Conservativity and Time-Flow Invertibility of Boundary Control Systems

We give sufficient and necessary conditions for a boundary control system (in the sense of Salamon) to define a Livšic – Brodskiĭ operator node; i.e. a linear (scattering) conservative system. This appears to be a special case of a more general result involving time-flow invertible linear systems. Finally, an example involving the wave equation is considered.