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. Necessary and sufficient conditions for disspativity preservation after the time-discretization are derived (preservation of the stioarge function, the supply rate and the dissipation function). The possible state jumps are also analyzed [46] . It is shown that excepted when the system is state lossless and theta = 0.5, the conditions are very stringent.

Lur'e systems are quite popular in Automatic Control since the fifties. Set-valued Lur'e systems possess a static feedback nonlinearity that is a multivalued function. This study consists in the mathematical analysis (existence and uniqueness of solutions) and the stability analysis (Lyapunov stability, invariance principle) of classes of set-valued Lur'e systems, with applications in complementarity dynamical systems, relay systems, mechanical systems with dry friction, electrical circuits, etc.Our works in this field started in [40] . The results in [42] extend those in [41] with an accurate characterization of the maximal monotonicity of the central operator of these systems. Concrete and verifiable criteria are provided for the above classes (complementarity, relay systems).