Sampled-Data System Stability

The map from $\left[\begin{array}{c}r\\ d\end{array}\right]$ to $\left[\begin{array}{c}u\\ e\\ y\end{array}\right]$ is the function that sends $r(t),d(t)$ to the resulting $u(t),e(t),y(t)$.

• This is basically a more generalized version of a transfer function.

Sampled-Data System Closed-Loop Stability

A sampled-data system is closed-loop stable if the map from from $\left[\begin{array}{c}r\\ d\end{array}\right]$ to $\left[\begin{array}{c}u\\ e\\ y\end{array}\right]$ is BIBO stable.