## 1 Introduction  
In the last decade, event-triggered control attracts more and more attention due to the advantages of reducing the number of control task executions and the cost of communication resources. In this control strategy, the control task execution is decided by an event instead of a certain fixed period of time. The latter is known as periodic sampling or time-triggered control [1]. The event is generated by the designed event condition, which is a state-related criterion. Therefore, event-triggered control can make the control tasks executed when necessary as the way a human performs [2]. In [3; 4; 5], the authors studied the state-feedback event-triggered control from an input-to-state stable point of view and proposed several types of event conditions to guarantee the asymptotic stability of the closed-loop systems. It is noted that the aforementioned works assumed that all the states are available to the controller, but this assumption is excessive and inappropriate in some situations. Therefore, [6; 7] studied the dynamic output feedback event-triggered control for certain and uncertain linear systems. Furthermore, the quantization effect on the dynamic output-feedback event-triggered control was considered in [8]. Ref. [9] applied a cyclic small-gain approach to analyze the event-triggered control systems with partial states and output feedback. The centralized or decentralized event-triggered control in networks was studied in [10; 11; 12]. The latest survey on event-triggered control can be found in [13; 14]. To further improve the sampling performance, such as enlarging the average inter-event time or equivalently decreasing the sampling numbers within a fixed time interval, a novel integral-based event-triggered control scheme was recently proposed in [15; 16]. Literally, the integral-based event-triggered control utilizes the integrals of the measurement signals to construct the event conditions. By this means, this control scheme can allow the Lyapunov function to be non-decrescent between two consecutive triggering instants. Consequently, the integral-based event-triggered control can be proved to yield better sampling performance than the scheme in [3]. Additionally, actuator saturation is a ubiquitous phenomenon in practical control systems due to the limitation of the facilities. It has been observed that the actuator saturation has a remarkable effect on the performance of the control systems (see [17] and the references therein). There are few literatures studied event-triggered control with saturated inputs. In [18] and its follow-up work [19], the authors studied event-triggered output feedback control for linear systems with actuator saturation, where the practical stability is guaranteed. Then, they applied the anti-windup approach to improve the performance of the systems. For a discrete-time linear plant, the event-triggered control subject to actuator saturation was studied in [20]. Recently, Ref. [21] studied the event-triggered asymptotic stabilization of a continuous-time plant with saturated inputs in both static state feedback and dynamic output feedback configurations. A kind of centralized relative event condition is employed in [21], which is also applied in [3; 22]. In this paper, we study the event-triggered asymptotic stabilization of a continuous-time linear plant with output feedbacks and saturated inputs. The contributions of this paper are described as follows. First, the decentralized event-triggered control with actuator saturation and output feedback is considered. In some situations, such as implementations over Wireless Sensor Actuator Networks, the sensors and actuators are grouped physically into several nodes and each of them has no access to the measurements of the others (see, e.g., [23; 24; 25]). As a result, the event condition of each node can only utilize its own measurement, and, hence, the event-triggered control in this paper is executed in a decentralized manner.