Geometric Method for Passivation and Cooperative Control of Equilibrium-Independent Passive-Short Systems

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