LMIs in Control/pages/Positive Real Lemma
< LMIs in Control | pages
Positive Real Lemma
The Positive Real Lemma is a variation of the Kalman–Popov–Yakubovich (KYP) Lemma. The Positive Real Lemma can be used to determine if a system is passive (positive real).
The System
editwhere , , , at any .
The Data
editThe matrices are known.
The LMI: The Positive Real Lemma
editSuppose is the system. Then the following are equivalent.
Conclusion:
editThe Positive Real Lemma can be used to determine if the system is passive. Note from the (1,1) block of the LMI we know that is Hurwitz.
Implementation
editThis implementation requires Yalmip and Sedumi. https://github.com/eoskowro/LMI/blob/master/Positive_Real_Lemma.m
Related LMIs
editExternal Links
editA list of references documenting and validating the LMI.
- 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.