Solution to Sylvester equation associated to linear descriptor systems

Mohamed Darouach (1)

1 CRAN - Centre de Recherche en Automatique de Nancy

This paper presents the solution of the constrained Sylvester equation associated to linear descriptor systems. This problem has been recently studied in (E.B. Castelan, V.G da Silva, Syst. Cont. Let., 2005), 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 (E.B. Castelan, V.G da Silva, Syst. Cont. Let., 2005) are necessary and sufficient.

Mots clés: Descriptor systems; Sylvester equation; Existence conditions; Observers; Regional pole placement

Domaines: Automatique

Mohamed Darouach. Solution to Sylvester equation associated to linear descriptor systems. Systems and Control Letters, 2006, 55 (10), pp.835-838. ⟨10.1016/j.sysconle.2006.04.004⟩. ⟨hal-00105181⟩