## Section: Partnerships and Cooperations

### International Initiatives

#### Inria International Partners

##### Informal International Partners

We have a long standing informal collaboration with Martin Otter (DLR, Munich, Germany) and Hilding Helmqvist (Mogram AB, Lund, Sweden). In 2019, this fruitful collaboration has resulted in one publication [7]. The publication draws links between two radically different, but equivalent approaches to the same problem: the impulsive behavior of some multimode DAE, when it is switching from one mode to another. The first approach relies on a transformation of the multimode DAE system to a special index one form, for which state-jumps are proved to be solution of a system of algebraic equations relating right limits to left limits. The second approach builds on the use of nonstandard analysis, combined with the heritage of synchronous programming languages, particularly on the concept of constructive semantics. This gives a formulation of the state-jumps, as a system of difference equations, with an infinitesimal time-step. The latter approach is more general than the former, in the sense that impulsive behavior can be characterized for a larger class of multimode DAE systems. Yet, both approaches coincide on a restricted class of multimode DAEs.