Symmetry structures in linear physical systems

Physical systems with symmetry structures arise abundantly in applications, often admit scalable control laws, and are important building blocks in synthesis problems. The present paper focusses on linear reciprocal systems and input–output Hamiltonian systems. Their characterization is studied from an input–output, as well as from a state space point of view. Geometrically both are seen to define Lagrangian subspaces with corresponding generating functionals. Furthermore, the relation of reciprocity and input–output Hamiltonian structure with time reversibility is analyzed.