Section: New Results

Dissipativity preserving methods

Participants : Vincent Acary, Bernard Brogliato.

This work concerns the analysis of so-called theta-methods applied to linear complementarity systems that are dissipative (in the sense of Willems). Necessary and sufficient conditions for dissipativity preservation after the time-discretization are derived (preservation of the storage function, the supply rate and the dissipation function). The possible state jumps are also analyzed [57] . It is shown that excepted when the system is state lossless and theta = 0.5, the conditions for dissipativity preservation are very stringent. In this article we also provide (for the first time, to the best of our knowledge) a rigorous definition of numerical dissipation, which remained until now a vague notion in numerical analysis.