  Soft-reset controllers are introduced as a way to approximate hard-reset
controllers. The focus is on implementing reset controllers that are (strictly)
passive and on analyzing their interconnection with passive plants. A passive
hard-reset controller that has a strongly convex energy function can be
approximated as a soft-reset controller. A hard-reset controller is a hybrid
system whereas a soft-reset controller corresponds to a differential inclusion,
living entirely in the continuous-time domain. This feature may make soft-reset
controllers easier to understand and implement. A soft-reset controller
contains a parameter that can be adjusted to better approximate the action of
the hard-reset controller. Closed-loop asymptotic stability is established for
the interconnection of a passive soft-reset controller with a passive plant,
under appropriate detectability assumptions. Several examples are used to
illustrate the efficacy of soft-reset controllers.
