User:Margav06/sandbox/Click here to continue/Linear Systems/Positive Real Lemma
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 edit
where , , , at any .
The Data edit
The matrices are known.
The LMI: The Positive Real Lemma edit
Suppose is the system. Then the following are equivalent.
Conclusion: edit
The 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 edit
This implementation requires Yalmip and Sedumi. https://github.com/eoskowro/LMI/blob/master/Positive_Real_Lemma.m
Related LMIs edit
External Links edit
A 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.