I need to cut the formation of the LMI via symbolic variables for performance. Did a timing test on a size 20 state, input, output system, 99% of the time is spent constructing the LMI and converting to cvxopt form.

The initial disussion is here: #732

Thanks for the initiative!

As far as I understand, you introduce 3 new depenendies because you work with symbolic matrices:

• sympy
• lmi_sdp -- https://github.com/cdsousa/PyLMI-SDP, "About" says unmaintained
• cvxopt -- http://cvxopt.org/ has complex dependencies on various numeric libraries

Would it be possible to implement the matrix handling and solving with NumPy and SciPy functions only?

Would it be possible to implement the matrix handling and solving with NumPy and SciPy functions only?

I'm about 60% sure cvxopt is necessary to solve the linear matrix inequality. Sympy and lmi_sdp can definitely be dropped.

Cvxopt only requires BLAS/LAPACK, which it seems that slycot also requires. So this passivity package could be setup to be optional?

CVXOPT is available on conda-forge and as wheels with bundled libraries on PyPI. They link and bundle OpenBLAS. I am not sure how well that plays with "Generic" Netlib linked NumPy and Slycot packages. But we can worry about that when it comes up.

It must be installed in the test suite, so we need to add it to the requirements. It can be set as optional similar to how we do it with Slycot.

@bnavigator I've removed sympy and lmi-sdp from the function, and I attempted to setup cvxopt in the test suite.

Coverage increased (+0.02%) to 94.549% when pulling c2255b0 on Mark-Yeatman:passivity-tools into d98ed29 on python-control:main.

@bnavigator I believe I've resolved all the outstanding review comments?

Instead of writing things in the standard SDP notation, you might want to use CVXPY notation (which acts like YALMIP) so you don't have to use the tiresome basis matrices.

Also note that strictly proper systems cannot be checked via positive real lemma via strict inequalities due zero D + D.T block forcing the optimization problem to infeasibilty. You either have to use extended version or nudge D block with epsilon*np.eye(m). Alternatively you can solve the LMI < alpha*eye(n) and minimize alpha and if it is sufficiently small then you can call it feasible.

I would definitely be up for using cvxpy, but it looks like it has more dependencies than just using cvxopt (https://www.cvxpy.org/install/#install-from-source vs https://cvxopt.org/install/#building-and-installing-from-source)? That seems like an issue for a project maintainer.

You're right about the D = 0 case, I will nudge it as you suggested. Thanks for catching that.

CVXPY: I don't think it is necessary to employ a full domain specific language with all its dependencies for one hardcoded optimization problem.

I took the liberty of fixing the missing skips. I hope you don't mind.