On the Equivalence Between Strict Positive Realness and Strict Passivity of Linear Systems

This technical note presents a proof of the equivalence between the strict passivity of linear time-invariant (LTI) controllable and observable systems and the strict positive realness of their transfer function matrices, where the direct feedthrough D is possibly a non-zero matrix. Although both properties guarantee asymptotic stability, the former is a time domain condition and the latter is a frequency domain concept. A numerical example illustrates our main results.