# Can a state space model have changing state size over time?

I have worked with state space models in relation to Kalman estimation. Here I have always seen state space models with fixed state size over time, i.e. the state transition matrix is square. Let us for example define: $$x_{t+1} = A_t x_t + B_t u_t\\ y_t = C_t x_t + D_t v_t$$ Then $A_t$ is $n \times n$.

I suppose I could easily allow the state to change size at time $t_\text{change}$ by allowing $A_{t_\text{change}}$ to be of size $m \times n$ where $m\neq n$. Is this "allowed" in state space models in general? And does this entail any problems in applying a Kalman filter to estimate the state $x_t$ for $t$ "across" the point $t_\text{change}$?