Decoupling of cubic polynomial matrix systems

Differential Polynomial Rings of Triangular Matrix Rings

Decoupling in singular systems: a polynomial equation approach

In this paper, the row by row decoupling problem by static state feedback is studied for regularizable singular square systems. The problem is handled in matrix polynomial equation setting. The necessary and sufficient conditions on decouplability are introduced and an algorithm for calculation of feedback gains is presented. A structural interpretation is also given for decoupled systems.

Solving Polynomial Systems by Matrix Computations

Two main approaches are used, nowadays, to compute the roots of a zero-dimensional polynomial system. The rst one involves Grrbner basis computation, and applies to any zero-dimensional system. But, it is performed with exact arithmetic and, usually, big numbers appear during the computation. The other approach is based on resultant formulations and can be performed with oating point arithmetic...

Algebraic adjoint of the polynomials-polynomial matrix multiplication

This paper deals with a result concerning the algebraic dual of the linear mapping defined by the multiplication of polynomial vectors by a given polynomial matrix over a commutative field

Tabulation of cubic function fields via polynomial binary cubic forms

We present a method for tabulating all cubic function fields over Fq(t) whose discriminant D has either odd degree or even degree and the leading coefficient of −3D is a non-square in Fq , up to a given bound B on deg(D). Our method is based on a generalization of Belabas’ method for tabulating cubic number fields. The main theoretical ingredient is a generalization of a theorem of Davenport an...