Springer), 17, 0–0. doi:10.1007/PL00011638.
  • Yakubovich, V. (1962). The solution of certain matrix inequalities appearing in the theory of automatic control. Avtomatika i Telemehanika, 143, 1304–1307.
  • Yu, X., & Kaynak, O. (2009, September). Sliding-mode control with soft computing: A survey. IEEE Transactions on Industrial Electronics, 56(9), 3275–3285. doi:10.1109/TIE.2009.2027531.
  • Yu, X. H., & Xu, J.-X. (2000). Advances in variable structure systems: Analysis, integration and applications. In Proceedings of the 6th IEEE international workshop on variable structure systems. Gold Coast, Queensland, December 7–9. World Scientific.
  • Zuoxin, G., Weigao, G., Suxia, Z., & Yongxian, W. (2001, January). Absolute stability of general Lurie type indirect control systems. Acta Mathematicae Applicatae Sinica, English Series, 17, doi:10.1007/bf02669687.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.