Incrementally passive infinite dimensional systems with a constrained state variable

In this paper, we show that the passivity property of a linear infinite dimensional system, with respect to a given supply rate, is preserved in the presence of a saturating integrator, which restricts a one dimensional component of the state to a compact interval. The resulting nonlinear system is incrementally passive with the same supply rate. We give an application of our main result to a boundary controlled string equation, where the displacement of the string at some interior point is restricted to a compact interval.