LMIs in Control/Click here to continue/Fundamentals of Matrix and LMIs/Minimizing Norm by Scaling

Minimizing Norm by Scaling There are many cases in which a norm should be minimized, such as in applications of the or norm optimal control. The System is a matrix . is some diagonal, nonsingular . The Data The optimal diagonally scaled norm of a matrix is defined as , where is diagonal and nonsingular. The LMI:Minimizing Norm by Scaling Therefore, is the optimal value of the generalized eigenvalue problem minimize subject to and diagonal, Conclusion: This result can be extended in many ways, such as in applications of or optimal control. Implementation This implementation requires Yalmip and Sedumi. Minimizing Norm by Scaling Related LMIs 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. LMIs in Control Systems: Analysis, Design and Applications - by Guang-Ren Duan and Hai-Hua Yu, CRC Press, Taylor & amp; Francis Group, 2013. Return to Main Page: LMIs in Control: https://en.wikibooks.org/wiki/LMIs_in_Control