LMIs in Control/Click here to continue/Fundamentals of Matrix and LMIs/Variable Reduction Lemma

Introduction The variable reduction lemma allows the solution of algebraic Riccati inequality that involve a matrix of unknown dimension. This often arises when finding the controller that minimizes the H∞ norm. The Data In order to find the unknown matrix we need matrices , & . The Optimization Problem Given a symmetric matrix and two matrices & of column dimension n, consider the problem of finding matrix of compatible dimensions such that The above equation is solvable for some if and only if the following two conditions hold Where and are matrices whose columns are bases for the null spaces of & , respectively. Conclusion Using this technique we can get the value of unknown matrix . External Links A list of references documenting and validating the LMI. https://web.mit.edu/braatzgroup/33 A tutorial on linear and bilinear matrix inequalities.pdf - A journal paper on the said LMI https://onlinelibrary.wiley.com/doi/abs/10.1002/rnc.4590040403 - Research paper on the said LMI and its proof <noinclude> Return to Main Page https://en.wikibooks.org/wiki/LMIs_in_Control