This paper addresses the event-triggered \(H_\infty \) control for switched linear systems without stable subsystems. A novel event-triggered-based switching strategy is designed to remove the requirement of real-time availability of system state which is a prerequisite for the traditional min-switching law to work. Instead, we only need to check the switching conditions at the discrete triggering instants, and unfavorable asynchronous switching behavior is also avoided. However, under the designed switching strategy, the value of the Lyapunov function may be increasing during the active interval caused by the possibility of the mismatch between the min-switching and triggering. To handle this challenge, we then construct an improved two-side looped-functional, which is also event-triggered-based and can remove conservative nonincreasing requirements of multiple Lyapunov functions. Sufficient conditions with less conservative for the considered switched linear systems to be asymptotically stable with \(H_\infty \) performance are obtained. Besides, Zeno phenomenon of both switching and triggering is also avoided. Finally, two examples are exploited to verify the applicability and effectiveness of the developed method.
