Motion planning of multi-robot systems has been extensively investigated. Many proposed approaches assume that all robots are reliable. However, robots with priori known levels of reliability may be used in applications to account for: (1) the cost in terms of unit price per robot type, and (2) the cost in terms of robot wear in long term deployment. In the former case, higher reliability comes at a higher price, while in the latter replacement may cost more than periodic repairs, e.g., buses, trams, and subways. In this study, we investigate robust control of multi-robot systems, such that the number of robots affected by the failed ones is minimized. It should mandate that the failure of a robot can only affect the motion of robots that collide directly with the failed one. We assume that the robots in a system are divided into reliable and unreliable ones, and each robot has a predetermined and closed path to execute persistent tasks. By modeling each robot's motion as a labeled transition system, we propose two distributed robust control algorithms: one for reliable robots and the other for unreliable ones. The algorithms guarantee that wherever an unreliable robot fails, only the robots whose state spaces contain the failed state are blocked. Theoretical analysis shows that the proposed algorithms are practically operative. Simulations with seven robots are carried out and the results show the effectiveness of our algorithms. (C) 2018 Elsevier Ltd. All rights reserved.