### 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 language | English |
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Place of Publication | Tilburg |

Publisher | Operations research |

Number of pages | 20 |

Volume | 2008-90 |

Publication status | Published - 2008 |

### Publication series

Name | CentER Discussion Paper |
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Volume | 2008-90 |

### Keywords

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

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## Cite this

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.