Title: Passivation and Cooperative Control of Equilibrium-Independent Passivity-Short Systems,
Abstract: Maximal equilibrium-independent passivity (MEIP) is a recently introduced
system property which has acquired special attention in the study of networked
dynamical systems. MEIP requires a system to be passive with respect to any
forced equilibrium configuration and the associated steady-state input-output
map must be maximally monotone. In practice, however, most of the systems are
not well behaved and possess shortage of passivity or non-passiveness in their
operation. In this paper, we consider a class of passivity-short systems,
namely equilibrium-independent passivity-short (EIPS) systems, and presents an
input-output transformation based generalized passivation approach to ensure
their MEIP properties. We characterize the steady-state input-output relations
of the EIPS systems and establish their connection with that of the transformed
MEIP systems. We further study the diffusively-coupled networked interactions
of such EIPS systems and explore their connection to a pair of dual network
optimization problems, under the proposed matrix transformation. A simulation
example is given to illustrate the theoretical results.