In distributed consensus control of Multi-Agent Systems (MASs), multiple autonomous agents work together to achieve a collective behavior, called consensus, by using only local interactions via a communication network. A MAS has reached consensus when all its agents agree about some variable of interest (for instance achieving a common internal state). The value of the consensus state can depend on the interest of all agents or given by a leader agent. A consensus protocol can be designed to guarantee that a MAS achieves consensus enforcing a desired convergence rate: asymptotic, finite-time, fixed-time or predefined-time convergence. In this thesis, the problem of designing a distributed predefined-time consensus protocol is addressed. It is done for a class of high-order MASs with nonlinear agent's dynamics over undirected communication topologies of the network and for directed topologies having a spanning tree. Three different consensus protocols are proposed, they are based on the so-called time base generators (TBGs), which are time-dependent functions used as time-varying gains and reference trajectories to be tracked by means of feedback controllers. Some leaderless and leader-follower consensus protocols have been designed, in which the settling time can be off-line predefined according to task requirements. The main contributions of this thesis are threefold: First, to our best knowledge, it is the first-time to raise and solve predefined-time consensus problems for high-order MASs under leaderless protocols and robust leader-follower protocols. Two, the proposed controllers yield smoother and smaller control signals than other approaches reported in the literature for first-order MASs. Third, the proposed consensus protocols do not have parameters depending on the connectivity of the graph considered.