LMIs in Control/KYP Lemma (Bounded Real Lemma)

KYP Lemma (Bounded Real Lemma) The Kalman–Popov–Yakubovich (KYP) Lemma is a widely used lemma in control theory. It is sometimes also referred to as the Bounded Real Lemma. The KYP lemma can be used to determine the norm of a system and is also useful for proving many LMI results. The System where , , , at any . The Data The matrices are known. The Optimization Problem The following optimization problem must be solved. The LMI: The KYP or Bounded Real Lemma Suppose is the system. Then the following are equivalent. Conclusion: The KYP Lemma can be used to find the bound on the norm of a system. 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 Positive Real Lemma 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: