LMI decision variables interdependency

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Johannes 2024-2-28

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https://ww2.mathworks.cn/matlabcentral/answers/2087921-lmi-decision-variables-interdependency

回答： arushi 2024-4-2

Hi,

I want to solve a LMI problem with decision variables that are interdependent such that e.g. one matrix entry nested in my inner matrix for one LMI consists of X = [x1 x2-x3;x5-x4 0] with xi as decision variables (i=1,..,5)

If I implement this with Matlab's internal syntax and solver, the decision variables are identified as integers and thus are subtracted from each other. This renders my LMI infeasible of course. For example x2-x3 wil be 2 - 3 = -1

How can I declare decision variables as interdependent and subtract them from each other in lmivar()?

Thank you in advance!

Best regards,

Johannes

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Answer 1

arushi 2024-4-2

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Hi Johannes,

To solve a Linear Matrix Inequality (LMI) problem in MATLAB where decision variables are interdependent (e.g., one matrix entry in your LMI consists of variables that are subtracted from each other, like X = [x1 x2-x3; x5-x4 0]), you need to use the LMI Lab. The "lmivar" function is used to define the structure of the LMI variables, but it does not directly handle the arithmetic operations between decision variables. Instead, you may use the "lmiterm" function to specify the terms of your LMI, including any interdependencies between variables.

Please refer to the documentation for more information on "lmiterm" function -

https://www.mathworks.com/help/robust/ref/lmiterm.html

More information on how to declare decision variables as interdependent -

https://www.mathworks.com/help/robust/ug/advanced-topics.html

Hope this helps.