Questions tagged [hurwitz-matrices]

A square matrix $A$ is a Hurwitz matrix if all eigenvalues of $A$ have strictly negative real parts.

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Define$$H_1=\left( \begin{matrix} -A & B \\ -{{B}^{T}} & 0 \\ \end{matrix} \right),$$ where $A\in {{\mathbb{R}}^{n\times n}}$ is a symmetric positive definite matrix. $B\in {{\mathbb{R}... • 11 1 vote 2 answers 59 views Hurwitz stability status of two matrices I have a complex symmetric matrix (it is not Hermitian), i.e.$\textbf{A}\in\mathbb{C}^{n\times n}$. Can you prove that$\textbf{A}$and$\textbf{B}=\textbf{A}+\textbf{A}^*$have similar Hurwitz ... 0 votes 0 answers 40 views About linear subspace of Hurwitz Matrix Manifold In this question I want to investigate the linear subspace of the Hurwitz matrix family. That is to say, suppose$M_H = \{A \in R^{n \times n}: \operatorname{Re} \lambda_i(A) \leq 0, \forall i \leq n\}...
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I am working with a Hurwitz-stable, Metzler matrix $A$ with nonpositive diagonal ($A_{ii}\leq0$ for all $i$) and nonegative off diagonal ($A_{ij}\geq0$ for all $i\neq j$). I want its exponential to be ...