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STOCHASTIC STABILITY IN TERMS OF AN ASSOCIATED TRANSFER FUNCTION MATRIX FOR SOME HYBRID SYSTEMS WITH MARKOVIAN SWITCHING

Year 2018, Volume: 67 Issue: 1, 198 - 210, 01.02.2018

Chafai Imzegouan

https://doi.org/10.1501/Commua1_0000000842
Cited By: 1

Abstract

This work is devoted to stability for a dynamical system withMarkovian switched controller and a finite number of linear diğerential subsystems. We suppose conditions on a state space representation ofan associated transfer function matrix which guarantees stochastic stability.The given examples are detailed to illustrate the main result

Keywords

Hybrid switching system transfer matrix Markov jump companion

References

  • M. Balde, U. Boscain and P. Mason, A note on stability conditions for planar switched systems, Internat. J. Control 82, no. 10, (2009) pp. 1882-1888.
  • M. Benaîm, S. Le Borgne, F. Malrieu and P. A. Zitt, On the stability of planar randomly switched systems, Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 24 (1), (2014) pp. 292-311.
  • H. Bouzahir and X. Fu, Controllability of neutral functional diğerential equations with in…nite delay, Acta Mechanica Sinica, 31(1), (2011) pp. 73-80.
  • O. L. V. Costa, M. D. Fragoso and M. G. Todorov, continuous-time Markov jump linear systems, Springer-Verlag Berlin Heidelberg 2013.
  • F. El Guezar, H. Bouzahir and D. Fournier-Prunaret, Event detection occurrence for planar piece-wise a¢ ne hybrid systems, Nonlinear Anal. Hybrid Syst. 5 no. 4 (2011), pp. 626-638.
  • C. Imzegouan, H. Bouzahir, B. Benaid and F. El Guezar, A note on exponential sto- chastic stability of Markovian switching Systems, International Journal of Evolution Equations, Vol 10, Issue 2, (2016), pp. 189-198.
  • Z. H. Guan, T. H. Qian and X. Yu, On controllability and observability for a class of impulsive systems, Systems Control Lett. 47 (2002) pp. 247-257.
  • R. A. Horn, and C. R. Johnson, Matrix analysis, Cambridge university Press, 1990.
  • T. Kailath, Linear systems, Englewood Cliğs, NJ: Prentice Hall. (1980).
  • Y. Kouhi, N. Bajcinca, J. Raisch and R. Shorten, A new stability result for switched linear systems, Proceedings of the European control conference, (2013) pp. 2152-2156.
  • Y. Kouhi, N. Bajcinca, J. Raisch and R. Shorten, On the quadratic stability of switched linear systems associated with symmetric transfer function matrices, Au- tomatica J. IFAC 50, no. 11, (2014) pp. 2872-2879.
  • L. Knockaert, F. Ferranti and T. Dhaene, Generalized eigenvalue passivity assessment of descriptor systems with applications to symmetric and singular systems, Interna- tional Journal of Numerical Modeling: Electronic Networks, Devices and Fields, 26 (1), (2013) pp. 1-14.
  • X. Mao, Stability of stochastic diğerential equations with Markovian switching, Sto- chastic Process. Appl. 79, no. 1 (1999) pp. 45-67.
  • L. Perko, Diğerential equations and dynamical systems, Springer, 3rd Ed., New York, (2001).
  • A. Rantzer, On the Kalman-Yakubovich-Popov lemma, Systems and Control Letters (1996) pp. 7-10.
  • Z. Sun and S. S. Ge, Stability theory of switched dynamical systems, Springer-Verlag London Limited, 2011.
  • R. N. Shorten and K. S. Narendra, On common quadratic Lyapunov functions for pairs of stable LTI systems whose system matrices are in companion form, IEEE Transactions on Automatic Control, 48(4) (2003) pp. 618-621.
  • G. Yin and C. Zhu, On the notion of weak stability and related issues of hybrid diğusion systems, Nonlinear Anal.: Hybrid Sys. 1, no. 2 (2007) pp. 173-187.
  • G. Yin, G. Zhao and F. Wu, Regularization and stabilization of randomly switching dynamic systems, SIAM J. Appl. Math. Vol. 72, no. 5 (2012) pp. 1361-1382
  • C. Yuan and X. Mao, Asymptotic stability in distribution of stochastic diğerential equations with Markovian switching, Stochastic Process. Appl. 103, no. 2 (2003) pp. 291.
  • S. Zhendong and S. G. Shuzhi, Stability theory of switched dynamical systems, Com- munications and Control Engineering Series. Springer, London, 2011.
  • C. Zhu, G. Yin and Q. S. Song, Stability of random-switching systems of diğerential equations, Quart. Appl. Math. 67, no. 2 (2009) pp. 201-220. Current address

