---
date: '2024-02-06'
description: stability condition for linear time-invariant control systems requiring all coefficients in first column of routh array to have same sign.
id: Routh-Hurwitz criterion
modified: 2026-06-05 15:08:23 GMT-04:00
tags:
  - seed
title: Routh-Hurwitz criterion
created: '2024-02-06'
published: '2024-02-06'
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---
> Condition for the stability of linear time-invariant (LTI) [[tags/sfwr3dx4|control system]]

> \[!tip\] 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)