A Characterization of Passivizing Input-Output Transformations of Nonlinear MIMO Systems

This letter provides a characterization of linear passivizing input-output transformations for MIMO systems with known passivity indices. Building on recent results for SISO systems, we show that any transformation mapping an I/O $({\rho },~{\nu })$ -passive MIMO system to an I/O $(\rho ^{*},\nu ^{\star })$ -passive system can be expressed as the product of three matrices - two depending on the original and desired passivity indices, and a matrix satisfying a matrix inequality. This parameterization enables formulation of optimal passivation problems that we explore as an application example.