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The design of a decentralized discrete-time block control scheme, for a multi-agent system with a fixed topology, to achieve formation and trajectory tracking is proposed in this work. Each agent dynamics is represented either by a first-order or second-order discrete-time system, only the position of each agent's neighbors is measured and their velocity and acceleration are unknown, and exclusively the agents that are connected to the virtual agent have full information of the reference. Each agent is provided with discrete-time state observers for the velocity and acceleration of its neighbors. It is proved that formation and trajectory tracking can be achieved applying the proposed block control with a consensus scheme. The stability of the controlled system with the state observer is proved.

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Every new computer server introduced to the market aims at delivering the best tradeoff between performance and power consumption. This goal is crucial in the case of servers for cloud computing hardware infrastructure. In this context, power delivery (PD) experts are adopting higher frequency switching voltage regulators (VR) to reduce platform's cost as well as total cost of ownership (TCO). Because of this fact, the real estate of components, such as voltage regulators and output inductors, is shrinking as VR frequency increases. As a consequence, achieving the best performance of the VR implies looking into phase shedding schemes, as well as EM coupled inductor design, among other techniques, to mitigate power losses. This paper focuses on the study of the best angle arrangement possible for high frequency VR applications, by exploring angle settings under light load scenarios, aiming to minimize VR's power loss and output's voltage ripple.

In this paper, a decentralized control scheme for group formation and trajectory tracking of multi-agent systems is designed. In this scheme, each agent dynamics is represented by a single-input singleoutput linear system and the information that each controller requires is only the output of the others agents. With the proposed decentralized control law, multiagent system tracks asymptotically the trajectory and formation of the agents, even in the presence of smooth changes of formations. Moreover, the agent dynamics (structure and dimension) are not restricted to be the same, as usually assumed in the literature.A simulation example is provided in order to illustrate the application of the proposed control.