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Lyapunov functions for nabla discrete fractional order systems
Yiheng Wei1, Yuquan Chen1, Tianyu Liu1
1Department of Automation, University of Science and Technology of China, Hefei, 230026, China.
Abstract:
This paper focuses on the fractional difference of Lyapunov functions related to Riemann-Liouville, Caputo and Grünwald-Letnikov definitions. A new way of building Lyapunov functions is introduced and then five inequalities are derived for each definition. With the help of the developed inequalities, the sufficient conditions can be obtained to guarantee the asymptotic stability of the nabla discrete fractional order nonlinear systems. Finally, three illustrative examples are presented to demonstrate the validity and feasibility of the proposed theoretical results.
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