Solution to Sylvester equation associated to linear descriptor systems

@article{Darouach2006SolutionTS,
  title={Solution to Sylvester equation associated to linear descriptor systems},
  author={Mohamed Darouach},
  journal={Systems & Control Letters},
  year={2006},
  volume={55},
  pages={835-838}
}
This paper presents the solution of the constrained Sylvester equation associated to linear descriptor systems. This problem has been recently studied in [1], where sufficient conditions for the existence of the solution are given. In the present paper, a simple and direct method is developed to solve this problem. This method shows that the conditions given in [1] are necessary and sufficient. 
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