Feasibility Conditions for Indirect Feedback Passivation

This paper studies feasibility conditions for making a single-input-single-output system non-strictly indirectly passive (positive real) with respect to an external input by state feedback, which is an extension from the strictly positive real feasibility conditions but is more challenging. Positive real feasibility conditions for systems without zero dynamics and systems with zero dynamics but relative degree less than three are derived, respectively. For relative degree three systems, necessary conditions are given. The asymptotic stability of the closed-loop systems is also analyzed, since the positive real property itself only guarantees that the systems are stable rather than asymptotically stable. Two examples are given to verify the theoretical results.