Cooperative control of multi-agent systems has been a popular topic in the control and robotics communities over the past two decades, due to many applications such as formation control of mobile robots and coordination of unmanned aerial vehicles. The cooperative control problems are often addressed through distributed control protocols, where each agent only utilizes its own information and that of its neighboring agents. In practice, agents often have limited resources such as energy and communication bandwidth. To improve resource utilization efficiency, several distributed event-triggered control protocols have been developed. However, most of the existing protocols assume fixed graphs as the communication topologies.

This thesis focuses on developing distributed event-triggered control protocols for multi-agent systems under jointly connected digraphs that only require the unions of the subgraphs over a sequence of consecutive bounded time intervals to contain a spanning tree. The main results of this thesis consist of two parts. In the first part, we address the cooperative output regulation problem of heterogeneous linear multi-agent systems by distributed and fully distributed event-triggered control protocols. In the second part, the research is extended to uncertain strict-feedback nonlinear multi-agent systems in the normal form and uncertain Euler--Lagrange multi-agent systems. The main challenges in these problems arise from the jointly connected digraphs, the lack of global information about the communication networks, and the complexity of system dynamics. The main results of this thesis are summarized as follows.

1. The distributed event-triggered cooperative output regulation problem of heterogeneous linear multi-agent systems is investigated. The communication network is assumed to be jointly connected digraphs, which is a very mild assumption. Both distributed state feedback and distributed output feedback event-triggered control protocols are proposed to solve this problem. To deal with the jointly connected digraphs potentially becoming disconnected at any time, a novel method based on a contraction argument is utilized to analyze the closed-loop system under these control protocols. It is demonstrated that the closed-loop system under these protocols achieves exponential stability.

2. The cooperative output regulation problem of heterogeneous linear multi-agent systems over jointly connected digraphs is investigated, considering that the exosystem matrix is only known by the neighbors of the exosystem. A novel fully distributed event-triggered control protocol is proposed, which contains an event-based observer and a distributed dynamic control law. The event-based observer is employed to estimate both the exosystem matrix and the exogenous signal simultaneously, using a time-dependent power function as the event-triggering threshold. To achieve the convergence analysis of the estimation errors, a new analytical method based on the weighted mean-value theorem for integrals and Bellman--Grõnwall lemma is developed. It is shown that the tracking errors of the agents converge to zero asymptotically under the fully distributed event-triggered control protocol.

3. The robust distributed cooperative output regulation problem of strict-feedback nonlinear multi-agent systems in the normal form with nonidentical relative degrees is studied. A novel event-triggered distributed observer is proposed, leveraging the internal model method to estimate the uncertain exogenous signal. An estimator for the observer is designed to remove continuous communication between neighboring agents. Subsequently, distributed controllers are developed using the backstepping method to enable individual agents to track the estimated signals from the observers. It is found that the internal model system matrices for the observer should be designed with small enough traces and norms to achieve the control objective under jointly connected digraphs.

4. A fully distributed event-triggered control protocol is proposed to address the consensus problem of uncertain Euler--Lagrange multi-agent systems under jointly connected digraphs. Distributed event-based reference generators are proposed, which generate continuously differentiable reference signals using event-based communication that only transmit the states of the agents. Adaptive controllers are utilized based on these reference generators, allowing each agent to track the reference signals. Additionally, under the initial excitation assumption, the uncertain parameters of the system converge to their true values. Theoretical analysis shows that the multi-agent system achieves state consensus asymptotically under the proposed fully distributed event-triggered control protocol.

In the above results, Zeno behavior is excluded for each agent by providing a positive minimum inter-event time to ensure the feasibility of the proposed protocols.