论文标题
关于分数顺序的一类线性系统的稳定域
On the stability domain of a class of linear systems of fractional order
论文作者
论文摘要
在本文中，对Caputo正向差异操作员D^q定义的一类差异系统的稳定域S^q的形状进行了数值分析。从数值上表明，由于负基在稳定结构域表达中负基的力量，除了已知的心脏样形状外，S^q还可以呈现未验证稳定性的补充区域。分数顺序的mandelbrot图被视为一个说明性示例。此外，可以推测，对于$ Q <0.5 $，S^Q的形状不能像整数订单的情况下那样覆盖基础式Mandelbrot集合的主体。
In this paper, the shape of the stability domain S^q for a class of difference systems defined by the Caputo forward difference operator D^q of order q\in (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, S^q 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 S^q does not cover the main body of the underlying Mandelbrot set of fractional order as in the case of integer order.
