  Gaussian Process State Space Models (GP-SSMs) are a non-parametric model
class suitable to represent nonlinear dynamics. They become increasingly
popular in data-driven modeling approaches, i.e. when no first-order
physics-based models are available. Although a GP-SSM produces well-behaved
approximations and gains increasing popularity, the fundamental system dynamics
are just sparsely researched. In this paper, we present stability results for
the GP-SSM depending on selected covariance function employing a deterministic
point of view as widely done in the literature. The focus is set on the squared
exponential function which is one of the most used covariance functions for
nonlinear regression. We start with calculations according to the equilibrium
points of GP-SSM and continue with conditions for stability.

Systems and Control