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给出了Caputo分数阶导数的若干新性质,并利用这些性质,建立了分数阶非线性系统渐近稳定的一个充分条件。利用Backsteping方法,针对一类分数阶非线性三角系统,提出了一种状态反馈控制器的设计方法。最后用例子说明理论结果的有效性。
Some new properties of Caputo fractional derivatives are given. By using these properties, a sufficient condition for the asymptotic stability of fractional nonlinear systems is established. Using Backsteping method, a kind of state feedback controller design method is proposed for a class of fractional order nonlinear trigonometric system. Finally, an example is given to illustrate the validity of the theoretical results.