{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T19:53:32Z","timestamp":1778615612319,"version":"3.51.4"},"reference-count":31,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,7]],"date-time":"2023-01-07T00:00:00Z","timestamp":1673049600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This study outlines the necessary and sufficient criteria for swarm stability asymptotically, meaning consensus in a class of fractional-order multi-agent systems (FOMAS) with interval uncertainties for both fractional orders 0 &lt; \u03b1 &lt; 1 and 1 &lt; \u03b1 &lt; 2. The constraints are determined by the graph topology, agent dynamics, and neighbor interactions. It is demonstrated that the fractional-order interval multi-agent system achieves consensus if and only if there are some Hermitian matrices that satisfy a particular kind of complex Lyapunov inequality for all of the system vertex matrices. This is done by using the existence condition of the Hermitian matrices in a Lyapunov inequality. To do this, at first it is shown under which conditions a multi-agent system with unstable agents can still achieve consensus. Then, using a lemma and a theory, the Lyapunov inequality regarding the negativity of the maximum eigenvalue of an augmented matrix of a FOMAS is used to find some Hermitian matrices by checking only a limited number of system vertex matrices. As a result, the necessary and sufficient conditions to reach consensus in a FOMAS in the presence of internal uncertainties are obtained according to the Lyapunov inequalities. Using the main theory of the current paper, instead of countless matrices, only a limited number of vertex matrices need to be used in Lyapunov inequalities to find some Hermitian matrices. As a confirmation of the notion, some instances from numerical simulation are also provided at the end of the paper.<\/jats:p>","DOI":"10.3390\/axioms12010065","type":"journal-article","created":{"date-parts":[[2023,1,9]],"date-time":"2023-01-09T06:38:27Z","timestamp":1673246307000},"page":"65","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Robust Consensus in a Class of Fractional-Order Multi-Agent Systems with Interval Uncertainties Using the Existence Condition of Hermitian Matrices"],"prefix":"10.3390","volume":"12","author":[{"given":"Mohammadreza","family":"Riazat","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, K. N. Toosi University of Technology, Tehran 1631714191, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6772-743X","authenticated-orcid":false,"given":"Aydin","family":"Azizi","sequence":"additional","affiliation":[{"name":"School of Engineering, Computing and Mathematics, Wheatley Campus, Oxford Brookes University, Oxford OX33 1HX, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6311-7220","authenticated-orcid":false,"given":"Mojtaba","family":"Naderi Soorki","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Sharif University of Technology, Tehran 1458889694, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Abbasali","family":"Koochakzadeh","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran 1591634311, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Paducel, I., Safirescu, C.O., and Dulf, E.-H. 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