## 1 Introduction
The authors of [36] combined an ETC with an observer-based SMC controller to address the problem of LFC for multi-area power systems. The constructed ETC in [36] was adaptive in the sense that the triggering threshold was time-varying and not fixed. The overall system was described as an LTI continuous-time system. The authors of [37] proposed a dynamic ETC technique for a nonlinear multi-area power system to ensure the \(H_{\infty}\) stability of the closed-loop system against transmission delays. The stability analysis was carried out in continuous-time using Lyapunov-Krasovskii functions. In [38], new ETC conditions were synthesized based on sampled memory signals of the output feedback for the LFC of power systems. The closed-loop system was described as a T-S fuzzy system with time-varying delay and stability was studied in continuous-time. A partition-based ETC approach was developed in [39] for the LFC problem with input/output time delay. The communication instants over the sensor-to-controller and the controller-to-plant channels were produced by two independent ETCs. The closed-loop system was described in the discrete-time domain and a uniform ultimate boundedness stability was guaranteed. We should note that all the aforementioned results were either performed in continuous-time [31; 32; 33; 35; 36; 37; 38] or in discrete-time [34; 39]. However, SDC systems involve the two dynamical behaviors and, hence, it is more natural to model such systems as a hybrid dynamical system (HDS). The objective of this paper is to synthesize the stabilizing state-feedback ETCs for the LFC control problem in isolated hybrid power systems. The control design problem is solved sequentially in two steps, following the emulation approach. In other words, first,the sampling effect is neglected and a state-feedback law is designed in continuous-time to stabilize the closed-loop system. Then, an event-triggering rule is derived to maintain the closed-loop stability while ensuring that the Zeno behavior is ruled out. The latter characteristic is attained through the time regularization technique, such that the minimum dwell time is enforced between each triggering instant. The entire system is formulated as a hybrid dynamical system to deal with both continuous-time dynamics and discrete changes [40]. A linear matrix inequality (LMI) condition is used to present the required conditions, which allows systematic design methodology. The presented method guarantees that the closed-loop system is \(\mathcal{L}_{2}\)-gain-stable. Note that a similar ETC mechanism was constructed in [41] by switching between periodic sampling and event-triggering for output feedback linear systems. However, the approach of [41] was developed for static output feedback control, which, in practice, is restrictive to impose since such a static controller may not be feasible, even if the plant model is controllable and observable [42]. In contrast to [41], the developed approach in this study is focused on dynamic output feedback control, which is more general and ensures the existence of a stabilizing feedback law for any controllable and observable system. In addition, the enforced minimum time in our ETM is designed as the maximally allowable transmission interval (MATI) for time-triggered implementation based on [23], which is not the case in [41]. Moreover, the modeling framework and the stability in this study are different from those in [41] since we investigate the closed-loop stability in the framework of a hybrid dynamical system, as opposed to the time-delay approach in [41]. A simulation comparison with [43] was made to emphasize the effectiveness of the approach. The comparison results show that the approach [43] can ensure a larger periodic sampling time than what we guarantee. On the other hand, our proposed technique generates fewer triggering instant numbers than [43].