Structure and Input-Output Properties in Networks of Nonlinear Systems
*** THIS PROJECT IS NO LONGER ACTIVE ***
This project aims to overcome the design complexity in networked dynamical systems by representing the components with input-output properties as abstractions of their complex dynamical models. The component-level task is to assign and certify the prescribed input-output properties; the network-level task is to combine this input-output information with the interconnection structure to deduce global dynamical behavior. The specific research topics include: (1) Developing analytical and numerical procedures for the certification of input-output properties; (2) Developing sharp stability tests for types of interconnection topologies; (3) Developing modified tests that account for time delays; (4) Generalizing the proposed techniques from stability to synchronization of variables in spatially distributed models; (5) Identifying key system properties that lead to violation of our synchrony conditions, and revealing the associated spatial phenomena.