LMIs in Control/LMI Matrix Properties/Maximum Singular Value of a Complex Matrix

Maximum Singular Value of a Complex Matrix The System Consider as well as . A maximum singular value of a matrix is less than if and only if , where is the conjugate transpose or Hermitian transpose of the matrix . The Data The matrix is the only data required. The Optimization Problem The LMI: Maximum Singular Value of a Complex Matrix Using the Shur complement procedure, the following LMIs can be constructed: The following LMI is also equivalent: Conclusion: The results from this LMI will give the maximum complex value of the matrix : Implementation A link to CodeOcean or other online implementation of the LMI Related LMIs [\\ Minimum singular value of a complex matrix] 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: