On estimating the separation associated with the periodic continuous Sylvester equation.

The sensitivity of the solution of the periodic continuous Sylvester equation AkXkDk − BkXk⊕1Ck = Ek, k = 0,1,...,K − 1, depends on the separation of two periodic matrix pairs { (A k , B k) } k = 0 K − 1 and { (C k , D k) } k = 0 K − 1 . In this paper, we derive upper and lower bounds of this separation in terms of periodic generalized Schur decompositions. The theoretical results are verified by a numerical example. [ABSTRACT FROM AUTHOR]