Decoupling Approximation Design Using Operator Norms

Abstract: Coordinate coupling raises numerical, analysis, and design difficulties that grow with the size of the system. Decoupled dynamic equations simplify the above processes since each equation can be treated independently. Most models of physical systems are not decoupled so developing accurate approximations is of interest.

In this talk the issue of building such accurate decoupled approximations is addressed. Specifically, operator norms are used to characterize the approximation error. Then some system parameters are selected to minimize this error. The advantage of using operator norms is that the decoupling approximation is guaranteed to be accurate over large spaces of theoretically and practically relevant signals. These ideas are illustrated on tensegrity structures which are designed to yield accurate decoupled models with respect to finite energy and finite peak signals. Further analysis corrects several misconceptions regarding decoupling and system properties.