Stability regions for linear fractional differential systems and their discretizations

作者：Cermak Jan^*; Kisela Tomas; Nechvatal Ludek

来源：Applied Mathematics and Computation, 2013, 219(12): 7012-7022.

DOI：10.1016/j.amc.2012.12.019

• Fractional differential system
• Fractional difference system
• Asymptotic stability
• Laplace transform

This paper concerns with basic stability properties of linear autonomous fractional differential and difference systems involving derivative operators of the Riemann-Liouville type. We derive stability regions for special discretizations of the studied fractional differential systems including a precise description of their asymptotics. Our analysis particularly shows that discretizations based on backward differences can retain the key qualitative properties of underlying fractional differential systems. In addition, we introduce the backward discrete Laplace transform and employ some of its properties as the main proof tool.

• 出版日期2013-2-15