To discribe Lmi term-regarding

Hai Team,

I am NARENSHAKTHI T. Recently working related to LMI tool box. Usually I used to represent the term as

lmiterm([lmi 1 1 O1],-2,1)

where O1 is a matrix. If I want to add an element's inverse term as

lmiterm([lmi 1 1 inv(O1)],-2,1)

But it gives error. so i want your guidance team.

Thanks in adavance

[Umar]

Hi @ NARENSHAKTHI,

Have you tried precomputing the inverse of O1 and then referencing it in the lmiterm function?

[Walter Roberson]

[lmi 1 1 O1]

It seems unlikely that the [] operation would work if O1 is a 2D matrix ?

[NARENSHAKTHI]

Hello sorir @Umar,

No sir i didnt try. thank you sir i will try in this sence.

[NARENSHAKTHI]

@Walter Roberson sir,

I take the matrix O1 of order 2*2 only.

[Walter Roberson]

I have doubts that [lmi 1 1 O1] will work.

[NARENSHAKTHI]

mm yes...it can

[Rahul]

Hi @NARENSHAKTHI,

According to this documentation for 'lmiterm':

https://www.mathworks.com/help/releases/R2024a/robust/ref/lmiterm.html?searchHighlight=lmiterm&s_tid=doc_srchtitle

the 4th term inside the [] of 'lmiterm' is required to be a Matrix variable or Scalar variable.

Please check if you are using the correct format for these terms. Thanks.

[NARENSHAKTHI]

Hi @Rahul,

I checked, its correct. in that documentation they didnt given for inverse term. I want to know about this only.

thanks.

[Umar]

Hi @ NARENSHAKTHI,

After studying lmiterm at <https://www.mathworks.com/help/robust/ref/lmiterm.html?searchHighlight=lmiterm&s_tid=srchtitle_support_results_1_lmiterm lmiterm link>, it is much clear now to me about how to add an element's inverse term using lmiterm. So, first, I will initialize the LMI description using the setlmis function and declare the matrix variables using the lmivar function. This step is necessary before specifying the term content.

setlmis([]);
O1 = lmivar(1, [n 1]);

Then, specify the term content using the lmiterm function. In this case, you want to add the inverse term of an element.

lmiterm([lmi 1 1 O1], -2, 1);

Solve the LMI using the mincx function to obtain the optimal solution.

c = mat2dec(ones(1, n), O1);
options = [1e-5, 0, 0, 0, 1];
[copt, xopt] = mincx(c, options);

And then retrieve the optimal solution.

O1_opt = dec2mat(xopt, O1);

Please bear in mind that the dec2mat function is used to retrieve the optimal value of the matrix variable O1. That's it! you should be able to add an element's inverse term using the lmiterm function in Matlab now. Remember to adjust the code according to your specific problem and variable names. Please let me know if this helps resolve your problem.