Stability and L₂-Gain Analysis of Linear Periodic Event-Triggered Systems With Large Delays

This brief studies the stability and $\mathcal {L}_{2}$ -gain properties of dynamic periodic event-triggered control systems with large time-varying communication delays. By introducing recursive auxiliary variables to identify the actual transmitted data at the current instant, the closed-loop system is modeled as an impulsive delay-free system. Combining the impulsive system approach with quasi-periodic Lyapunov functions, sufficient conditions for the quantitative relationship between the sizes of time delays, sampling period, and $\mathcal {L}_{2}$ -gain of the periodic event-triggered systems are established. Compared with the lifting-based results, the derived conditions can be applied to the plant with polytopic type uncertainties and sporadic measurements. The theoretical results are demonstrated by a batch reactor.