  We consider the problem of global stability of nonlinear sampled-data
systems. Sampled-data systems are a form of hybrid model which arises when
discrete measurements and updates are used to control continuous-time plants.
In this paper, we use a recently introduced Lyapunov approach to derive
stability conditions for both the case of fixed sampling period (synchronous)
and the case of a time-varying sampling period (asynchronous). This approach
requires the existence of a Lyapunov function which decreases over each
sampling interval. To enforce this constraint, we use a form of slack variable
which exists over the sampling period, may depend on the sampling period, and
allows the Lyapunov function to be temporarily increasing. The resulting
conditions are enforced using a new method of convex optimization of polynomial
variables known as Sum-of-Squares.We use several numerical examples to
illustrate this approach.
