# Clustering state-space models according to similarity

I have a plant that can be modeled with nonlinear equations as $$f(x,u,p)=0$$ where $x$ is the state vector, $u$ the control vector, and $p$ the model parameters.

In order to control this system, I compute the discrete state-space model $$x_{k+1}=A_p x_k+B_p u_k$$ where $A_p$ and $B_p$ depend on the parameters $p$.

Now, I consider $N$ different $p$ vectors referring to possible malfunctions of the plant. Thus, I get $N$ possible state-space models. I am searching for a methodology to cluster these state-space models according to their "similarity" and end up with a subset of $M(<N)$ cluster state-space models.

A trivial example is when the plant has two identical components sharing some task, when one malfunctions ($p_1$), I get the state-space model $(A_{p_1},B_{p_1})$. When the second malfunctions ($p_2$), I get $(A_{p_2},B_{p_2})$. However, the two state-space models are the same and I need only to consider one of them.

Any references to papers or techniques are appreciated.