  The development of feedback controllers is undergoing a paradigm shift from
$\textit{modelic}$ (model-driven) control to $\textit{datatic}$ (data-driven)
control. Stability, as a fundamental property in control, is less well studied
in datatic control paradigm. The difficulty is that traditional stability
criteria rely on explicit system models, which are not available in those
systems with datatic description. Some pioneering works explore stability
criteria for datatic systems with special forms such as linear systems,
homogeneous systems, and polynomial systems. However, these systems imply too
strong assumptions on the inherent connection among data points, which do not
hold in general nonlinear systems. This paper proposes a stability verification
algorithm for general datatic control systems called $\eta$-testing. Our
stability criterion only relies on a weak assumption of Lipschitz continuity so
as to extend information from known data points to unmeasured regions. This
information restricts the time derivative of any unknown state to the
intersection of a set of closed balls. Inside the intersection, the worst-case
time derivative of Lyapunov function is estimated by solving a quadratically
constrained linear program (QCLP). By comparing the optimal values of QCLPs to
zero in the whole state space, a sufficient condition of system stability can
be checked. We test our algorithm on three datatic control systems, including
both linear and nonlinear ones. Results show that our algorithm successfully
verifies the stability, instability, and critical stability of tested systems.
