A Game Theoretic Approach to Linear Systems with L2-bounded Disturbances

W.A. van den Broek, J.C. Engwerda, J.M. Schumacher

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The aim of the present study is to construct a state feedback controller for a given linear system that minimizes the worst-case effect of an L2 -bounded disturbance. Our setting is different from the usual framework of H -theory in that we consider nonzero initial conditions. The situation is modeled in a game theoretical framework, in which the controller designer acts as a minimizing player, and the uncertainty as a maximizing player. We show that a saddle-point equilibrium exists and find an optimal controller.
Original languageEnglish
Place of PublicationTilburg
Number of pages12
Publication statusPublished - 2000

Publication series

NameCentER Discussion Paper


  • Linear uncertain systems
  • game theory
  • algebraic Riccati equations


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