Stability analysis for control systems with aperiodically sampled data using an augmented Lyapunov functional method

This study analyses the stability of aperiodically sampled-data control systems with and without communication delays by using a new augmented Lyapunov functional method. Compared with most of existing methods that commonly require each term of a Lyapunov-Krasovskii functional (LKF) to be non-negative, the proposed method waives this requirement by introducing an augmented term, which has zero value and zero derivative, into the LKF. Several stability criteria with less conservatism are obtained from the relaxation of constraint conditions for guaranteeing the non-negativeness of the LKF. These criteria are extended to investigate the stability of the systems with polytopic uncertainties and the exponential stability of the system. Three numerical examples are given to show the effectiveness of the proposed method.