Stabilization and Non-Weighted L ₂ Gain Analysis of Switched Systems With Distributed Delay Under Asynchronous Event-Triggered Control

This paper considers the asymptotic stabilization and non-weighted $\mathcal {L}_{2}$ gain of switched linear systems with infinite-time distributed delay by designing dynamic output feedback observer with event-triggered control. Two asynchronous mode-dependent event-triggered controller (ETC) schemes are respectively designed for the observer and the controller to save communication resources effectively. The novelty consists in the proposed discretized Lyapunov-Krasovskii functional (LKF) method, which guarantees that the LKF is continuous at system’s switching instant and its value after the controller’s switching instant is smaller than that before the instant. By utilizing this novel method, the non-weighted $\mathcal {L}_{2}$ gain of the switched time-delay systems is easily estimated without using additional conservative transformation. Sufficient conditions formulated by linear matrix inequalities (LMIs) are derived. Moreover, the closed system are allowed to be convergent or divergent in spite of match between the system mode and the ETC mode. An optimization algorithm is provided to design the controller gain, observer gain, and to estimate the optimal $\mathcal {L}_{2}$ gain. Numerical simulations verify the effectiveness and merits of the theoretical analysis.