Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2020, Cilt: 49 Sayı: 1, 162 - 169, 06.02.2020
https://doi.org/10.15672/HJMS.2019.669

Öz

Kaynakça

  • [1] F. Amato, R. Ambrosino, M. Ariola, and C. Cosentino, Finite-time stability of linear time-varying systems with jumps, Automatica J. IFAC 45, 1354–1358, 2009.
  • [2] F. Amato, M. Ariola, and P. Dorato, Finite-time control of linear systems subject to parametric uncertainties and disturbances, Automatica J. IFAC 37, 1459–1463, 2001.
  • [3] M. Bohner, T.S. Hassan, and T. Li, Fite–Hille–Wintner-type oscillation criteria for second-order half-linear dynamic equations with deviating arguments, Indag. Math. (N.S.) 29, 548–560, 2018.
  • [4] P. Dorato, Short-time stability in linear time-varying systems, in: Proceedings of the IRE International Convention Record Part 4, New York, pp. 83–87, 1961.
  • [5] J.P. Hespanha and A.S. Morse, Stability of switched systems with average dwell-time, in: Proceedings of the 38th IEEE Conference on Decision and Control, Phoenix, pp. 2655–2660, 1999.
  • [6] Z. Ji, L.Wang, and X. Guo, On controllability of switched linear systems, IEEE Trans. Automat. Control 53, 796–801, 2008.
  • [7] T. Li and Yu.V. Rogovchenko, Oscillation criteria for second-order superlinear Emden–Fowler neutral differential equations, Monatsh. Math. 184, 489–500, 2017.
  • [8] D. Liberzon, Switching in Systems and Control (Birkhäuser, Boston, 2003).
  • [9] H. Lin and P.J. Antsaklis, Stability and stabilizability of switched linear systems: a survey on recent results, IEEE Trans. Automat. Control 54, 308–322, 2009.
  • [10] X. Lin, H. Du, and S. Li, Finite-time boundedness and L2-gain analysis for switched delay systems with norm-bounded disturbance, Appl. Math. Comput. 217, 5982–5993, 2011.
  • [11] X. Lin, X. Li, S. Li, and Y. Zou, Finite-time boundedness for switched systems with sector bounded nonlinearity and constant time delay, Appl. Math. Comput. 274, 25– 40, 2016.
  • [12] X. Liu, Stability analysis of a class of nonlinear positive switched systems with delays, Nonlinear Anal. Hybrid Syst. 16, 1–12, 2015.
  • [13] J. Liu, J. Lian, and Y. Zhuang, Output feedback L1 finite-time control of switched positive delayed systems with MDADT, Nonlinear Anal. Hybrid Syst. 15, 11–22, 2015.
  • [14] D. Liu, X. Liu, and G. Xiao, Stability and L2-gain analysis for switched systems with interval time-varying delay, IET Control Theory Appl. 9, 1644–1652, 2015.
  • [15] F. Pan, X.-B. Chen, and L. Lin, Practical stability analysis of stochastic swarms, in: The 3rd International Conference on Innovative Computing, Information and Control, Dalian, pp. 32–36, 2008.
  • [16] Y. Tian, Y. Cai, Y. Sun, and H. Gao, Finite-time stability for impulsive switched delay systems with nonlinear disturbances, J. Franklin Inst. 353, 3578–3594, 2016.
  • [17] P. Wang and X. Liu, Rapid convergence for telegraph systems with periodic boundary conditions, J. Funct. Spaces 2017, 1–10, 2017.
  • [18] M. Xiang and Z. Xiang, Exponential stability of discrete-time switched linear positive systems with time-delay, Appl. Math. Comput. 230, 193–199, 2014.
  • [19] Y. Zhang, M. Wang, H. Xu, and K.L. Teo, Global stabilization of switched control systems with time delay, Nonlinear Anal. Hybrid Syst. 14, 86–98, 2014.
  • [20] K. Zhou and P.P. Khargonekar, Robust stabilization of linear systems with normbounded time-varying uncertainty, Systems Control Lett. 10, 17–20, 1988.
  • [21] G. Zong, R. Wang, W.X. Zheng, and L. Hou, Finite-time stabilization for a class of switched time-delay systems under asynchronous switching, Appl. Math. Comput. 219, 5757–5771, 2013.