Year 2018, Volume: 67 Issue: 1, 198 - 210, 01.02.2018

Chafai Imzegouan

https://doi.org/10.1501/Commua1_0000000842
Cited By: 1

Abstract

References

  • M. Balde, U. Boscain and P. Mason, A note on stability conditions for planar switched systems, Internat. J. Control 82, no. 10, (2009) pp. 1882-1888.
  • M. Benaîm, S. Le Borgne, F. Malrieu and P. A. Zitt, On the stability of planar randomly switched systems, Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 24 (1), (2014) pp. 292-311.
  • H. Bouzahir and X. Fu, Controllability of neutral functional diğerential equations with in…nite delay, Acta Mechanica Sinica, 31(1), (2011) pp. 73-80.
  • O. L. V. Costa, M. D. Fragoso and M. G. Todorov, continuous-time Markov jump linear systems, Springer-Verlag Berlin Heidelberg 2013.
  • F. El Guezar, H. Bouzahir and D. Fournier-Prunaret, Event detection occurrence for planar piece-wise a¢ ne hybrid systems, Nonlinear Anal. Hybrid Syst. 5 no. 4 (2011), pp. 626-638.
  • C. Imzegouan, H. Bouzahir, B. Benaid and F. El Guezar, A note on exponential sto- chastic stability of Markovian switching Systems, International Journal of Evolution Equations, Vol 10, Issue 2, (2016), pp. 189-198.
  • Z. H. Guan, T. H. Qian and X. Yu, On controllability and observability for a class of impulsive systems, Systems Control Lett. 47 (2002) pp. 247-257.
  • R. A. Horn, and C. R. Johnson, Matrix analysis, Cambridge university Press, 1990.
  • T. Kailath, Linear systems, Englewood Cliğs, NJ: Prentice Hall. (1980).
  • Y. Kouhi, N. Bajcinca, J. Raisch and R. Shorten, A new stability result for switched linear systems, Proceedings of the European control conference, (2013) pp. 2152-2156.
  • Y. Kouhi, N. Bajcinca, J. Raisch and R. Shorten, On the quadratic stability of switched linear systems associated with symmetric transfer function matrices, Au- tomatica J. IFAC 50, no. 11, (2014) pp. 2872-2879.
  • L. Knockaert, F. Ferranti and T. Dhaene, Generalized eigenvalue passivity assessment of descriptor systems with applications to symmetric and singular systems, Interna- tional Journal of Numerical Modeling: Electronic Networks, Devices and Fields, 26 (1), (2013) pp. 1-14.
  • X. Mao, Stability of stochastic diğerential equations with Markovian switching, Sto- chastic Process. Appl. 79, no. 1 (1999) pp. 45-67.
  • L. Perko, Diğerential equations and dynamical systems, Springer, 3rd Ed., New York, (2001).
  • A. Rantzer, On the Kalman-Yakubovich-Popov lemma, Systems and Control Letters (1996) pp. 7-10.
  • Z. Sun and S. S. Ge, Stability theory of switched dynamical systems, Springer-Verlag London Limited, 2011.
  • R. N. Shorten and K. S. Narendra, On common quadratic Lyapunov functions for pairs of stable LTI systems whose system matrices are in companion form, IEEE Transactions on Automatic Control, 48(4) (2003) pp. 618-621.
  • G. Yin and C. Zhu, On the notion of weak stability and related issues of hybrid diğusion systems, Nonlinear Anal.: Hybrid Sys. 1, no. 2 (2007) pp. 173-187.
  • G. Yin, G. Zhao and F. Wu, Regularization and stabilization of randomly switching dynamic systems, SIAM J. Appl. Math. Vol. 72, no. 5 (2012) pp. 1361-1382
  • C. Yuan and X. Mao, Asymptotic stability in distribution of stochastic diğerential equations with Markovian switching, Stochastic Process. Appl. 103, no. 2 (2003) pp. 291.
  • S. Zhendong and S. G. Shuzhi, Stability theory of switched dynamical systems, Com- munications and Control Engineering Series. Springer, London, 2011.
  • C. Zhu, G. Yin and Q. S. Song, Stability of random-switching systems of diğerential equations, Quart. Appl. Math. 67, no. 2 (2009) pp. 201-220. Current address
There are 22 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Chafai Imzegouan This is me

