On the characteristic polynomial of matrices with prescribed columns and the stabilization and observability of linear systems

• Tipo: Artigo em Revista Científica Internacional
• Data: 1998

Autores

Susana Margarida Figueiredo de Sousa Borges Furtado (Autor) FEP; Fernando Silva (Autor) Outra

Revista

Título: Electronic Journal of Linear Algebra

Vol. 4

Páginas: 19-31

ISSN: 1537-9582

Editora: INT LINEAR ALGEBRA SOC

Indexação

ISI Web of Science

Scopus - 3 Citações

Classificação Científica

FOS: Ciências exactas e naturais

Outras Informações

ID Authenticus: P-007-BWM

Abstract (EN): Let A ¿ FnXn, B ¿ FnXt, where F is an arbitrary field. In this paper, the possible characteristic polynomials of [A B], when some of its columns are prescribed and the other columns vary, are described. The characteristic polynomial of [A B] is defined as the largest determinantal divisor (or the product of the invariant factors) of [xI n - A - B]. This result generalizes a previous theorem by H. Wimmer which studies the same problem when t = 0. As a consequence, it is extended to arbitrary fields a result, already proved for infinite fields, that describes all the possible characteristic polynomials of a square matrix when an arbitrary submatrix is fixed and the other entries vary. Finally, applications to the stabilization and observability of linear systems by state feedback are studied.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 12