Encyclopedia of Systems and Control

Living Edition
| Editors: John Baillieul, Tariq Samad

Linear Quadratic Zero-Sum Two-Person Differential Games

  • Pierre BernhardEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5102-9_29-1


As in optimal control theory, linear quadratic (LQ) differential games (DG) can be solved, even in high dimension, via a Riccati equation. However, contrary to the control case, existence of the solution of the Riccati equation is not necessary for the existence of a closed-loop saddle point. One may “survive” a particular, nongeneric, type of conjugate point. An important application of LQDGs is the so-called H -optimal control, appearing in the theory of robust control.

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Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  1. 1.INRIA-Sophia Antipolis-MéditerranéeSophia AntipolisFrance