Sampling-interval-dependent stability for sampled-data systems with variable sampling

This paper aims at sampling-interval-dependent stability of sampled-data systems with variable sampling. A new Lyapunov-like functional is first constructed to derive sampling-interval-dependent stability results. The Lyapunov-like functional has three features. First, it depends on time explicitly. Second, it may be discontinuous at the sampling instants. Third, it is not required to be positive definite within a sampling interval. Moreover, the new Lyapunov-like functional can employ the information of both ends of the sampling interval. By proposing a new lemma to estimate the derivative for this Lyapunov-like functional, a less conservative sampling-interval-dependent stability criterion is derived. When the sampled-data system involves polytopic uncertainties, a robust sampling-interval-dependent stability criterion is also obtained. Finally, two examples are listed to illustrate the reduced conservatism of the stability criteria.