### Abstract

Original language | English |
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Place of Publication | Eindhoven |

Publisher | Technische Hogeschool Eindhoven |

Number of pages | 14 |

Publication status | Published - 1978 |

### Publication series

Name | Memorandum COSOR |
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Volume | 7812 |

ISSN (Print) | 0926-4493 |

### Fingerprint

### Cite this

*Nonsingular factors of polynomial matrices and (A,B)-invariant subspaces*. (Memorandum COSOR; Vol. 7812). Eindhoven: Technische Hogeschool Eindhoven.

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*Nonsingular factors of polynomial matrices and (A,B)-invariant subspaces*. Memorandum COSOR, vol. 7812, Technische Hogeschool Eindhoven, Eindhoven.

**Nonsingular factors of polynomial matrices and (A,B)-invariant subspaces.** / Emre, E.

Research output: Book/Report › Report › Academic

TY - BOOK

T1 - Nonsingular factors of polynomial matrices and (A,B)-invariant subspaces

AU - Emre, E.

PY - 1978

Y1 - 1978

N2 - Given a polynomial matrix B(s), we consider the class of nonsingular polynomial matrices L(s) such that B(s) = R(s)L(s) for some polynomial matrix R(s). It is shown that finding such factorizations is equivalent to finding (A,B)-invariant subspaces in the kernel of C where A,B,C are linear maps determined by B(s). In particular, the results yield, as a corollary, a method to determine simultaneously a row proper greatest right divisor of a left invertible polynomial matrix as well as the resulting polynomial matrix whose greatest right divisors are unimodular. The results also relate, the same way, such subspaces of constant systems (C,A,B) where (C,A) is observable and (A,B) is reachable, to the nonsingular right factors of the numerator polynomial matrices in coprime factorizations of the form D^-1 (s)B(s) of their transfer matrices.

AB - Given a polynomial matrix B(s), we consider the class of nonsingular polynomial matrices L(s) such that B(s) = R(s)L(s) for some polynomial matrix R(s). It is shown that finding such factorizations is equivalent to finding (A,B)-invariant subspaces in the kernel of C where A,B,C are linear maps determined by B(s). In particular, the results yield, as a corollary, a method to determine simultaneously a row proper greatest right divisor of a left invertible polynomial matrix as well as the resulting polynomial matrix whose greatest right divisors are unimodular. The results also relate, the same way, such subspaces of constant systems (C,A,B) where (C,A) is observable and (A,B) is reachable, to the nonsingular right factors of the numerator polynomial matrices in coprime factorizations of the form D^-1 (s)B(s) of their transfer matrices.

M3 - Report

T3 - Memorandum COSOR

BT - Nonsingular factors of polynomial matrices and (A,B)-invariant subspaces

PB - Technische Hogeschool Eindhoven

CY - Eindhoven

ER -