411 REFERENCE · Wikibooks
LMIs in Control/pages/Dissipativity of Affine Parametric Varying Systems
Reference material by Wikibooks contributors. This retains its source identity and is not 411 news reporting.
The System
where and
depend affinely on parameter .
The Data
The matrices .
The Optimization Problem:
Solve the following semi-definite program
Implementation
https://github.com/mkhajenejad/Mohammad-Khajenejad/commit/b6cd6b81f75be4a2052ba3fa76cad1a2f9c49caa
Conclusion
The dissipativity of (see [Boyd,eq:6.59]) exceeds if and only if the above LMI holds and the value function returns the minimum provable dissipativity.
Remark
It is worth noticing that passivity corresponds to zero dissipativity.
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.
Return to Main Page: