Polynomial matrices and feedback

Polynomial Matrices, Lmis and Static Output Feedback

In the polynomial approach to systems control, the static output feedback problem can be formulated as follows: given two polynomial matrices D(s) and N(s), nd a constant matrix K such that polynomial matrix D(s) + KN(s) is stable. In this paper, we show that solving this problem amounts to solving a linear matrix inequality with a non-convex rank constraint. Several numerical experiments illus...

Rational and Polynomial Matrices

where λ = s or λ = z for a continuousor discrete-time realization, respectively. It is widely accepted that most numerical operations on rational or polynomial matrices are best done by manipulating the matrices of the corresponding descriptor system representations. Many operations on standard matrices (such as finding the rank, determinant, inverse or generalized inverses, nullspace) or the s...

Polynomial Equations and Circulant Matrices

1. INTRODUCTION. There is something fascinating about procedures for solving low degree polynomial equations. On one hand, we all know that while general solutions (using radicals) are impossible beyond the fourth degree, they have been found for quadratics, cubics, and quartics. On the other hand, the standard solutions for the the cubic and quartic are complicated, and the methods seem ad hoc...

Kronecker Matrices and Polynomial Gcds

Some results on the polynomial numerical hulls of matrices

In this note we characterize polynomial numerical hulls of matrices $A in M_n$ such that$A^2$ is Hermitian. Also, we consider normal matrices $A in M_n$ whose $k^{th}$ power are semidefinite. For such matriceswe show that $V^k(A)=sigma(A)$.