An iterative state-space component modal synthesis approach for damped systems

•A high efficient state-space CMS method for solving exact eigen-pairs and/or ROM of damped systems.•A novel iterative procedure for complex CMS methods with a complete theoretical framework.•A proof of the validity of the complex free-interface CMS method for a defective global system.•A real decoupled transformation for conducting complex CMS methods with only real operations.•A high efficient method for reanalysis and parallel programming.