Closed-Loop Nash Games for Interconnected Positive Nonlinear Systems with \(H_\infty \) Constraint

  • Hiroaki MukaidaniEmail author
  • Hua Xu
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 480)


In this paper, infinite horizon closed-loop Nash games for interconnected positive nonlinear systems with \(H_\infty \) constraint are investigated. The systems considered here are cooperative systems defined by Abara, Ticozzi, Altafini (IEEE Trans Autom Control, 63:402–417, (2018), [1]) and the \(H_\infty \) control recovers the influence of modeling error caused by linearization. For this class of positive systems, we provide conditions that guarantee the existence of Nash equilibrium via state feedback strategy. These conditions can be formulated in terms of cross-coupled algebraic Riccati equations (CCAREs) and a linear matrix inequality (LMI).


Nash games Interconnected positive nonlinear systems \(H_\infty \) control Multiple players 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Hiroshima UniversityHigashi-HiroshimaJapan
  2. 2.University of TsukubaTokyoJapan

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