Differential Equivalence for Linear Differential Algebraic Equations

Differential-algebraic equations (DAEs) are a widespread dynamical model that describes continuously evolving quantities defined with differential equations, subject to constraints expressed through algebraic relationships. As such, DAEs arise in many fields ranging from physics, chemistry, and engineering. In this article, we focus on linear DAEs, develop theory for their minimization up an equivalence relation. We present equivalence, which relates DAE variables have equal solutions at all time points (thus requiring them start initial conditions) extends the line of research bisimulations developed Markov chains ordinary equations. apply our results electrical engineering domain, showing can explain invariances certain networks as well analyze could not be originally treated due size.