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Year 2020, Volume: 8 Issue: 2, 423 - 428, 27.10.2020

Ayşegül Keten Ahmet Duman Kemal Aydın

Abstract

References

  • [1]  Ö. Akın and H. Bulgak, Linear Difference Equations and Stability Theory, Selçuk University, Research Center of Applied Mathematics, Konya, 1998. in Turkish
  • [2] K. Aydın, Condition number for asymptotic stability of periodic ordinary differential equation systems, Ph.D. thesis, Institute of Science and Technology, Selçuk University (1995), in Turkish.
  • [3] D. Betounes, Differential Equations: Theory and Applications, Springer, 2nd ed., 2010.
  • [4] H. Bulgak, Pseudoeigenvalues, spectral portrait of a matrix and their connections with different criteria of stability, in Error Control and Adaptivity in Scientific Computing, eds. H. Bulgak and C. Zenger, NATO Science Series, Series C: Mathematical and Physical Sciences, (Kluwer Academic Publishers, Dordrecht) 536 (1999): 95-124.
  • [5] A.Ya. Bulgakov, An effectively calculable parameter for the stability quality of systems of linear differential equations with constant coefficients, Sib. Math. J. 21 (1980), 339-347.
  • [6] A.Ya. Bulgakov and S.K. Godunov, Circle dichotomy of the matrix spectrum, Sib. Math. J. 29 (1988), no. 5, 59-70.
  • [7] A.Ya. Bulgakov, Matrix Computations with Guaranteed Accuracy in Stability Theory, Selçuk University, The Research Center of Applied Mathematics, Konya, 1995.
  • [8] A. Duman and K. Aydın, Sensitivity of Schur stability of linear difference equation systems with constant coefficients, Sci. Res. Essays 6 (2011), no. 28, 5846-5854.
  • [9] A. Duman and K. Aydın, Sensitivity of Hurwitz stability of linear differential equation systems with constant coefficients, Int. J. Geom. Methods Mod. Phys. 14 (2017), no. 6.
  • [10] S.N. Elaydi, An Introduction to Difference Equations. Springer, Verlag, New York, 1999.
  • [11] S.K. Godunov, Modern Aspects of Linear Algebra, RI: American Mathematical Society, Translation of Mathematical Monographs 175. Providence, 1998.
  • [12] Li, Z., Y. Li, C. Wu and B. Chen, Study on bifurcation behaviors and stabilization in current mode controlled Buck converter, Power System Protection and Control 44 (2016) no. 18, 54-60.
  • [13] G.L. Kenneth and P.W. Likins, Infinite determinant methods for stability analysis of periodic- coefficient differential equations, AIAA Journal 8 (1970), no. 4, 680-686.
  • [14] J.R. Wilson, Linear System Theory, New Jersey, Prentice Hall, Second Edition, 1996.
  • [15] P.T. Jianjun and J. Wang, Some results in Floquet theory, with application to periodic epidemic models, Appl. Anal. 94 (2014), no. 6, 1128-1152.
  • [16] W. Walter, Ordinary Differential Equations, Springer-Verlag, New York, 1998.
  • [17] J.H. Wilkinson, The Algebraic Eigenvalue Problem, Clarendon Press, Oxford, 1965.
  • [18] A. Neubauer, J. Freudenberger, V. Kühn, Coding Theory: Algorithms, Architectures, and Ap- plications, England, 2007.

Sensitivity of Hurwitz Stability of Linear Differential Equation Systems with Periodic Coefficients

Year 2020, Volume: 8 Issue: 2, 423 - 428, 27.10.2020

Ayşegül Keten Ahmet Duman Kemal Aydın

Abstract

By using Hurwitz stability of a linear differential equation system (in short, LDES) with constant coefficients, and using Schur stability of a linear difference equation system (in short, LDIES) with constant coefficients, we have obtained two new continuity theorems for sensitivity of Hurwitz stability of a LDES with periodic coefficients. Our approach to the theorems is based on Floquet theory. Also, we have determined stability regions and supported the obtained results by a numerical example.

Keywords

differential equations Floquet theory Hurwitz stability sensitivity Schur stability

