**1. Introduction**

A networked control system (NCS) is a feedback control system with feedback loop closed through a communication network. As the signal in an NCS is exchanged via a network, the network-induced delay, packet dropout, and limited network bandwidth can degrade the control performance. Many results have been proposed for dealing with these issues [1–5]. In the early stages, the studies on NCSs were mainly based on periodic task models [4–6]. The number of data packets to be transmitted will be large as the sampling period is small. This leads to a conservative usage of network resources and possibly leads to a congested network traffic. Therefore, how to design networked feedback controllers to achieve desired performance with low network usage is an important issue in NCSs.

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Recently, some sporadic task models have been presented in NCSs without degrading system performance. An important approach is the event-triggered scheme [7–26]. In [7], the state transmitting and the control signal updating events were triggered only if the error between the current measured state and the last transmitted state is larger than a threshold condition. In [8], event-triggered distributed NCSs with transmission delay were studied. Based on the designed event-triggered policy, an allowable upper bound of the transmission delay was derived. In [9], for distributed control systems, an implementation of event-triggering control policy in sensor-actuator network was introduced. In [10], the authors concerned with the design of event-triggered state feedback controllers for distributed NCSs with transmission delay and possible packet dropout. Under the proposed triggering policy, the tolerable packet delay and packet dropout were derived. In [11], an event-triggered control policy was developed for discrete-time control systems. In [12], under stochastic packet dropouts, an event-triggered control law for NCSs was calculated by the proposed algorithms. In [13], an event-triggered scheme was developed for uncertain NCSs under packet dropout. In [14], an event-based controller and a scheduler scheme were proposed for NCSs under limited bandwidth. The NCSs were modeled as discrete-time switched control systems. A sufficient condition for the existences of event-based controllers and schedulers was derived by the LMI optimization approach. Recently, the event-triggered scheme has been extended to *H∞* control of NCSs for achieving the disturbance attenuation performance [15–21]. In [15] and [18], with considering transmission delays, event-triggered *H∞* state feedback controllers for NCSs were proposed. Criterion for stability and criterion for co-designing both the controller gains and the trigger parameters were derived. In [16], an event-triggered state feedback control scheme was proposed for guaranteeing finite *L2*-gain stability of a linear control system. In [17], an event-triggered state feedback *H<sup>∞</sup>* controller for sampled-data control system was proposed. In [19], the design of event-triggered networked feedback controllers for discrete-time NCS was considered. In [20], based on Lyapunov-Krasovskii function, an event-triggered state feedback *H∞* controller was derived for NCSs under time-varying delay and quantization.

All the results in [7–20] are derived in the assumption that the system states are available for measurement. For practical control systems, system states are often unavailable for direct measurement. In the literature, only few results have been proposed for output-based eventtriggered NCSs [22–26]. In [22], a dynamic output feedback event-triggered controller for NCSs was proposed for guaranteeing the asymptotic stability. In [23] and [24], by the passivity theory approach, output-based event-triggered policies were derived for guaranteeing the satisfac‐ tion of *L*2-gain requirements of dynamic output feedback NCSs in the presence of time-varying delays. The synthesis of controllers has not been discussed. In [25] and [26], under nonuniform sampling, new output-based event-triggered *H∞* transmission policies were proposed of NCSs under time-varying transmission delays. Furthermore, the design of static output feedback *H<sup>∞</sup>* controllers for NCSs was discussed. Conditions for the existence of *H<sup>∞</sup>* controllers were presented in terms of bilinear matrix inequalities. A non-convex minimization problem must be solved to get a static output feedback *H∞* controller.

On the other hand, few results have been proposed in the literature for simultaneous stabili‐ zation of NCSs. The consideration of simultaneous stabilization is important since it allows us to design highly reliable controllers that are able to accommodate possible element failures in control systems. As the signal transmitted through network, the solvability of simultaneous stabilization problem of NCSs is quite different to that of point-to-point wiring control systems. Only few results have been proposed for relevant issues [21, 27]. In [27], based on the average dwell time approach, the simultaneous stabilization for a collection of NCSs was considered. A sufficient condition for guaranteeing simultaneous stabilization was proposed. In [21], under the assumption that the network communication channel is ideal (no delay, no packet dropout, and no quantization error), we considered the design of state feedback eventtriggered simultaneous *H∞* transmission policies for a collection of NCSs. Under the proposed event-triggered transmission policies, the *L2*-gain stability of all the closed-loop NCSs can be guaranteeing under low network usages.

It is known that static output feedback controllers are preferred in practical applications since their implementations are much easier than dynamic output feedback controllers. However, the design of static output feedback controllers is much more difficult than dynamic ones. In this chapter, we extend our previous work [21] to static output feedback case. Furthermore, we consider the network-induced time-varying delay that has not been considered in [21]. We develop an event-triggered static output feedback simultaneous *H∞* transmission policy for a collection of continuous-time linear NCSs under time-varying delay. It is shown that, under mild assumptions, conventional point-to-point wiring delayed static output feedback simul‐ taneous *H∞* controllers can be obtained by solving LMIs with a LME constraint. Based on the obtained static output feedback simultaneous *H∞* controllers, an event-triggered transmission policy was derived for reducing network usage. Different to the results presented in [25] and [26] that only considering the design of an event-triggered *H<sup>∞</sup>* controller for a single system, this chapter considers the design of a fixed event-triggered *H<sup>∞</sup>* controller that is able to *L2* stabilize a collection of NCSs simultaneously. By the proposed method, highly reliable NCSs that are able to accommodate possible element failures with low network usage can be designed. Even simplifying our results to the single system case, our method for designing static output feedback *H<sup>∞</sup>* controllers is quite different from those in [25] and [26]. In [25] and [26], a non-convex minimization problem must be solved for getting a static output feedback *H∞* controller. Moreover, the obtained controller can only guarantee uniform ultimate boundedness but not internal stability. In our approach, (simultaneous) static output feedback *H∞* controllers are obtained by solving LMIs with a LME constraint. Moreover, internal stabilities of the closed-loop NCSs can be guaranteed.
