A Stepwise Approach for the Generalized Eigenstructure Assignment Problem
George S. Miminis · SIAM Journal on Matrix Analysis and Applications · 2001
The DEscriptor Multi-input Eigenstructure Assignment problem using State feedback (DEMESAS) is considered. It is pointed out, by referring to the relevant literature, that in many situations the final step of the DEMESAS is (or can be) the solution of the matrix equation (0.1)(A-BF) X=EXL\Longleftrightarrow BFX=AX-EXL with respect to F. Little attention has been paid, up to now, on deriving a numerically sound algorithm for the computation of F. Consequently, a straightforward approach has often been used. We show that this approach has numerical problems, and we introduce a new approach for the solution of (0.1). We illustrate the reasons that make the new approach numerically better than the straightforward approach, and we present two numerical examples that support our claim.