摘要
介绍了Riemann-Liouville和Caputo分数微积分的定义及其部分性质。给出了分数阶线性定常微分方程的一般定义形式,并指出它是整数阶线性定常微分方程的推广。给出分数阶线性定常系统的传递函数和状态方程描述,并与整数阶线性定常系统的传递函数和状态方程作一比较,指出它们的异同点。运用拉普拉斯变换推导出其两种求解方法:直接求解法和状态空间法。最后给出一个实例说明这两种方法的有效性。
An introduction of the definitions of Riemann-Liouville and Caputo fractional calculus is given as well as some of their properties. The general form of fractional linear time-invariant (LTI) equations is proposed, and it is pointed out that they are the generalizations of integer LTI equations. The transfer function and the state-space representation are given for fractional LTI systems, and a comparison is made with integer LTI systems, and their differences and similarities are also pointed out. Two solving methods are deduced using Laplace transform: the direct solving method and the state-space method. Finally an example is given to show the effectiveness of the two methods aforementioned.
出处
《系统仿真学报》
CAS
CSCD
2004年第4期810-812,共3页
Journal of System Simulation
基金
上海市科技发展基金资助项目(011607033)
关键词
分数微积分
分数阶微分方程
分数阶微分系统
系统建模
fractional calculus
fractional-order differential equations
fractional-order differential systems
system modeling
