On the Stability Domain of a Class of Linear Systems of Fractional Order

被引：4
|
作者：
Danca, Marius-F. [1 ,2 ]
机构：
[1] Babes Bolyai Univ, UBB Inst, STAR, Cluj Napoca 400084, Romania
[2] Romanian Inst Sci & Technol, Cluj Napoca 400487, Romania
来源：
FRACTAL AND FRACTIONAL | 2023年 / 7卷 / 01期
关键词：
Caputo forward difference operator; stability domain; matignon criterion; Mandelbrot set of fractional order; ASYMPTOTIC STABILITY;
D O I：
10.3390/fractalfract7010049
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, the shape of the stability domain Sq for a class of difference systems defined by the Caputo forward difference operator delta(q) of order q is an element of (0,1) is numerically analyzed. It is shown numerically that due to of power of the negative base in the expression of the stability domain, in addition to the known cardioid-like shapes, Sq could present supplementary regions where the stability is not verified. The Mandelbrot map of fractional order is considered as an illustrative example. In addition, it is conjectured that for q < 0.5, the shape of Sq does not cover the main body of the underlying Mandelbrot set of fractional order as in the case of integer order.
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页数：10
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