LMIs in Control/Matrix and LMI Properties and Tools/Singular Value Bounds of a Matrix through LMIs

The singular values of a real-valued matrix can be bounded through the use of LMI techniques. Required Data The real-valued matrix of interest, , is needed. Maximum Singular Value Consider matrix and such that . The maximum singular value of is strictly less than (that is, ) if and only if . Using the Schur complement, we see that is equivalent to Which is also equivalent to: if and only if or Minimum Singular Value Consider matrix and such that . If , then the minimum singular vale of is strictly greater than (that is, The maximum singular value of is strictly less than (that is, ) if and only if . If , then if and only if . Conclusion: LMI techniques can be used to establish bounds on the the singular values of any real-valued matrix. Related LMIs Singular Value Bounds for complex-valued matrices https://en.wikibooks.org/wiki/LMIs_in_Control/pages/Maximum_Singular_Value_of_a_Complex_Matrix https://en.wikibooks.org/wiki/LMIs_in_Control/pages/Minimum_Singular_Value_of_a_Complex_Matrix Return to Main Page: </noinclude>