Stability and Passivity for a Class of Distributed Port-Hamiltonian Networks

We consider a class of infinite dimensional (distributed) dissipative port-Hamiltonian systems whose dynamics is generated by a block operator in a Hilbert space that has a bounded dissipative diagonal and a possibly unbounded skew-adjoint off-diagonal. Sufficient conditions for the strong and exponential stability of the underlying semigroup generators are provided along with the derivation of a power-balance equation for classical solutions of the associated boundary control system. Furthermore, we consider interconnections of several such distributed pH systems and show that Kirchhoff-type interconnections preserve the underlying structure of the considered block operators. The results are illustrated for a power network connecting several prosumers via distributed transmission lines that are modeled based on the telegraph equations.