Stability analysis of asynchronous sampled-data systems with discrete-time constant input delay

Aperiodic sampled-data systems controlled by a delayed state-feedback controller arise naturally in networked control systems. We propose a novel way to analyze the stability of sampled-data systems with discrete-time constant input delay by, first, reformulating the system into an aperiodic discrete-time system with constant delay and by, then, considering a mixture of a discrete-time Lyapunov-Krasovskii functional and a looped-functional in order to account for the presence of the delay and the sampling aperiodicity, respectively. Stability criteria, expressed as linear matrix inequalities, are derived for both certain and uncertain (time-varying) systems. An example is given for illustration.