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The Optimal Linear Quadratic Feedback State Regulator Problem for Index One Descriptor Systems


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  • Engwerda, J.C.
  • Salmah, Y.
  • Wijayanti, I.E.

    (Tilburg University, Center for Economic Research)


In this note we present both necessary and sufficient conditions for the existence of a linear static state feedback controller if the system is described by an index one descriptor system. A priori no definiteness restrictions are made w.r.t. the quadratic performance criterium. It is shown that in general the set of solutions that solve the problem constitutes a manifold. This feedback formulation of the optimization problem is natural in the context of differential games and we provide a characterization of feedback Nash equilibria in a deterministic context.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2008-90.

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Date of creation: 2008
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Handle: RePEc:dgr:kubcen:200890

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Keywords: linear quadratic optimal control; descriptor systems; static stabilizing state feedback control;

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  1. Engwerda, J.C. & Salmah, Y., 2008. "The Open-Loop Linear Quadratic Differential Game for Index One Descriptor Systems," Discussion Paper 2008-35, Tilburg University, Center for Economic Research.
  2. Broek, W.A. van den & Engwerda, J.C. & Schumacher, J.M., 2003. "An equivalence result in linear-quadratic theory," Open Access publications from Tilburg University urn:nbn:nl:ui:12-91412, Tilburg University.
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