  Equilibrium-independent passive-short (EIPS) systems are a class of systems
that satisfy a passivity-like dissipation inequality with respect to any forced
equilibria with non-positive passivity indices. This paper presents a geometric
approach for finding a passivizing transformation for such systems, relying on
their steady-state input-output relation and the notion of projective quadratic
inequalities (PQIs). We show that PQIs arise naturally from passivity-shortage
characteristics of an EIPS system, and the set of their solutions can be
explicitly expressed. We leverage this connection to build an input-output
mapping that transforms the steady-state input-output relation to a monotone
relation, and show that the same mapping passivizes the EIPS system. We show
that the proposed transformation can be implemented through a combination of
feedback, feed-through, post- and pre-multiplication gains. Furthermore, we
consider an application of the presented passivation scheme for the analysis of
networks comprised of EIPS systems. Numerous examples are provided to
illustrate the theoretical findings.
