不协调分数微分方程系统的稳定性检验算法
A Stability Testing Algorithm for Incommensurate Fractional Differential Equation Systems
AI总结：
本文提出了一种用于判断分数阶微分方程系统是否渐近稳定的算法，特别针对各方程阶数不一致的不协调情况，通过数值线性代数的方法简化了传统方法。
摘要：
我们考虑确定给定的分数阶微分方程系统是否（渐近）稳定的问題。特别是，我们接受每个组成部分方程可能有自己阶数的情况，即讨论所谓的不协调情况。利用基于数值线性代数的想法，我们提出了一种算法，该算法可以用来回答这个问题，比已知的方法要简单得多。我们详细讨论了线性问题中阶数比为有理数的情况，并指出如何利用已知技术将我们的发现应用于具有任意阶数的一般非线性问题。提供了一个MATLAB实现。
英文摘要：
We consider the question of determining whether or not a given system of fractional-order differential equations is (asymptotically) stable. In particular, we admit systems where each constituent equation may have its own order, independent of the order of the other equations in the system, i.e. we discuss the so-called incommensurate case. Exploiting ideas based in numerical linear algebra, we present an algorithm that can be used to answer this question that is much simpler than known methods. We discuss in detail the case of linear problems where the ratios of orders are rational and indicate how known techniques can be used to apply our findings also to general nonlinear problems with arbitrary orders. A MATLAB implementation of the code is provided.
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