Summary: A matrix is called a P-matrix if all its principal minors are positive. P-matrices have found important applications in functional analysis, mathematical programming, and dynamical systems theory. We introduce a new class of real matrices denoted \(\mathbb{E}^{\mathbb{P}}\). A matrix \(A\) is in \(\mathbb{E}^{\mathbb{P}}\) if \(\exp (At)\) is a P-matrix any \(t\geq 0\). We analyze the properties of this new class of matrices and describe an application of the theoretical results to opinion dynamics.