Group for Research in Decision Analysis

Stabilizing and tracking periodic operating conditions

Roger W. Brockett Harvard University, United States

Since the work of Huygens in the 17th century, and continuing until the present day, there have been a steady stream of technological problems whose solution requires the synchronization of oscillators. In this talk we consider a general n-dimensional, autonomous differential equation model and investigate the types of coupling between the various modes that lead to synchronization. We will argue that when the coupling is weak there is a particular "simplest" form of coupling leading to synchronization and stability. The conclusions are based on a new result on eigenvalue placement and a complete analysis of the controllability of a class of systems with quadratic right-hand sides.

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Welcome to everyone!