References

  • [1]  Ö. Akın and H. Bulgak, Linear Difference Equations and Stability Theory, Selçuk University, Research Center of Applied Mathematics, Konya, 1998. in Turkish
  • [2] K. Aydın, Condition number for asymptotic stability of periodic ordinary differential equation systems, Ph.D. thesis, Institute of Science and Technology, Selçuk University (1995), in Turkish.
  • [3] D. Betounes, Differential Equations: Theory and Applications, Springer, 2nd ed., 2010.
  • [4] H. Bulgak, Pseudoeigenvalues, spectral portrait of a matrix and their connections with different criteria of stability, in Error Control and Adaptivity in Scientific Computing, eds. H. Bulgak and C. Zenger, NATO Science Series, Series C: Mathematical and Physical Sciences, (Kluwer Academic Publishers, Dordrecht) 536 (1999): 95-124.
  • [5] A.Ya. Bulgakov, An effectively calculable parameter for the stability quality of systems of linear differential equations with constant coefficients, Sib. Math. J. 21 (1980), 339-347.
  • [6] A.Ya. Bulgakov and S.K. Godunov, Circle dichotomy of the matrix spectrum, Sib. Math. J. 29 (1988), no. 5, 59-70.
  • [7] A.Ya. Bulgakov, Matrix Computations with Guaranteed Accuracy in Stability Theory, Selçuk University, The Research Center of Applied Mathematics, Konya, 1995.
  • [8] A. Duman and K. Aydın, Sensitivity of Schur stability of linear difference equation systems with constant coefficients, Sci. Res. Essays 6 (2011), no. 28, 5846-5854.
  • [9] A. Duman and K. Aydın, Sensitivity of Hurwitz stability of linear differential equation systems with constant coefficients, Int. J. Geom. Methods Mod. Phys. 14 (2017), no. 6.
  • [10] S.N. Elaydi, An Introduction to Difference Equations. Springer, Verlag, New York, 1999.
  • [11] S.K. Godunov, Modern Aspects of Linear Algebra, RI: American Mathematical Society, Translation of Mathematical Monographs 175. Providence, 1998.
  • [12] Li, Z., Y. Li, C. Wu and B. Chen, Study on bifurcation behaviors and stabilization in current mode controlled Buck converter, Power System Protection and Control 44 (2016) no. 18, 54-60.
  • [13] G.L. Kenneth and P.W. Likins, Infinite determinant methods for stability analysis of periodic- coefficient differential equations, AIAA Journal 8 (1970), no. 4, 680-686.
  • [14] J.R. Wilson, Linear System Theory, New Jersey, Prentice Hall, Second Edition, 1996.
  • [15] P.T. Jianjun and J. Wang, Some results in Floquet theory, with application to periodic epidemic models, Appl. Anal. 94 (2014), no. 6, 1128-1152.
  • [16] W. Walter, Ordinary Differential Equations, Springer-Verlag, New York, 1998.
  • [17] J.H. Wilkinson, The Algebraic Eigenvalue Problem, Clarendon Press, Oxford, 1965.
  • [18] A. Neubauer, J. Freudenberger, V. Kühn, Coding Theory: Algorithms, Architectures, and Ap- plications, England, 2007.
There are 18 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Ayşegül Keten

Ahmet Duman

Kemal Aydın 0000-0002-5843-3058

Publication Date October 27, 2020
Submission Date September 29, 2020
Acceptance Date October 26, 2020
Published in Issue Year 2020 Volume: 8 Issue: 2

Cite

APA Keten, A., Duman, A., & Aydın, K. (2020). Sensitivity of Hurwitz Stability of Linear Differential Equation Systems with Periodic Coefficients. Konuralp Journal of Mathematics, 8(2), 423-428.
AMA Keten A, Duman A, Aydın K. Sensitivity of Hurwitz Stability of Linear Differential Equation Systems with Periodic Coefficients. Konuralp J. Math. October 2020;8(2):423-428.
Chicago Keten, Ayşegül, Ahmet Duman, and Kemal Aydın. “Sensitivity of Hurwitz Stability of Linear Differential Equation Systems With Periodic Coefficients”. Konuralp Journal of Mathematics 8, no. 2 (October 2020): 423-28.
EndNote Keten A, Duman A, Aydın K (October 1, 2020) Sensitivity of Hurwitz Stability of Linear Differential Equation Systems with Periodic Coefficients. Konuralp Journal of Mathematics 8 2 423–428.
IEEE A. Keten, A. Duman, and K. Aydın, “Sensitivity of Hurwitz Stability of Linear Differential Equation Systems with Periodic Coefficients”, Konuralp J. Math., vol. 8, no. 2, pp. 423–428, 2020.
ISNAD Keten, Ayşegül et al. “Sensitivity of Hurwitz Stability of Linear Differential Equation Systems With Periodic Coefficients”. Konuralp Journal of Mathematics 8/2 (October 2020), 423-428.
JAMA Keten A, Duman A, Aydın K. Sensitivity of Hurwitz Stability of Linear Differential Equation Systems with Periodic Coefficients. Konuralp J. Math. 2020;8:423–428.
MLA Keten, Ayşegül et al. “Sensitivity of Hurwitz Stability of Linear Differential Equation Systems With Periodic Coefficients”. Konuralp Journal of Mathematics, vol. 8, no. 2, 2020, pp. 423-8.
Vancouver Keten A, Duman A, Aydın K. Sensitivity of Hurwitz Stability of Linear Differential Equation Systems with Periodic Coefficients. Konuralp J. Math. 2020;8(2):423-8.
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