Margin Gate Is a Model Contract - Electronic Circuits IX: Feedback Control and Stability Margins Step by Step

The scalar sampled model uses the exact gate zero less than c less than two. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Fractions inside the gate pass

Correction 1/2 passes, and correction 3/2 also passes.

0<{1\over 2}<2,\quad 0<{3\over 2}<2

The boundary and larger corrections fail

Correction 2 fails at the boundary; correction 5/2 fails past it.

c=2\Rightarrow \text{fail},\quad c={5\over 2}\Rightarrow \text{fail}