一种分数阶线性系统求解方法

针对在实际情况中应用越来越广泛的分数阶微积分系统,首先介绍了分数阶微积分定义及其基本性质.由于分数阶系统的特征方程一般说来不是真正的多项式,它是一个具有复变量的分数阶指数的伪多项式,可以将其近似化成高阶的整数阶系统,然后运用整数阶系统的控制方法去研究、分析.最后提出了一种基于分数阶微积分定义分析分数阶线性系统的方法,并用具体实例验证了该方法的有效性.

A Solution to Fractional Order Linear Syetems

Defines the factional order calculus and clarifies its basic characteristics because the fractional order systems have been used much wider than before in application.Generally the characteristic equation of a fractional order system is not a real polynomial but a pseudo-polynomial function of complex variable with fractional exponent,which can be approximated and converted into a high-order integral exponent system so as to study it by existing control approaches.A method is thus proposed to analyze fractional order linear systems on the basis of the definition of fractional calculus,and its effectiveness is verified via a simulation example.