MIMO systems properties preservation under SPR substitutions

The preservation of some control-oriented positive real properties (passivity, positivity, bounded realness, as well as input-output behavior) in multi-input multi-output transfer functions is studied, when performing substitutions (of the complex Laplace variable s) by a particular class of rational strictly positive real (SPR) functions, the so-called SPR functions of zero relative degree (SPR0 functions). We also consider here the preservation of stability properties of a class of unforced linear time-invariant systems with memoryless (possibly time-varying nonlinear) input depending on the system output.