{"department":[{"_id":"263"}],"_id":"40803","place":"Maui, Hawaii, USA","year":"2012","citation":{"ama":"Ito H, Jiang Z-P, Dashkovskiy SN, Rüffer BS. A cyclic small-gain condition and an equivalent matrix-like criterion for iISS networks. In: <i>Proc. 51st IEEE Conf. Decis. Control</i>. ; 2012:4158–4164.","apa":"Ito, H., Jiang, Z.-P., Dashkovskiy, S. N., &#38; Rüffer, B. S. (2012). A cyclic small-gain condition and an equivalent matrix-like criterion for iISS networks. <i>Proc. 51st IEEE Conf. Decis. Control</i>, 4158–4164.","chicago":"Ito, Hiroshi, Zhong-Ping Jiang, Sergey N. Dashkovskiy, and Björn S. Rüffer. “A Cyclic Small-Gain Condition and an Equivalent Matrix-like Criterion for IISS Networks.” In <i>Proc. 51st IEEE Conf. Decis. Control</i>, 4158–4164. Maui, Hawaii, USA, 2012.","mla":"Ito, Hiroshi, et al. “A Cyclic Small-Gain Condition and an Equivalent Matrix-like Criterion for IISS Networks.” <i>Proc. 51st IEEE Conf. Decis. Control</i>, 2012, pp. 4158–4164.","ieee":"H. Ito, Z.-P. Jiang, S. N. Dashkovskiy, and B. S. Rüffer, “A cyclic small-gain condition and an equivalent matrix-like criterion for iISS networks,” in <i>Proc. 51st IEEE Conf. Decis. Control</i>, 2012, pp. 4158–4164.","short":"H. Ito, Z.-P. Jiang, S.N. Dashkovskiy, B.S. Rüffer, in: Proc. 51st IEEE Conf. Decis. Control, Maui, Hawaii, USA, 2012, pp. 4158–4164.","bibtex":"@inproceedings{Ito_Jiang_Dashkovskiy_Rüffer_2012, place={Maui, Hawaii, USA}, title={A cyclic small-gain condition and an equivalent matrix-like criterion for iISS networks}, booktitle={Proc. 51st IEEE Conf. Decis. Control}, author={Ito, Hiroshi and Jiang, Zhong-Ping and Dashkovskiy, Sergey N. and Rüffer, Björn S.}, year={2012}, pages={4158–4164} }"},"abstract":[{"lang":"eng","text":"This paper considers nonlinear dynamical networks consisting of individually iISS (integral input-to-statestable) subsystems which are not necessarily ISS (input-to-statestable). Stability criteria for internal and external stability of the networks are developed in view of both necessity and sufficiency. For the sufficiency, we show how we can construct a Lyapunov function of the network explicitly under the assumption that a cyclic small-gain condition is satisfied. The cyclic small-gain condition is shown to be equivalent to a matrix-like condition. The two conditions and their equivalence precisely generalize some central ISS results in the literature. Moreover, the necessity of the matrix-like condition is established. The allowable number of non-ISS subsystems for stability of the network is discussed through several necessity conditions."}],"date_created":"2023-01-30T11:51:54Z","publication":"Proc. 51st IEEE Conf. Decis. Control","page":"4158–4164","author":[{"full_name":"Ito, Hiroshi","first_name":"Hiroshi","last_name":"Ito"},{"first_name":"Zhong-Ping","last_name":"Jiang","full_name":"Jiang, Zhong-Ping"},{"full_name":"Dashkovskiy, Sergey N.","first_name":"Sergey N.","last_name":"Dashkovskiy"},{"full_name":"Rüffer, Björn S.","first_name":"Björn S.","last_name":"Rüffer"}],"status":"public","date_updated":"2023-01-30T11:58:14Z","title":"A cyclic small-gain condition and an equivalent matrix-like criterion for iISS networks","user_id":"43497","type":"conference"}