Publication Date February 1, 2018
Published in Issue Year 2018 Volume: 67 Issue: 1

Cite

APA Imzegouan, C. (2018). STOCHASTIC STABILITY IN TERMS OF AN ASSOCIATED TRANSFER FUNCTION MATRIX FOR SOME HYBRID SYSTEMS WITH MARKOVIAN SWITCHING. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 67(1), 198-210. https://doi.org/10.1501/Commua1_0000000842
AMA Imzegouan C. STOCHASTIC STABILITY IN TERMS OF AN ASSOCIATED TRANSFER FUNCTION MATRIX FOR SOME HYBRID SYSTEMS WITH MARKOVIAN SWITCHING. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2018;67(1):198-210. doi:10.1501/Commua1_0000000842
Chicago Imzegouan, Chafai. “STOCHASTIC STABILITY IN TERMS OF AN ASSOCIATED TRANSFER FUNCTION MATRIX FOR SOME HYBRID SYSTEMS WITH MARKOVIAN SWITCHING”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67, no. 1 (February 2018): 198-210. https://doi.org/10.1501/Commua1_0000000842.
EndNote Imzegouan C (February 1, 2018) STOCHASTIC STABILITY IN TERMS OF AN ASSOCIATED TRANSFER FUNCTION MATRIX FOR SOME HYBRID SYSTEMS WITH MARKOVIAN SWITCHING. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67 1 198–210.
IEEE C. Imzegouan, “STOCHASTIC STABILITY IN TERMS OF AN ASSOCIATED TRANSFER FUNCTION MATRIX FOR SOME HYBRID SYSTEMS WITH MARKOVIAN SWITCHING”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 67, no. 1, pp. 198–210, 2018, doi: 10.1501/Commua1_0000000842.
ISNAD Imzegouan, Chafai. “STOCHASTIC STABILITY IN TERMS OF AN ASSOCIATED TRANSFER FUNCTION MATRIX FOR SOME HYBRID SYSTEMS WITH MARKOVIAN SWITCHING”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67/1 (February 2018), 198-210. https://doi.org/10.1501/Commua1_0000000842.
JAMA Imzegouan C. STOCHASTIC STABILITY IN TERMS OF AN ASSOCIATED TRANSFER FUNCTION MATRIX FOR SOME HYBRID SYSTEMS WITH MARKOVIAN SWITCHING. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2018;67:198–210.
MLA Imzegouan, Chafai. “STOCHASTIC STABILITY IN TERMS OF AN ASSOCIATED TRANSFER FUNCTION MATRIX FOR SOME HYBRID SYSTEMS WITH MARKOVIAN SWITCHING”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 67, no. 1, 2018, pp. 198-10, doi:10.1501/Commua1_0000000842.
Vancouver Imzegouan C. STOCHASTIC STABILITY IN TERMS OF AN ASSOCIATED TRANSFER FUNCTION MATRIX FOR SOME HYBRID SYSTEMS WITH MARKOVIAN SWITCHING. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2018;67(1):198-210.

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Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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