Stability Analysis for Sampled-data Systems Based on Multiple Lyapunov Functional Method

This paper develops a novel method to deal with the stability problem of sampled-data systems. The multiple Lyapunov function method used in switched systems is extended to sampled-data systems and a multiple Lyapunov functional method is developed for nonlinear sampled-data systems. An application is presented where two different Lyapunov functionals are constructed in order to determine the stability of a linear sampled-data system for variable sampling frequency. The method in this paper needs neither the restriction of connecting adjacent Lyapunov functions at switching point nor the condition pertaining to dwell time, and thus the results provide an effective example of an application of multiple Lyapunov function technique. If more Lypunov functionals are employed, much less conservative results may be obtained.