Stability Criterion of a Class of Non-causal Systems of Differential Equations

In this paper, we focus on a class of non-causal systems of differential equations, namely systems the variables of which can depend not only from the current or past time, but also from future time. For this type of systems, we study their solutions and present new and easily testable conditions under which any state of the system is stable. The stability analysis of a future-state-dependent set of differential equations has its relevance also in practical applications. Numerical examples, as well as an application in electric power engineering, are provided to justify our theory.