Sensitivity of Schur stability of systems of linear difference equations with periodic coefficients

Abstract

In this study, the sensitivity of Schur stability of systems of linear difference equations with periodic coefficients has been examined. The modified continuity theorems based on the parameters w₁ and w₂ have been given for Schur stability of linear difference equations with periodic coefficients. Also, new results have been obtained for sensitivity ofw w*Schur stability based on the parameters  w₁ and w₂. All the results have been applied to linear difference equations with periodic coefficients with order k. kD*ball regions of Schur stability and w*Schur stability have been determined. In addition, the results related to kD*ball regions have been given.

Keywords

• difference equation systems,monodromy matrix,periodic coefficients,Schur stability parameters,practical Schur stability

Kaynakça

1. Akın O. and Bulgak H., Linear difference equations and stability theory, Konya Selcuk University, Research Center of Applied Mathematics, (1998). (in Turkish)
2. Elaydi S.N., An introduction to difference equations, New York; Springer-Verlag, (1999).
3. Godunov S.K., Modern aspects of linear algebra, RI: American Mathematical Society, Translation of Mathematical Monographs 175. Providence, (1998).
4. Bulgak H., “Pseudoeigenvalues, spectral portrait of a matrix and their connections with different criteria of stability”, Error Control and Adaptivity in Scientific Computing, NATO Science Series, Series C: Mathematical and Physical Sciences, in: H. Bulgak and C. Zenger(Eds), Kluwer Academic Publishers, (1999), 536, 95-124.
5. Voicu M. and Pastravanu O., “Generalized matrix diagonal stability and linear dynamical systems”, Linear Algebra and its Applications, (2006), 419, 299-310.
6. Wilkinson J. H., “The algebraic eigenvalue problem”, Clarendom Pres Oxford, (1965).
7. A.Ya. Bulgakov (H. Bulgak), “An effectively calculable parameter for the stability quality of systems of linear differential equations with constant coefficients”, Siberian Math. J. (1980), 21, 339–347.
8. Aydın K., Bulgak H. and Demidenko G. V., “Numeric characteristics for asymptotic stability of solutions to linear difference equations with periodic coefficients”, Siberian Mathematical Journal, (2000), 41, 1005-1014.

9. Aydın K., “Schur stable difference equations with constant coefficients”, Zonguldak Karaelmas University, Integral Geometry and Inverse Problem Workshop, May 08-09,(2004), Zonguldak.
10. Duman A. and Aydın K., “Sensitivitiy of linear difference equation systems with constant coefficients”, Scientific Research and Essays, (2011), 6(28) 5846-5854.
11. Aydın K., Bulgak H. and Demidenko G. V., “Continuity of numeric characteristics for asymptotic stability of solutions to linear difference equations with periodic coefficients”, Selc¸uk Journal Applied Mathematics, (2001), 2, 5-10.
12. Aydın K., Bulgak H. and Demidenko G. V., “Asymptotic stability of solutions to perturbed linear difference equations with periodic coefficients”, Siberian Mathematical Journal, (2002), 43, 389-401.
13. Duman A. and Aydın K., “Sensitivity of Schur stability of monodromy matrix”, Applied Mathematics and Computation, (2011), 217, 6663–6670.
14. Roger AH., Charles RJ., Matrix analysis, Cambridge University Press, Cambridge, (1999).
15. Bulgak H. and Eminov D., “Computer dialogue system MVC”, Selc¸uk Journal Applied Mathematics, (2001), 2, 17-38.