Scale-invariant Controller Synthesis in Mass Chains

This paper studies the disturbance suppression problem for a homogeneous mass chain, i.e., chain of identical point masses interconnected by mechanical impedances. The particular focus is placed on whether attenuation level arbitrary length can be uniformly bounded with size-independent controller. We explicitly represent scalar transfer functions from disturbances to given intermass displacement as function number masses. an extension previous work author that established boundedness H-infinity norm when one end perturbed. propose new method drastically simplifies its derivation process and provide complete forms all our interest.