LMIs in Control/LMI Matrix Properties/Maximum Singular Value of a Complex Matrix
Appearance
LMIs in Control/LMI Matrix Properties/Maximum Singular Value of a Complex Matrix
Maximum Singular Value of a Complex Matrix
The System
[edit | edit source]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
[edit | edit source]The matrix is the only data required.
The Optimization Problem
[edit | edit source]The LMI: Maximum Singular Value of a Complex Matrix
[edit | edit source]Using the Shur complement procedure, the following LMIs can be constructed:
The following LMI is also equivalent:
Conclusion:
[edit | edit source]The results from this LMI will give the maximum complex value of the matrix :
Implementation
[edit | edit source]A link to CodeOcean or other online implementation of the LMI
Related LMIs
[edit | edit source]- [\\ Minimum singular value of a complex matrix]
External Links
[edit | edit source]- 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.