Spectral conditions for strict positive realness of reciprocal descriptor systems

Non-Hamiltonian generalized necessary and sufficient spectral conditions for strict positive realness of reciprocal systems assuming a regular index-one linear descriptor realization are proposed. The spectral conditions prescribe the positivity of the Hermitian part of the system transfer function matrix along the imaginary axis and the behavior upon its rank deficiency at infinity by prohibiting the real negative eigenvalues and requiring semisimple zero eigenvalues of a fixed algebraic multiplicity, respectively.