Secure $\mathcal {L}_{2}$ Stabilization of Switched T-S Fuzzy Systems With Mixed Delay via Asynchronous Event-Triggered Control

This article investigates multiasynchronous control for asymptotic stabilization (AS) in mean-square and nonweighted
$\mathcal {L}_{2}$
-gain for a class of switched Takagi–Sugeno fuzzy systems with both time-varying delay and infinite-time distributed delay (mixed delays) as well as cyber-attacks. The proposed event-triggered controller not only is mode-dependent but also excludes Zeno behavior automatically with two tunable parameters to adjust the event-triggering (ET) number. A novel Lyapunov–Krasovskii functional (LKF) with a negative term is established to greatly reduce the conservatism and simplify the analysis of nonweighted
$\mathcal {L}_{2}$
-gain by ensuring its increment at switching instants be smaller than one. Three main results are provided to guarantee the AS in mean-square and design the control gains and weights of the ET mechanism, as well as the optimal nonweighted
$\mathcal {L}_{2}$
-gain. Compared with existing results, the new asynchronous control techniques eliminate the limitation of divergence in mismatched intervals for LKF. Numerical simulations demonstrate the merits of the theoretical analysis.