Routh-Hurwitz criterion

Condition for the stability of linear time-invariant (LTI) control system

sufficient condition for Stability

All coefficients in the first column complete Routh array are the same sign

For a system with transfer function $\hat{G}(s) = \frac{\mathcal{N}(s)}{\mathcal{D}(s)}$

Input-output stability implies that all root of $\mathcal{d}(s)$ are in the Left Half Plane (LHP)