include time in as an additional input variable [@perez:13:gaussian; @Chowdhary13_ACC2] is that they can account for intricate spatiotemopral couplings. However, there are two key challenges with these approaches: the first challenge is in ensuring the scalability of the model to large scale phenomena. This is difficult due to the fact that the hyperparameter optimization problem is not convex in general, and because when time is used as a kernel input, it is nontrivial to restrict the number of kernels used without losing modeling fidelity [@garg2012AAAI; @ma2003nonstationary; @plagemann2008nonstationary]. The second very important challenge is concerned with the formulation of feasible control strategies utilizing predictive kernel-based models of spatiotemporal phenomena. In particular, when the spatiotemporal evolution is embedded in the design of complex covariance kernel, the resulting model of functional evolution can be highly nonlinear and difficult to utilize in control design.

In this paper, we pursue an alternative systems-theoretic approach to the modeling, control, and estimation of spatiotemporally varying functions that fuses the strengths of kernel methods with systems theory. Our main contribution is to provide a systems-theoretic formulation for approximating, with very high accuracy, spatiotemporal functional evolution by layering a linear dynamical systems prior over temporal evolution of weights of 