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LMIs in Control/Positive Real Lemma
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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
where , , , at any .
The Data
The matrices are known.
The LMI: The Positive Real Lemma
Suppose is the system. Then the following are equivalent.
Conclusion:
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
A link to CodeOcean or other online implementation of the LMI (in progress)
Related LMIs
KYP Lemma (Bounded Real Lemma)
External Links
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.
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