Generalized Hilbert Networks
Václav Doležal · SIAM Journal on Control and Optimization · 1976
In the paper a general model of a nonlinear network is constructed. The model considered is a generalization of the Hilbert network introduced in [1]. It is assumed that the generalized Hilbert network consists of at most countably many lumped elements described by nonlinear multivalued operators from a subset of a Hilbert space $\mathcal{H}$ into $\mathcal{H}$. Several theorems are proved on the existence and uniqueness of the solution of the network. Also, conditions are established under which the admittance operator of a generalized Hilbert network is causal.