Robust stability criterion for perturbed singular systems of linearized differential equations

In this article, we consider a class of singular linear systems of differential equations whose coefficients are constant matrices, and study the response of its stability after a perturbation is applied into the system. We use a linear fractional transformation and through its properties we provide a practical test for robust stability. This test requires only the knowledge of the invariants of the initial system. This means it can be used without resorting to any further processes of computations to obtain invariants of any other perturbed system. Finally, numerical examples are given to support and discuss practical applications of the proposed theory.