A Matrix Sign Function Based Solution of Parameter Dependent Sylvester Equations

Jeremie Guerra (1) , Mohamed Yagoubi (1) , Philippe Chevrel (1, 2)

1 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes
2 Mines Nantes - Mines Nantes

This paper focuses on some parameter dependent Sylvester equations arising in systems and control theory. The matrices involved are assumed to be i) parameter dependent, ii) not necessarily of the same size, and iii) with possible common eigenvalues depending on the parameter value. A matrix sign function based solution is proposed, considering two main cases: the square coefficient matrices are diagonalizable or block-diagonalizable.

Domaines: Automatique

Jeremie Guerra, Mohamed Yagoubi, Philippe Chevrel. A Matrix Sign Function Based Solution of Parameter Dependent Sylvester Equations. 13th European Control Conference 2014., Jun 2014, France. pp.xx-xx. ⟨hal-00985897⟩