Singular transfer function matrix and System singularity

Question

I have a linearized dynamic system that can be summarized as:

[ΔY] = [A][ΔX]

The transfer function matrix, [A], is singular for steady state.

My question is that does such thing make sense?

Does the system fall in the category of singular systems? And can I apply the methods for assessing stability of singular systems to it?

In general I am a bit confused on what is the difference between a singular system and a singular transfer function matrix?

Note: I have already seen several definitions on the internet and tried reading papers but I couldn't understand them as my background is neither in Maths nor in Control.

Answer 1

Singularity would mean that either one or more of the inputs are redundant, or one or more of the outputs are.

Singularity just at the frequency $s=0$ (steady state), I don't think it means much. Also, the matrix $A$ can perfectly well not be square, so perhaps in that case you are thinking about $A$ losing rank?

Anyway, this doesn't have much to do with singular systems. To investigate stability, look at the poles of the transfer function. Or perhaps easier for your background, the eigenvalues of the matrix that appears in the linear differential equation that led to the transfer function.