Well-posedness and passivity for a class of bilinear control systems

We study an abstract class of bilinear infinite-dimensional systems that arises in various applications, including district heating systems and quantum control. First, we analyze the existence of mild and classical solutions for abstract bilinear systems with admissible input operators in Banach spaces and study continuous dependence on the data. When the underlying space is a Hilbert space, these results are used to show passivity for a suitably defined co-located output and for mild solutions. The results are applied to the bilinear Schrödinger equation, the Fokker–Planck equation, and a district heating or cooling pipe.