A Stability Testing Algorithm for Incommensurate Fractional Differential Equation Systems
For researchers working on stability analysis of fractional-order systems, this offers a more straightforward computational approach compared to existing methods.
The paper presents a simpler algorithm for testing asymptotic stability of incommensurate fractional differential equation systems, leveraging numerical linear algebra. The method handles rational order ratios and extends to nonlinear problems, with a MATLAB implementation provided.
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.