# CDS 110b: Robust Stability

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This lecture describes how to model uncertainty in ${\displaystyle H_{\infty }}$ control and provides conditions for checking robust stability in this framework.

## Lecture Outline

1. Modeling uncertainty
2. Robust stability
3. Preview: robust performance

## Frequently Asked Questions

Q: Is there any way to bode plot (exp(-ts)-1) in MATLAB?

You can't use the 'bode' command, since the exponential makes that expression not a polynomial transfer function. If all you're interested in is the magnitude though, (as in this week's homework set) you can plot that explicitly, as follows. (This should look familiar for those of you who took 110A, since we had you do a bode plot without using the bode command a long time ago.)

omega = logspace(some_start, some_end, some_num); loglog(omega, abs(exp(-t*i*omega)-1));

I recommend doing help logspace and help loglog to understand what those functions do -- they're not too tricky.