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LMIs in Control/pages/Hankel Norm for Affine Parametric Varying Systems
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The System
where and
depend affinely on parameter .
The Data
The matrices .
The Optimization Problem:
Solve the following semi-definite program
where is the controllability Gramian, i.e., .
Implementation
https://github.com/mkhajenejad/Mohammad-Khajenejad/commit/0faedcdd9fba92bc27a318d80159c04a0b342f35
Conclusion
The Hanakel norm (i.e., the square root of the maximum eigenvalue) of is less than if and only if the above LMI holds and the value function returns the maximum provable Hankel norm.
Remark
is assumed to be zero.
External Links
LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.
LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.
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