Finite-time stability of switched systems with delayed arguments and nonlinear perturbations

Yıl 2020, Cilt: 49 Sayı: 1, 162 - 169, 06.02.2020
https://doi.org/10.15672/HJMS.2019.669

Öz

This paper is concerned with the problem of finite-time stability (FTS)  of a class of switched systems with delayed arguments and nonlinear perturbations which are related not only with the current state and the delayed state but also with time $t$. Novel Lyapunov--Krasovskii functions are introduced, and a new finite-time stability criterion is derived  by employing the average dwell time (ADT) approach and linear matrix inequality technique.  An example is given to illustrate the effectiveness of the proposed method.

Kaynakça

  • [1] F. Amato, R. Ambrosino, M. Ariola, and C. Cosentino, Finite-time stability of linear time-varying systems with jumps, Automatica J. IFAC 45, 1354–1358, 2009.
  • [2] F. Amato, M. Ariola, and P. Dorato, Finite-time control of linear systems subject to parametric uncertainties and disturbances, Automatica J. IFAC 37, 1459–1463, 2001.
  • [3] M. Bohner, T.S. Hassan, and T. Li, Fite–Hille–Wintner-type oscillation criteria for second-order half-linear dynamic equations with deviating arguments, Indag. Math. (N.S.) 29, 548–560, 2018.
  • [4] P. Dorato, Short-time stability in linear time-varying systems, in: Proceedings of the IRE International Convention Record Part 4, New York, pp. 83–87, 1961.
  • [5] J.P. Hespanha and A.S. Morse, Stability of switched systems with average dwell-time, in: Proceedings of the 38th IEEE Conference on Decision and Control, Phoenix, pp. 2655–2660, 1999.
  • [6] Z. Ji, L.Wang, and X. Guo, On controllability of switched linear systems, IEEE Trans. Automat. Control 53, 796–801, 2008.
  • [7] T. Li and Yu.V. Rogovchenko, Oscillation criteria for second-order superlinear Emden–Fowler neutral differential equations, Monatsh. Math. 184, 489–500, 2017.
  • [8] D. Liberzon, Switching in Systems and Control (Birkhäuser, Boston, 2003).
  • [9] H. Lin and P.J. Antsaklis, Stability and stabilizability of switched linear systems: a survey on recent results, IEEE Trans. Automat. Control 54, 308–322, 2009.
  • [10] X. Lin, H. Du, and S. Li, Finite-time boundedness and L2-gain analysis for switched delay systems with norm-bounded disturbance, Appl. Math. Comput. 217, 5982–5993, 2011.
  • [11] X. Lin, X. Li, S. Li, and Y. Zou, Finite-time boundedness for switched systems with sector bounded nonlinearity and constant time delay, Appl. Math. Comput. 274, 25– 40, 2016.
  • [12] X. Liu, Stability analysis of a class of nonlinear positive switched systems with delays, Nonlinear Anal. Hybrid Syst. 16, 1–12, 2015.
  • [13] J. Liu, J. Lian, and Y. Zhuang, Output feedback L1 finite-time control of switched positive delayed systems with MDADT, Nonlinear Anal. Hybrid Syst. 15, 11–22, 2015.
  • [14] D. Liu, X. Liu, and G. Xiao, Stability and L2-gain analysis for switched systems with interval time-varying delay, IET Control Theory Appl. 9, 1644–1652, 2015.
  • [15] F. Pan, X.-B. Chen, and L. Lin, Practical stability analysis of stochastic swarms, in: The 3rd International Conference on Innovative Computing, Information and Control, Dalian, pp. 32–36, 2008.
  • [16] Y. Tian, Y. Cai, Y. Sun, and H. Gao, Finite-time stability for impulsive switched delay systems with nonlinear disturbances, J. Franklin Inst. 353, 3578–3594, 2016.
  • [17] P. Wang and X. Liu, Rapid convergence for telegraph systems with periodic boundary conditions, J. Funct. Spaces 2017, 1–10, 2017.
  • [18] M. Xiang and Z. Xiang, Exponential stability of discrete-time switched linear positive systems with time-delay, Appl. Math. Comput. 230, 193–199, 2014.
  • [19] Y. Zhang, M. Wang, H. Xu, and K.L. Teo, Global stabilization of switched control systems with time delay, Nonlinear Anal. Hybrid Syst. 14, 86–98, 2014.
  • [20] K. Zhou and P.P. Khargonekar, Robust stabilization of linear systems with normbounded time-varying uncertainty, Systems Control Lett. 10, 17–20, 1988.
  • [21] G. Zong, R. Wang, W.X. Zheng, and L. Hou, Finite-time stabilization for a class of switched time-delay systems under asynchronous switching, Appl. Math. Comput. 219, 5757–5771, 2013.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Youliang Fu Bu kişi benim 0000-0003-4571-6830

