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Articles

Robust pole assignment for interval polynomial based on positive interval Routh-table: positive property of Routh-table of binomial coefficients

Pages 833-842 | Received 04 Aug 2012, Accepted 27 Jul 2014, Published online: 23 Apr 2015

References

  • Bandyopadhyay, B., A. Upadhye, and O. Ismail. 1997. “γ-δ Routh Approximation for Interval Systems.” IEEE Transactions on Automatic Control 42 (8): 1127–1130. doi:10.1109/9.618241.
  • Bandyopadhyay, B., O. Ismail, and R. Gorez. 1994. “Routh-Pade Approximation for Interval Systems.” IEEE Transactions on Automatic Control 39 (12): 2454–2456. doi:10.1109/9.362850.
  • Chapellat, H., M. Dahleh, and S. P. Bhattacharyya. 1991. “On Robust Stability of Interval Control Systems.” IEEE Transactions on Automatic Control 36 (1): 59–67. doi:10.1109/9.62268.
  • Dahleh, M., A. Tesi, and A. Vicino. 1992. “Robust Stability and Performance of Interval Plants.” Systems & Control Letters 19 (5): 353–363. doi:10.1016/0167-6911(92)90085-7.
  • Dahleh, M., A. Tesi, and A. Vicino. 1993. “On the Robust Popov Criterion for Interval Lur’e Systems.” IEEE Transactions on Automatic Control 38 (9): 1400–1405. doi:10.1109/9.237655.
  • Dolgin, Y. 2005. “Author’s Reply.” IEEE Transactions on Automatic Control 50 (2): 274–275. doi:10.1109/TAC.2005.843849.
  • Dolgin, Y., and E. Zeheb. 2003. “On Routh-Pade Model Reduction of Interval Systems.” IEEE Transactions on Automatic Control 48 (9): 1610–1612. doi:10.1109/TAC.2003.816999.
  • Duan, G.-R., and H.-H. Yu. 2008. “Robust Pole Assignment in High-order Descriptor Linear Systems via Proportional plus Derivative State Feedback.” IET Control Theory and Applications 2 (4): 277–287. doi:10.1049/iet-cta:20070164.
  • Hansen, E. 1965. “Interval Arithmetic in Matrix Computations, Part I.” SIAM Journal on Numerical Analysis 2 (2): 308–320. doi:10.1137/0702025.
  • Hollot, C. V., and R. Tempo. 1994. “On the Nyquist Envelope of an Interval Plant Family.” IEEE Transactions on Automatic Control 39 (2): 391–396. doi:10.1109/9.272342.
  • Howie, J. M. 2006. Fields and Galois Theory. London: Springer-Verlag.
  • Hwang, C., and S.-F. Yang. 1999. “Comments on the Computation of Interval Routh Approximants.” IEEE Transactions on Automatic Control 44 (9): 1782–1787. doi:10.1109/9.788553.
  • Jaulin, L., M. Kieffer, O. Didrit, and E. Walter. 2001. Applied Interval Analysis. London: Springer-Verlag.10.1007/978-1-4471-0249-6
  • Juang, B.-Y. 2010. “Robustness of Pole Assignment for an Interval Polynomial in a Damping-cone Based on the Positive Interval Routh-table.” In Proceedings of the SICE Annual Conference 2010, the Grand Hotel, Taipei, Taiwan, 18–21 August 2010: 3572–3580. New York: IEEE.
  • Khadraoui, S., M. Rakotondrabe, and P. Lutz. 2012. “Interval Modeling and Robust Control of Piezo- Electric Microactuators.” IEEE Transactions on Control Systems and Technology 20 (2): 486–494. doi:10.1109/TCST.2011.2116789.
  • Rakotondrabe, M. 2011. “Performances Inclusion for Stable Interval Systems.” American Control Conference, San Francisco, CA, 29 June–1 July 2011: 4367–4372. New York: IEEE.
  • Soh, Y. C. 1989. “Robust Pole-placement for Uncertain Interval System.” IEE Proceedings D (Control Theory and Applications) 136 (6): 301–306. doi:10.1049/ip-d.1989.0039.
  • Vagia, M., and A. Tzes. 2011. “An Iterative Scheme for LMI-based Robust Pole Assignment with Control Input Saturation Constraints for Uncertain LTI Systems.” In Proceedings of 19th Mediterranean Conference on Control and Automation, Aquis Corfu Holiday Palace, Corfu, Greece, 20–23 June 2011: 706–711. New York: IEEE.
  • Walter, E., and L. Jaulin. 1994. “Guaranteed Characterization of Stability Domains via Set Inversion.” IEEE Transactions on Automatic Control 39 (4): 886–889. doi:10.1109/9.286277.
  • Wang, L. 2002. “H∞ Performance of Interval Systems.” Cornell University. http://www.arxiv.org/pdf/math/0211013.pdf.
  • Wang, G.-S., B. Liang, and G.-R. Duan. 2006. “H2-Optimal Control with Regional Pole Assignment via State Feedback.” International Journal of Control, Automation, and Systems 4 (5): 653–659.
  • Wang, G.-S., X.-X. Zhang, T.-Q. Chang, and B. Ling. 2010. “Robust Pole Assignment Design in Second-order Linear Systems.” In Proceedings of the 29th Chinese Control Conference, Beijing, China, 29–31 July 2010: 255–258. New York: IEEE.
  • Xu, S. J., M. Darouach, and J. Schaefers. 1993. “The Expansion of Det (A+B) and the Robustness Analysis of Uncertain State Space Systems.” IEEE Transactions on Automatic Control 38 (11): 1671–1675. doi:10.1109/9.262036.
  • Xu, S. J., A. Rachid, and M. Darouach. 1998. “Robustness Analysis of Interval Matrices Based on Kharitonov's Theorem.” IEEE Transactions on Automatic Control 43 (2): 273–278. doi:10.1109/9.661080.
  • Xu, H., and H.-Y. Zhu. 2011. “Approach of Robust Pole Assignment Based on Normal Matrix.” In Proceeding of International Conference on Electrical and Control Engineering (ICECE), Yichang, China, 16–18 September 2011: 3377–3380. New York: IEEE.
  • Yang, S.-F. 2005. “Comments on Routh-Pade Model Reduction of Interval Systems.” IEEE Transactions on Automatic Control 50 (2): 273–274. doi:10.1109/TAC.2004.841885.
  • Yang, F., M. Gani, and D. Henrion. 2007. “Fixed-order Robust H∞ Controller Design with Regional Pole Assignment.” IEEE Transactions on Automatic Control 52 (10): 1959–1963. doi:10.1109/TAC.2007.906242.

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