Schur Characteristic Polynomials

Recall that $\Delta [z]=N[z]f[z]+M[z]g[z]$ be defined from the associated DT system with $G[z]$ and $D[z]$. Then the SD system is stable if and only if the roots of $\Delta \in \mathbb{D}$ (theorem from class). However, finding the roots of a high order polynomial is very challenging in general. Here, we introduce methods to check if $\text{roots}(\Delta )\subset \mathbb{D}$ without finding the roots directly.

Schur

A characteristic polynomial $\Delta [z]$ is Schur if $\text{roots}(\Delta )\subset \mathbb{D}$.

See:

• Schur Leading Coefficient Lemma
• Jury Test
• Schur Checking Tutorial