Naxin Cui Bu kişi benim 0000-0001-9118-2951

Chenghui Zhang 0000-0003-2317-5930

Tongxing Li 0000-0002-4039-9648

Yayımlanma Tarihi 6 Şubat 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 49 Sayı: 1

Kaynak Göster

APA Fu, Y., Cui, N., Zhang, C., Li, T. (2020). Finite-time stability of switched systems with delayed arguments and nonlinear perturbations. Hacettepe Journal of Mathematics and Statistics, 49(1), 162-169. https://doi.org/10.15672/HJMS.2019.669
AMA Fu Y, Cui N, Zhang C, Li T. Finite-time stability of switched systems with delayed arguments and nonlinear perturbations. Hacettepe Journal of Mathematics and Statistics. Şubat 2020;49(1):162-169. doi:10.15672/HJMS.2019.669
Chicago Fu, Youliang, Naxin Cui, Chenghui Zhang, ve Tongxing Li. “Finite-Time Stability of Switched Systems With Delayed Arguments and Nonlinear Perturbations”. Hacettepe Journal of Mathematics and Statistics 49, sy. 1 (Şubat 2020): 162-69. https://doi.org/10.15672/HJMS.2019.669.
EndNote Fu Y, Cui N, Zhang C, Li T (01 Şubat 2020) Finite-time stability of switched systems with delayed arguments and nonlinear perturbations. Hacettepe Journal of Mathematics and Statistics 49 1 162–169.
IEEE Y. Fu, N. Cui, C. Zhang, ve T. Li, “Finite-time stability of switched systems with delayed arguments and nonlinear perturbations”, Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 1, ss. 162–169, 2020, doi: 10.15672/HJMS.2019.669.
ISNAD Fu, Youliang vd. “Finite-Time Stability of Switched Systems With Delayed Arguments and Nonlinear Perturbations”. Hacettepe Journal of Mathematics and Statistics 49/1 (Şubat 2020), 162-169. https://doi.org/10.15672/HJMS.2019.669.
JAMA Fu Y, Cui N, Zhang C, Li T. Finite-time stability of switched systems with delayed arguments and nonlinear perturbations. Hacettepe Journal of Mathematics and Statistics. 2020;49:162–169.
MLA Fu, Youliang vd. “Finite-Time Stability of Switched Systems With Delayed Arguments and Nonlinear Perturbations”. Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 1, 2020, ss. 162-9, doi:10.15672/HJMS.2019.669.
Vancouver Fu Y, Cui N, Zhang C, Li T. Finite-time stability of switched systems with delayed arguments and nonlinear perturbations. Hacettepe Journal of Mathematics and Statistics. 2020;49(1):162-9.