Geodesic
Transformation of optimal control problems of descriptor systems into problems with state-space systems
Kybernetika, Tome 48 (2012) no. 6, pp. 1156-1179.

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We show how we can transform the ${\mathscr H}_\infty$ and ${\mathscr H}_2$ control problems of descriptor systems with invariant zeros on the extended imaginary into problems with state-space systems without such zeros. Then we present necessary and sufficient conditions for existence of solutions of the original problems. Numerical algorithm for ${\mathscr H}_\infty$ control is given, based on the Nevanlinna-Pick theorem. Also, we present an explicit formula for the optimal ${\mathscr H}_2$ controller.
Classification : 49J15, 93D15
Keywords: parametrization of stabilizing controllers; inner matrices; ${\mathscr H}_\infty$ and ${\mathscr H}_2$ control 
@article{KYB_2012__48_6_a5,
     author = {Stefanovski, Jovan},
     title = {Transformation of optimal control problems of descriptor systems into problems with state-space systems},
     journal = {Kybernetika},
     pages = {1156--1179},
     publisher = {mathdoc},
     volume = {48},
     number = {6},
     year = {2012},
     mrnumber = {3052879},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2012__48_6_a5/}
}
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Stefanovski, Jovan. Transformation of optimal control problems of descriptor systems into problems with state-space systems. Kybernetika, Tome 48 (2012) no. 6, pp. 1156-1179. http://geodesic.mathdoc.fr/item/KYB_2012__48_6_a5/