A new approach to sampling-dependent stability for sampled-data systems under aperiodic samplings

This paper is concerned with a new Lyapunov functional approach to sampling-dependent stability for sampled-data systems under aperiodic samplings. A new Lyapunov functional is constructed by introducing the integral of the state. The improved Jensen inequality reported recently is used to estimate the derivative of the Lyapunov functional. Based on Lyapunov stability theory, a new sampling-dependent stability result is obtained for sampled-data systems under aperiodic samplings. Then, this stability result is extended to sampled-data systems with polytopic uncertainties under aperiodic samplings. At last, simulations show that the proposed results have less conservatism than some existing ones.