a kernel model. For a class of linearly evolving PDEs, such as the heat diffusion and the wave equation, our approach can lead to a very high-accuracy approximation. This modeling approach is also applicable to data-driven modeling of real-world phenomena, which we demonstrate on a challenging inference problem on satellite data of sea surface temperatures. One benefit of our model is that it can encode spatiotemporal evolution of complex nonlinear surfaces through an Ordinary Differential Equation (ODE) evolving in a Hilbert space induced by the specific kernel choice. Yet, the main benefit of our systems-theoretic approach is that it is highly conducive to control synthesis. To illustrate this fact, we demonstrate that feasible control strategies for a class of spatiotemporally evolving systems can be found using linear control synthesis. In particular, we derive sufficient conditions on the kernel selection to guarantee observability and controllability of the presented model. Furthermore, we demonstrate control synthesis for a diffusion PDE using simple Gaussian kernels distributed uniformly in the input domain.

The outline of this paper is as follows, Section \[sec:observers\] focuses on the development of a systems-theoretic kernel-based model of spatiotemporal evolution, Section \[sec:theory\_results\] presents the main theoretical results, Section \[sec:experimental\_results\] presents modeling 