Sampling-interval-dependent exponential stability for a networked control system model of sampled-data systems

This paper is concerned with a Lyapunov functional approach to stability for a networked control system model of sampled-data systems. The Lyapunov functional constructed has the sampling characteristic of the sampled-data system. Compared with usual Lyapunov functional, it is of the second order in time t and of every term being dependent on time t explicitly. Moreover, it may be discontinuous and it is not necessarily definite positive. This general Lyapunov functional can employs fully the information of sampled-data systems, especially that of the sampling interval. By proposing a lemma to the Lyapunov functional, a new sampling-interval-dependent exponential stability criterion is derived. Then this exponential stability criterion is extended to sampled-data systems with polytopic uncertainties. A new sampling-interval-dependent asymptotic stability criterion is also obtained. The stability criteria are demonstrated by examples that they are less conservative than some existing ones in the literature.