# 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

## Lecture Materials

$$P(s) = \frac{s - 1}{s - 1 + \epsilon}$$
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.