Controllability of regular systems and defective systems with repeated eigenvalues

Controllability plays a key role in the vibration control of a structure, which can keep structural stability. In order to get practical conditions of structural controllability, two necessary conditions of controllability of a repeated eigenvalues system (regular and defective system) and their proofs are given. At the same time two sufficient conditions and their proofs are also presented. Finally we give a method of selecting control force distribution matrix B and some numerical examples.