Sensitivity of Schur Stability of the $k-th$ Order Difference Equation System $y(n+k)=Cy(n)$

Yıl 2018, Cilt: 6 Sayı: 1, 98 - 101, 15.04.2018

Ahmet Duman Gülnur Çelik Kızılkan Kemal Aydın

Öz

In this study, it is investigated that the Schur stable difference equation systems $y(n+k)=Cy(n)$ under which perturbations remains Schur stable. Some continuity theorems of the first order systems in the literature are re-expressed for the $k-th$ order system $y(n+k)=Cy(n)$. All the results obtained are also supplemented by numerical examples.

Anahtar Kelimeler

Schur stability, difference equations, sensitivity, perturbation systems, condition number

Kaynakça

• [1] Akın, Ö., Bulgak, H.,Linear difference equations and stability theory, Selc¸uk University, Research Center of Applied Mathematics, Konya(in Turkish), 1998.
• [2] H. Bulgak, 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: Bulgak H and Zenger C (Eds), Kluwer Academic Publishers, Vol: 536 (1999), 95-124.
• [3] Godunov, S. K., Modern aspects of linear algebra, RI: American Mathematical Society, Translation of Mathematical Monographs 175. Providence, 1998.
• [4] A.Duman and K. Aydın, Sensitivity of Schur stability of systems of linear difference equations with constant coefficients, Scientific Research and Essays, Vol: 6, No. 28 (2011),5846–5854.
• [5] A.Y.Bulgakov, An effectively calculable parameter for the stability quality of systems of linear differential equations with constant coefficients. Sib. Math. J., Vol: 21 (1980),339-347.
• [6] A.Duman and K. Aydın, Sensitivity of Schur stability of monodromy matrix, Applied Mathematics and Computation, Vol: 217, No. 15 (2011),6663–6670.
• [7] A.Duman and K. Aydın, Some Results on the Sensitivity of Schur Stability of Linear Difference Equations with Constant Coefficients, Konuralp Journal of Mathematics, Vol: 2, No: 2 (2014), 22–34.
• [8] T. M. Apostol, Explicit Formulas for Solutions of the Second-Order Matrix Differential Equation Y00 = AY, The American Mathematical Monthly, Vol: 82, No. 2 (Feb., 1975)(1975), 159-162.
• [9] H. Bulgak and D. Eminov D ,Computer dialogue system MVC. Selc¸uk J. Appl. Math., Vol: 2 (2001), 17-38 (available from http://www5.in.tum.de/selcuk/sjam012203.html).