$u = -k y$, for $\dot x_1 = x_2$, $\dot x_2 = u$ with $y = x_1$

Example · Undergraduate

Terms

Term	This example	Why
output feedback	✓	$u = -k y$ is output feedback because the input uses only the measured position $y = x_1$, not the velocity. The closed loop $\ddot x_1 = -k x_1$ oscillates for every $k > 0$, so no static output feedback stabilizes the double integrator.
state feedback	✗

Distinctions using this example

• State feedback vs. output feedback

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