FINITE-TIME STABILITY IN MEAN FOR NABLA UNCERTAIN FRACTIONAL ORDER LINEAR DIFFERENCE SYSTEMS

Qinyun Lu, Yuanguo Zhu and Bo Li
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Qinyun Lu: School of Science, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, P. R. China
Yuanguo Zhu: School of Science, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, P. R. China
Bo Li: ��School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210023, Jiangsu, P. R. China

FRACTALS (fractals), 2021, vol. 29, issue 04, 1-12

Abstract: In this paper, the finite-time stability in mean for the uncertain fractional order linear time-invariant discrete systems is investigated. First, the uncertain fractional order difference equations with the nabla operators are introduced. Then, some conditions of finite-time stability in mean for the systems driven by the nabla uncertain fractional order difference equations with the fractional order 0 < ν < 1 are obtained by the property of Riemann–Liouville-type nabla difference and the generalized Gronwall inequality. Furthermore, based on these conditions, the state feedback controllers are designed. Finally, some examples are presented to illustrate the effectiveness of the results.

Keywords: Finite-time Stability in Mean; Uncertainty Theory; Nabla Fractional Order Difference Equations (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21500973

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