{"title":"A Two-Phase Approach to Stability of Networks Given in iISS Framework: Utilization of a Matrix-Like Criterion","_id":"40781","department":[{"_id":"263"}],"date_created":"2023-01-30T11:51:51Z","user_id":"43497","citation":{"chicago":"Ito, Hiroshi, and Björn S. Rüffer. “A Two-Phase Approach to Stability of Networks Given in IISS Framework: Utilization of a Matrix-Like Criterion.” In <i>Proc. IEEE American Contr. Conf.</i>, 4838–4843, 2013.","short":"H. Ito, B.S. Rüffer, in: Proc. IEEE American Contr. Conf., 2013, pp. 4838–4843.","apa":"Ito, H., &#38; Rüffer, B. S. (2013). A Two-Phase Approach to Stability of Networks Given in iISS Framework: Utilization of a Matrix-Like Criterion. <i>Proc. IEEE American Contr. Conf.</i>, 4838–4843.","bibtex":"@inproceedings{Ito_Rüffer_2013, title={A Two-Phase Approach to Stability of Networks Given in iISS Framework: Utilization of a Matrix-Like Criterion}, booktitle={Proc. IEEE American Contr. Conf.}, author={Ito, Hiroshi and Rüffer, Björn S.}, year={2013}, pages={4838–4843} }","ama":"Ito H, Rüffer BS. A Two-Phase Approach to Stability of Networks Given in iISS Framework: Utilization of a Matrix-Like Criterion. In: <i>Proc. IEEE American Contr. Conf.</i> ; 2013:4838–4843.","mla":"Ito, Hiroshi, and Björn S. Rüffer. “A Two-Phase Approach to Stability of Networks Given in IISS Framework: Utilization of a Matrix-Like Criterion.” <i>Proc. IEEE American Contr. Conf.</i>, 2013, pp. 4838–4843.","ieee":"H. Ito and B. S. Rüffer, “A Two-Phase Approach to Stability of Networks Given in iISS Framework: Utilization of a Matrix-Like Criterion,” in <i>Proc. IEEE American Contr. Conf.</i>, 2013, pp. 4838–4843."},"year":"2013","status":"public","author":[{"full_name":"Ito, Hiroshi","last_name":"Ito","first_name":"Hiroshi"},{"last_name":"Rüffer","full_name":"Rüffer, Björn S.","first_name":"Björn S."}],"abstract":[{"lang":"eng","text":"This article is concerned with global asymptotic stability (GAS) of dynamical networks. The case when subsystems are integral input-to-state stable (iISS) has been recognized as notoriously difficult to deal with in the literature. In fact, the lack of energy dissipation for large input denies direct application of the small-gain argument for input-to-state stable (ISS) subsystems. Here for networks consisting of iISS subsystems it is demonstrated that a two-phase approach allows us to make use of the ISS small-gain argument by separating a trajectory into a transient and a subsequent convergence. In contrast to the previous iISS results, the two-phase approach immediately leads to a sufficient criterion for GAS of general nonlinear networks in a matrix-like form (order condition)."}],"type":"conference","date_updated":"2023-01-30T11:59:51Z","publication":"Proc. IEEE American Contr. Conf.","page":"4838–4843"}