# CDS 110b: Norms of Signals and Systems

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Course Home | L7-2: Sensitivity | L8-1: Robust Stability | L9-1: Robust Perf | Schedule |

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

## Lecture Outline

- Norms of linear systems (con't)
- Internal stability

## Lecture Materials

- Blackboard lecture; no slides. MP3 lost (technical error)
- Lecture Notes on system norms
- Reading: DFT, Chapter 2
- HW #6 (due 22 Feb)

## References and Further Reading

## 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.