# CDS 110b: Norms of Signals and Systems

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This lecture provides an introduction to some of the signals and systems concepts required for the study of robust ( $H_{\infty }$) control.

## Lecture Outline

1. Norms of linear systems (con't)
2. Internal stability

## Frequently Asked Questions

Q: So you can do pole zero cancellations?

As long as they don't occur in the closed right half plane, pole zero cancellations are OK from the point of view of stability. It is generally not a good idea to rely on exact cancellations even if they are stable cancellations (LHP), but they are relatively benign.

Exercise: try plotting the frequency response for $P(s)={\frac {s-1}{s-1+\epsilon }}$

Q: I'm not sure if I really understand what "sup" is

Formally, the supremum (sup) of a set is the smallest real number that is larger than or equal to every element in the set. For a real-valued function $f(x)$, $\sup _{x}f(x)$ is smallest real number $y$ such that $f(x)\leq y$. Here's a pretty good Wikipedia article on supremum.