Residue calculus and partial fraction expansion are applied to invert the nabla Laplace transform, reducing the inverse contour integral to sums over poles or to transform-pair tables.
Lyapunov functions for nabla discrete fractional order systems
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abstract
This paper focuses on the fractional difference of Lyapunov functions related to Riemann-Liouville, Caputo and Grunwald-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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math.GM 1years
2019 1verdicts
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Analytical calculation of the inverse nabla Laplace transform
Residue calculus and partial fraction expansion are applied to invert the nabla Laplace transform, reducing the inverse contour integral to sums over poles or to transform-pair tables.