Study of Fixed-Points in the Self-Repair Process of a 3-D Printer

We present and prove a theorem guaranteeing global stability in a non-linear system representing the iterative self-repair process where a 3D printer repairs its timing pulley. The process consists of gradually improving the broken part in the 3D printer until the printer reaches its repaired state. To prove global stability, we verify that the limit of the self-repair sequence does not depend on the initial condition, and always converges to the repaired state. Even though the convergence of this process has been analyzed under strong assumptions, in the present work, the convergence is proven for a more general case.