Consider the standard Kalman filter as in here. I'm interested in understanding how $\mathbf{P}_{k|k}$ evolves, when $\mathbf{F}_k, \mathbf{Q}_k, \mathbf{R}_k$ change in $k$. I wonder if $\mathbf{F}_k, \mathbf{Q}_k, \mathbf{R}_k$ are bounded for all $k$, and given $\mathbf{P}_{0|0}$, one can ensure $\mathbf{P}_{k|k}$ doesn't exit a bounded set $D\subset\mathbb{R}^{n\times n}$ (where $n\times n$ is the dimension of $\mathbf{P}_{k|k}$).
I have tried to search for results in this direction in books/articles without success, possibly since I don't exactly know how to call this property. I would call it "invariance", but whenever I search invariance along with the Kalman filter, I always get very different results with what I am looking for.
EDIT: just a technical comment. By invariant sets I mean, forward in time.