Interlacing Properties of System-Poles, System-Zeros, and Spectral-Zeros in MIMO Systems

Single-input single-output (SISO), systems with zeros interlacing poles (ZIP) have been extensively studied in the literature and received interest widely. However, ZIP property for multiple-input multiple-output (MIMO), has not pursued sufficiently. In this article, we pursue MIMO link to strict passivity. For class of that admit a symmetric state-space realization, which SISO case is equivalent ZIP, obtain sufficient conditions under too ZIP. We also present new results context “spectral-zero” system, notion plays key role many optimal control estimation problems. formulate spectral-zeros system are real, further guarantee system-zeros, spectral-zeros, system-poles all interlaced systems.