**6. Conclusions**

This paper relies on partitioned Hermitian matrices and Cauchy's interlacing theorem and the associated stability results. Based on the fact that convergen<sup>t</sup> matrices are a discrete counterpart of stability matrices, the results presented above are then extended to sequences of convergen<sup>t</sup> matrices. Then, an example of a SIR-type epidemic model continuous-time consisting of intercommunity clusters is discussed relative to the previously given stability theoretic results under the proposed framework based on Cauchy's interlacing theorem, and which may be of interest for healthcare management. Later, a dynamic linear discrete aggregation model is discussed, which involves output delay and linear output feedback, and which can be also be reformulated for linear-state feedback by identifying state and output, that is, by taking the output matrix equal to the identity, provided that the state is available for measurement. The studied aggregation model is built through the successive incorporation of discrete subsystems with particular coupled dynamics. Stabilizing decentralized controllers are proposed and discussed for this type of aggregation model.

**Author Contributions:** The author contributed by himself the whole manuscript.

**Funding:** This research has been jointly supported by the Spanish Government and the European Commission with Grants RTI2018-094336-B-I00 (MINECO/FEDER, UE) and DPI2015-64766-R (MINECO/FEDER, UE).

**Acknowledgments:** The author is grateful to the Spanish Government for Grants RTI2018-094336-B-I00 and DPI2015-64766-R (MINECO/FEDER, UE).

**Conflicts of Interest:** The author declares that he has no competing interests regarding the publication of this article.
