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

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

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Abstract

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.
Original languageEnglish
Place of PublicationTilburg
PublisherOperations research
Number of pages20
Volume2008-90
Publication statusPublished - 2008

Publication series

NameCentER Discussion Paper
Volume2008-90

Keywords

  • linear quadratic optimal control
  • descriptor systems
  • static stabilizing state feedback control

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    Engwerda, J. C., Salmah, Y., & Wijayanti, I. E. (2008). The Optimal Linear Quadratic Feedback State Regulator Problem for Index One Descriptor Systems. (CentER Discussion Paper; Vol. 2008-90). Operations research.