H Infinity

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H Infinity
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1 H Infinity (LaTeX: \mathcal{H}_\infty)

The H Infinity control paradigm (LaTeX: \mathcal{H}_\infty) was developed in the early 1980's by Zames, Doyle and Glover and Kwakernak among others.

The LaTeX: \mathcal{H}_\infty method involves two processes:

  1. Definition of specifications based on the LaTeX: \infty-norm of the weighted sensitivity function or functions.
  2. Controller design and optimisation whereby specifications are met as closely as possible by shaping the weighted sensitivity transfer function.

2 Constraints and Specifications: Nominal Stability

Nominal stability is a fundamental requirement of the closed loop system, and simply ensures that under nominal conditions, the system will not be unstable.

3 Nominal Performance

For nominal performance, it is required that the LaTeX: \mathcal{H}_\infty norm should conform to the inequality

LaTeX: \|S(j\omega)W_{s}(j\omega)\|_{\infty}\leq 1

Where LaTeX: W_{s}(j\omega}) is the weighting for the primary sensitivity function LaTeX: S(j\omega)

4 See Also

5 References

Skogestad, S., Postlethwaite, I. 2005 Multivariable Feedback Control: Analysis and Design. 2nd. Wiley. ISBN 0470011688

5.1 Notes

This page was originally created by user CMatthews but when the old DB was wiped out by hackers, that user's info was also lost.