## Section: New Results

### Structural Analysis of Multi-Mode DAEs

Differential Algebraic Equation (DAE) systems constitute the
mathematical model supporting physical modeling languages such as
Modelica or Simscape. Unlike Ordinary Differential Equations, or
ODEs, they exhibit subtle issues because of their implicit
*latent equations* and related *differentiation index*.
Multi-mode DAE (mDAE) systems are much harder to deal with, not only
because of their mode-dependent dynamics, but essentially because of
the events and resets occurring at mode transitions. Unfortunately,
the large literature devoted to the numerical analysis of DAEs do
not cover the multi-mode case. It typically says nothing about mode
changes. This lack of foundations cause numerous difficulties to
the existing modeling tools. Some models are well handled, others
are not, with no clear boundary between the two classes.
InĀ [11], we develop a comprehensive
mathematical approach to the *structural analysis* of mDAE
systems which properly extends the usual analysis of DAE systems. We
define a constructive semantics based on nonstandard analysis and
show how to produce execution schemes in a systematic way. This work
has been accepted for presentation at the HSCC 2017
conferenceĀ [19] in April 2017.