  SISO passive systems with just one type of memory/storage element (either
only inductive or only capacitative) are known to have real poles and zeros,
and further, with the zeros interlacing poles (ZIP). Due to a variety of
definitions of the notion of a system zero, and due to other reasons described
in the paper, results involving ZIP have not been extended to MIMO systems.
This paper formulates conditions under which MIMO systems too have interlaced
poles and zeros.
  This paper next focusses on the notion of a `spectral zero' of a system,
which has been well-studied in various contexts: for example, spectral
factorization, optimal charging/discharging of a dissipative system, and even
model order reduction. We formulate conditions under which the spectral zeros
of a MIMO system are real, and further, conditions that guarantee that the
system-zeros, spectral zeros, and the poles are all interlaced.
  The techniques used in the proofs involve new results in Algebraic Riccati
equations (ARE) and Hamiltonian matrices, and these results help in formulating
new notions of positive-real balancing, and inter-relations with the existing
notion of positive-real balancing; we also relate the positive-real singular
values with the eigenvalues of the extremal ARE solutions in the proposed
`quasi-balanced' forms.
