  We present a new data-driven method to provide probabilistic stability
guarantees for black-box switched linear systems. By sampling a finite number
of observations of trajectories, we construct approximate Lyapunov functions
and deduce the stability of the underlying system with a user-defined
confidence. The number of observations required to attain this confidence level
on the guarantee is explicitly characterized. Our contribution is twofold:
first, we propose a novel approach for common quadratic Lyapunov functions,
relying on sensitivity analysis of a quasi-convex optimization program. By
doing so, we improve a recently proposed bound. Then, we show that our new
approach allows for extension of the method to Sum of Squares Lyapunov
functions, providing further improvement for the technique. We demonstrate
these improvements on a numerical example.
