Symmetries in special classes of passive state/signal systems

This article is devoted to a further development of the passive linear continuous time invariant s/s (state/signal) systems theory. The main focus is on the connections between certain symmetry properties (such as reality and reciprocity) of the external characteristics of a s/s system and the respective symmetry of the evolution of the inner state of the system. These connections are investigated for the following classes of passive s/s systems: simple conservative, controllable energy preserving, observable co-energy preserving, optimal, ⁎-optimal, and minimal balanced, out of which the last three are introduced and studied here for the first time. In each of these six classes a s/s system is defined by its external characteristics up to unitary similarity. Our results are connected with the respective results in the input/state/output systems theory, where the external characteristics of a system are scattering, impedance or transmission matrices.