Hi @AdamsK
The issue you're encountering may indeed be related to how the trace operator is handled in your code. When you use Tr(P*T) inside your LMI, it represents the trace of the product of matrices P and T. However, the trace operator is a linear operator, and the product of two matrices with the trace operator can't be simplified as Tr(P*T). Instead, you should compute the trace of the product explicitly.
To work around this issue, you can modify your code to compute the trace of the product P*T separately and then use it in the LMI. Here's how you can modify your code:
setlmis([]);
P = lmivar(1, [3, 1]);
d = lmivar(1, [1, 1]);
lmiterm([-1, 1, 1, P], 1, 1);
lmiterm([-1, 1, 1, P], A', -A);
lmiterm([-1, 1, 1, 0], -(M + K' * N * K)); % No trace here
lmiterm([-1, 1, 1, 0], P); % Adding P
lmiterm([-1, 1, 1, 0], T, 1); % Adding T with a coefficient of 1
lmiterm([-1, 1, 1, d], 1, -C' * C);
lmiterm([-2, 1, 1, P], 1, 1);
lmiterm([-3, 1, 1, d], 1, 1);
LMI = getlmis;
[tmin, xfeas] = feasp(LMI);
P = dec2mat(LMI, xfeas, P);
d = dec2mat(LMI, xfeas, d);
With this modification, you explicitly add the term P*T with a coefficient of 1 in the LMI. This should correctly account for the trace operation and give you a solution that satisfies your constraint P - A'PA - dC'C - Tr(PT)(M + K'NK) > 0.
However, it's also important to ensure that your matrices A, C, M, K, and N are defined correctly and consistently with the problem you're trying to solve, as errors in these matrices can also lead to issues with the feasibility of the LMI.
Also refer to the below documentation for more information on trace : https://in.mathworks.com/help/matlab/ref/double.trace.html
I hope this helps.
