Preservation of dissipativity properties with the (θ,γ)-discretization
Résumé
In this talk we deal with complementarity dynamical systems, with possible state jumps, and extensions of these in the class of multivalued Lur'e dynamical systems. In view of the state of the art on time discretization of such nonsmooth systems, higher order methods are not yet available and only first order methods (implicit or explicit Euler, Paoli-Schatzman's scheme) have been shown to converge. The problem that we tackle is as follows: Given an extended theta-discretization method (referred to as the (theta, gamma)-discretization), find the class of continuous-time dissipative systems such that their discretized counterpart is still dissipative with the same storage (energy) function set, supply rate (reciprocal variables) and dissipation function. Our results consist of classifying the various forms of preservation conditions, as well as clearly characterizing 'what is' numerical dissipation, with examples on switched circuits.