@article{bc34e012988b4e6d8926366ad4bec889,

title = "Dissipativity reinforcement in interconnected systems",

abstract = "This paper focuses on the reinforcement of the quantitative performance in interconnected dynamical systems. The following problem is addressed that concerns dissipativity reinforcement via interconnection: Find a class of subsystems and their interconnection rule such that the L2 gain bound of the entire interconnected system is reduced compared with that of each individual subsystem. We assume that each subsystem has a special passivity property that is characterized by two parameters, and has a bounded L2 gain. Then, the feedback connection and the more general interconnection of the subsystems are expressed by the transition of the two parameters inheriting the same passivity property. In addition, the L2 gain bound of the entire interconnected system, estimated with the parameters, is strictly reduced and becomes less than that of each subsystem. Finally, special interconnection rules are considered to show that the scale-expansion of the interconnected system, i.e., increasing the number of subsystems, gradually reduces the L2 gain bound.",

keywords = "Dissipativity, Large-scale systems, Network systems, Passivity, Stability",

author = "Masaki Inoue and Kengo Urata",

note = "Funding Information: Proposition 5 Because it holds that L IFB + L IFB T = 0 , the inequality (20) holds for β = 0 . Then, Π NW2 of (22) can be rewritten as Π NW2 = 0 1 1 − b − b a a E T − a E T L IFB T Ψ − 1 a E − a L IFB E , where Ψ ≔ b I N + a L IFB V V T L IFB T . From the definitions of E and L IFB , we have that L IFB E = 0 − ℓ T holds. Noting that V V T = 0 0 0 I N − 1 , we have the expression L IFB V V T L IFB T = ℓ ℓ T 0 0 0 . Then, noting that η = ℓ ℓ T , Ψ − 1 can be expressed as Ψ − 1 = b + a η 0 0 b I N − 1 − 1 . This reduces Π NW2 to Π NW2 = 0 1 1 − b − b a a 2 b + a η 0 0 a 2 η b = − a IFB 1 1 − b IFB . Then, it holds that Σ NW ( L IFB ) ∈ D ( a IFB , b IFB ) . From the fact that η > 0 , b IFB > b . Because a IFB b IFB = a b , we see that γ ( a IFB , b IFB ) < γ ( a , b ) holds. This completes the proof. □ Masaki Inoue was born in Aichi, Japan, in 1986. He received the M.E. and Ph.D. degrees in engineering from Osaka University in 2009 and 2012, respectively. He served as a Research Fellow of the Japan Society for the Promotion of Science from 2010 to 2012. From 2012 to 2014, he was a Project Researcher of FIRST, Aihara Innovative Mathematical Modelling Project, and also a Doctoral Researcher of the Graduate School of Information Science and Engineering, Tokyo Institute of Technology. Currently, he is an Assistant Professor of the Faculty of Science and Technology, Keio University. His research interests include stability theory of dynamical systems. He received several research awards including the best paper awards from SICE in 2013 and 2015, from ISCIE in 2014, and from IEEJ in 2017. He is a member of IEEE, SICE, ISCIE, and IEEJ. Kengo Urata was born in Miyagi, Japan, in 1992. He received the B.E. and M.E. degrees in applied physics and physico-informatics from Keio University, Kanagawa, Japan in 2015 and 2017, respectively. Since April 2017, he is working toward the Ph.D. degree in systems and control engineering from Tokyo institute of Technology, and serving as a Research Fellow of the Japan Society for the Promotion of Science. His research interests include the stability theory of dynamical systems and its application. He is a member of SICE. He was a winner of the SICE Annual Conference 2017 Young Author{\textquoteright}s Award. ",

year = "2018",

month = sep,

doi = "10.1016/j.automatica.2018.05.006",

language = "English",

volume = "95",

pages = "73--85",

journal = "Automatica",

issn = "0005-1098",

publisher = "Elsevier Limited",

}