Cooperative control of multi-agent systems has attracted tremendous attention over the past couple of decades, due to their potential applications in a variety of areas, such as groups of mobile robots, teams of unmanned aerial vehicles, sensor networks and so on. Various cooperative control problems including, but not limited to, consensus, containment, formation, and cooperative output regulation, have been widely investigated. These cooperative control problems are often addressed via distributed control protocols, where each agent is only accessible to the information of itself and its neighboring agents. Time delays, as a common phenomenon in many practical systems, often lead to system performance degradation or even instability, and thus have long been a research topic of considerable interest in the control community. Transmission delays, as one typical time delay for networked multi-agent systems, often occur in the process of information exchange between agents. Most existing works on cooperative control problems of multi-agent systems with transmission delays only focus on bounded delays. Unbounded delays, however, do arise in many practical systems in fields of engineering, biology, mechanics, social science and so on. Unbounded delays are more general and in fact include bounded delays as special cases. Recently, some efforts have been devoted to consensus control of simple multi-agent systems with unbounded transmission delays including first-order and homogeneous high-order agent dynamics. However, many practical multi-agent systems are heterogeneous and often subject to various uncertainties. Moreover, different control objectives other than consensus, such as containment and formation, are often desired in many practical applications. Thus, various cooperative control problems of more general multi-agent systems with unbounded transmission delays deserve further investigation.

This thesis investigates several cooperative control problems of heterogeneous multi-agent systems with unbounded transmission delays. The main objective is to develop distributed control laws to solve the concerned cooperative control problems without any prior knowledge of the unbounded delays. This thesis can be divided into two parts. The first part addresses cooperative output regulation, containment or formation-containment problems of heterogeneous linear multi-agent systems with unbounded distributed transmission delays via the distributed observer approach, where the system matrix of an exosystem or the system matrices of multiple leaders are available to all followers but the state of the exosystem or the states of multiple leaders are only available to their neighboring agents. The main results of this part are summarized as follows.

1. The robust cooperative output regulation problem of heterogeneous uncertain linear multi-agent systems under unbounded distributed transmission delays is considered. A novel distributed observer is first proposed to estimate the state of an exosystem in the presence of unbounded distributed transmission delays. Then two novel distributed controllers, one based on state feedback and the other based on output feedback, are further developed without any prior knowledge of the unbounded transmission delays. It is shown that the resulting closed loop multi-agent systems can achieve robust cooperative output regulation. This result includes cooperative output regulation problems of multi-agent systems with constant transmission delays and bounded distributed transmission delays as its special cases. In addition, this result can be directly applied to solve leader-following consensus problems of multi-agent systems with unbounded distributed, bounded distributed or constant transmission delays.

2. The output containment control problem of heterogeneous linear multi-agent systems under unbounded distributed transmission delays is considered. A novel distributed output feedback control law is proposed based on the distributed observers under unbounded distributed transmission delays. It is shown that the output of each follower, under the proposed control law, converges to the convex hull spanned by the outputs of the leaders. This result includes relevant results on output containment control of multi-agent systems with bounded distributed or constant transmission delays as special cases.

3. The formation-containment tracking problem of heterogeneous linear multi-agent systems with unbounded distributed transmission delays is considered. The multi-agent system under consideration consists of a reference leader with a desired trajectory, a group of formation-leaders with a prescribed formation, and a group of followers. Novel distributed control laws are proposed for the formation-leaders and followers, respectively. It is shown that under the proposed control laws, the outputs of the formation-leaders not only achieve a prescribed time-varying formation but also track the desired trajectory generated by the reference leader, while the output of each follower converges to the convex hull spanned by the outputs of those formation-leaders.

The second part of this thesis addresses the leader-following consensus problem and the containment control problem of heterogeneous linear multi-agent systems with unbounded distributed transmission delays via the adaptive distributed observer approach, where only the neighboring agents of a single leader or multiple leaders have access to both the system matrices and the state of the corresponding leader or leaders. The main results of this part are summarized as follows.

1. The leader-following consensus problem of heterogeneous linear multi-agent systems with unbounded distributed transmission delays via the adaptive distributed observer approach is considered. A novel distributed output feedback controller is proposed based on the adaptive distributed observer without any prior knowledge of transmission delays. It is shown that the resulting closed loop system achieves leader-following consensus. This result can be directly applied to solve leader-following consensus of linear multi-agent systems with constant transmission delays or bounded distributed transmission delays.

2. The containment control problem of heterogeneous linear multi-agent systems under unbounded distributed transmission delays via the adaptive distributed observer approach is considered. A novel distributed output feedback control law is proposed based on the adaptive distributed observer but without any prior knowledge of transmission delays. It is shown that all followers converge to the convex hull spanned by the leaders. This result includes relevant results on containment control of linear multi-agent systems with bounded distributed or constant transmission delays as special cases.