Non-normality and the localized control of extended systems

The idea of controlling the dynamics of spatially extended systems using a small number of localized perturbations is very appealing-such a setup is easy to implement in practice. However, when the distance between controllers generating the perturbations becomes large, control fails due to extreme sensitivity of the system to noise. This sensitivity results from strong non-normality of the evolution operator governing the dynamics of disturbances in the controlled system. We investigate how non-normality can arise in an originally normal system and study how the noise amplification depends on the distance between controllers.