Araştırma Makalesi
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Common Solutions to Stein Inequalities

Yıl 2023, , 1097 - 1103, 18.10.2023
https://doi.org/10.16984/saufenbilder.1260438

Öz

In this paper for linear discrete time switched systems, the problem of existence of a common solution to Stein inequalities is considered. A sufficient condition for robust Schur stability of a matrix polyope by using Schur complement lemma and a necessary and sufficient condition for the existence of a common solution of Stein equation are given. As in the case of continuous time systems, the problem of existence of a common solution is reduced to a convex optimization one. An efficient solution algorithm which requires solving a linear minimax problem at each step is suggested. The algorithm is supported with a number of examples from the literature and observed that the method desired results fastly.

Kaynakça

  • M. Akar, K. S. Narendra, “On the existence of common quadratic Lyapunov functions for second-order linear time-invariant discrete-time systems,” International Journal of Adaptive Control and Signal Processing, vol. 16, pp. 729-751, 2002.
  • J. C. Geromel, M. C. de Oliveira, L. Hsu, “LMI characterization of structural and robust stability,” Linear Algebra and its Applications, vol. 285, pp. 69-80, 1998.
  • O. Taussky, “Matrices C with C^n→0,” Journal of Algebra, vol. 1, pp. 5-10, 1964.
  • K. S. Narendra, J. A. Balakrishnan, “Common Lyapunov function for stable LTI systems with commuting A-matrices,” IEEE Transactions on Automatic Control, vol. 39(12), pp. 2469-2471, 1994.
  • S. P. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan, “Some standard problems involving LMIs” in Linear Matrix Inequalities in System and Control Theory, Philadelphia, PA, USA: SIAM, 1994, ch. 2, pp. 7-35.
  • D. Liberzon, J. P. Hespanha, A. S. Morse, “Stability of switched systems: a Lie-algebraic condition,” Systems & Control Letters, vol. 37, pp. 117–122, 1999.
  • R. N. Shorten, K. S. Narendra, “Necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for M stable second order linear time-invariant systems,” in Proceedings of the American Control Conference, Chicago, IL, USA, 2000, pp. 359–363.
  • V. Dzhafarov, T. Büyükköroğlu, “On one inner point algorithm for common Lyapunov functions,” Systems & Control Letters, vol. 167, pp. 1-4, 2022.
  • E. Kreyszig, Introductory Functional Analysis with Applications, John Wiley & Sons, 1978.
  • Ş. Yılmaz, “Hurwitz Stability of Matrix Segment and The Common Solution Set of 2 and 3-Dimensional Lyapunov Equations,” Sakarya University Journal of Science, vol. 24, no. 2, pp. 357-364, 2020.
  • Ş. Yılmaz, “Common qudratic Lyapunov functions for two stable matrices,” Eskişehir Technical University Journal of Science and Technology B - Theoretical Sciences, vol. 10, no.1, pp. 18-26, 2022.
Yıl 2023, , 1097 - 1103, 18.10.2023
https://doi.org/10.16984/saufenbilder.1260438

Öz

Kaynakça

  • M. Akar, K. S. Narendra, “On the existence of common quadratic Lyapunov functions for second-order linear time-invariant discrete-time systems,” International Journal of Adaptive Control and Signal Processing, vol. 16, pp. 729-751, 2002.
  • J. C. Geromel, M. C. de Oliveira, L. Hsu, “LMI characterization of structural and robust stability,” Linear Algebra and its Applications, vol. 285, pp. 69-80, 1998.
  • O. Taussky, “Matrices C with C^n→0,” Journal of Algebra, vol. 1, pp. 5-10, 1964.
  • K. S. Narendra, J. A. Balakrishnan, “Common Lyapunov function for stable LTI systems with commuting A-matrices,” IEEE Transactions on Automatic Control, vol. 39(12), pp. 2469-2471, 1994.
  • S. P. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan, “Some standard problems involving LMIs” in Linear Matrix Inequalities in System and Control Theory, Philadelphia, PA, USA: SIAM, 1994, ch. 2, pp. 7-35.
  • D. Liberzon, J. P. Hespanha, A. S. Morse, “Stability of switched systems: a Lie-algebraic condition,” Systems & Control Letters, vol. 37, pp. 117–122, 1999.
  • R. N. Shorten, K. S. Narendra, “Necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for M stable second order linear time-invariant systems,” in Proceedings of the American Control Conference, Chicago, IL, USA, 2000, pp. 359–363.
  • V. Dzhafarov, T. Büyükköroğlu, “On one inner point algorithm for common Lyapunov functions,” Systems & Control Letters, vol. 167, pp. 1-4, 2022.
  • E. Kreyszig, Introductory Functional Analysis with Applications, John Wiley & Sons, 1978.
  • Ş. Yılmaz, “Hurwitz Stability of Matrix Segment and The Common Solution Set of 2 and 3-Dimensional Lyapunov Equations,” Sakarya University Journal of Science, vol. 24, no. 2, pp. 357-364, 2020.
  • Ş. Yılmaz, “Common qudratic Lyapunov functions for two stable matrices,” Eskişehir Technical University Journal of Science and Technology B - Theoretical Sciences, vol. 10, no.1, pp. 18-26, 2022.
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Şerife Yılmaz 0000-0002-7561-3288

Birgül Aksoy 0000-0002-9502-3648

Erken Görünüm Tarihi 5 Ekim 2023
Yayımlanma Tarihi 18 Ekim 2023
Gönderilme Tarihi 5 Mart 2023
Kabul Tarihi 25 Temmuz 2023
Yayımlandığı Sayı Yıl 2023

Kaynak Göster

APA Yılmaz, Ş., & Aksoy, B. (2023). Common Solutions to Stein Inequalities. Sakarya University Journal of Science, 27(5), 1097-1103. https://doi.org/10.16984/saufenbilder.1260438
AMA Yılmaz Ş, Aksoy B. Common Solutions to Stein Inequalities. SAUJS. Ekim 2023;27(5):1097-1103. doi:10.16984/saufenbilder.1260438
Chicago Yılmaz, Şerife, ve Birgül Aksoy. “Common Solutions to Stein Inequalities”. Sakarya University Journal of Science 27, sy. 5 (Ekim 2023): 1097-1103. https://doi.org/10.16984/saufenbilder.1260438.
EndNote Yılmaz Ş, Aksoy B (01 Ekim 2023) Common Solutions to Stein Inequalities. Sakarya University Journal of Science 27 5 1097–1103.
IEEE Ş. Yılmaz ve B. Aksoy, “Common Solutions to Stein Inequalities”, SAUJS, c. 27, sy. 5, ss. 1097–1103, 2023, doi: 10.16984/saufenbilder.1260438.
ISNAD Yılmaz, Şerife - Aksoy, Birgül. “Common Solutions to Stein Inequalities”. Sakarya University Journal of Science 27/5 (Ekim 2023), 1097-1103. https://doi.org/10.16984/saufenbilder.1260438.
JAMA Yılmaz Ş, Aksoy B. Common Solutions to Stein Inequalities. SAUJS. 2023;27:1097–1103.
MLA Yılmaz, Şerife ve Birgül Aksoy. “Common Solutions to Stein Inequalities”. Sakarya University Journal of Science, c. 27, sy. 5, 2023, ss. 1097-03, doi:10.16984/saufenbilder.1260438.
Vancouver Yılmaz Ş, Aksoy B. Common Solutions to Stein Inequalities. SAUJS. 2023;27(5):1097-103.

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