Abstract
For past twenty years, the strictly positive real condition on the rational matrix F(s) is said to be equivalent to the condition FT(-jω)+F(jω)>0 (ω∈(-∞, ∞)), however, this is not true in general. This paper defines F to be pseudo-strictly positive real if it satisfies such a condition and shows that pseudo-strictly positive real condition is equivalent to strictly positive real condition if and only if DT+D>0 or (CAR)T+CAB<0 when det |D|≠0 or D=0, respectively.
This condition is deeply connected with the adaptive control and Popov's disk criterion, so the contents of this paper should give very important informations to the researches in these fields.
