Relationships between positive real, passive dissipative, & positive systems

This paper shows how: i) (strongly) positive real; ii) (asymptotically stable) dissipative (strictly-input) passive; and iii) (L^m₂-stable strictly) positive; continuous time system definitions are equivalent for linear time invariant (LTI) systems. In parallel this paper shows how: i) (strictly) positive real; ii) (asymptotically stable) dissipative (strictly-input) passive; and iii) (l^m₂-stable strictly) positive; discrete time system definitions are equivalent for LTI systems. A frequency test is derived to determine if a single input single output LTI system is strictly output passive. Finally, the necessary conditions to synthesize a system which is both passive and stable but neither strictly-input passive nor strictly-output passive are presented.