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Necessary conditions for global asymptotic stability of networks of iISS systems

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Abstract

In this paper, necessary conditions are investigated for global asymptotic stability of dynamical networks consisting of integral input-to-state stable (iISS) subsystems. Employing the dissipation formulation for subsystems, this paper naturally covers input-to-state stable (ISS) subsystems, which constitute a strict subset of the iISS. The number n of subsystems composing a network is allowed to be arbitrary. This paper gives answers to the question of how many non-ISS subsystems are allowed in the network, and the question of the necessity of small-gain-type properties. All the developments in this paper are natural, but non-trivial extensions of the results obtained previously for n = 2. This paper also proposes a concise representation of the iISS small-gain criteria for an arbitrary number of subsystems forming a cycle in networks.

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Authors and Affiliations

  1. Department of Systems Design and Informatics, Kyushu Institute of Technology, 680-4 Kawazu, Iizuka, 820-8502, Japan

    Hiroshi Ito

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  1. Hiroshi Ito
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Correspondence to Hiroshi Ito.

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The work is supported in part by Grant-in-Aid for Scientific Research of JSPS under Grant 19560446 and 22560449.

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Ito, H. Necessary conditions for global asymptotic stability of networks of iISS systems. Math. Control Signals Syst. 24, 55–74 (2012). https://doi.org/10.1007/s00498-012-0077-z

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  • DOI: https://doi.org/10.1007/s00498-012-0077-z

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