Complementarity and passivity for piecewise linear feedback systems

Piecewise linear feedback systems composed by a dynamical linear time invariant system closed in feedback through a static piecewise linear mapping are considered. By representing the closed loop system in the affine complementarity form, passivity is exploited in order to prove existence of absolute continuous solutions and stability of the equilibria. Assuming passivity of the open loop system and using results on equivalent circuit representations of piecewise linear mappings, conditions on the static feedback connection for preserving passivity in closed loop, are proposed and discussed.