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We describe a simple yet general method to analyze networks of coupled identical nonlinear oscillators and study applications to fast synchronization, locomotion, and schooling. Specifically, we use nonlinear contraction theory to derive exact and global (rather than linearized) results on synchronization, antisynchronization, and oscillator death. The(More)
We study synchronization conditions for distributed dynamic networks with different types of leaders. The role of a " power " leader specifying a desired global state trajectory through local interactions has long been recognized and modeled. This paper introduces the complementary notion of a " knowledge " leader holding information on the target dynamics,(More)
— We study stability of interacting nonlinear systems with time-delayed communications, using contraction theory and a simplified wave variable design inspired by robotic teleoperation. We show that contraction is preserved through specific time-delayed feedback communications, and that this property is independent of the values of the delays. The approach(More)
Nonlinear contraction theory allows surprisingly simple analysis of synchronisation phenomena in distributed networks of coupled nonlinear elements. The key idea is the construction of a virtual contracting system whose particular solutions include the individual subsystems' states. We also study the role, in both nature and system design, of co-existing "(More)
Milestone Reports serve as background materials for future research, development, and education relevant to technical fields led by the Coordinating Committees of IFAC indicated below. They contain current state of the art of the technologies such as key problems and recent accomplishments and future perspectives that address forecasting needs, challenges,(More)
The financial crisis renewed interest in the potential for convex incentives such as stock options to affect managerial risk-taking. We examine how executive stock options affect risk-taking by exploiting two distinct sources of variation in option compensation that arise from institutional features of multi-year grant cycles. We find that a 10 percent(More)