Dynamic load balancing on a cluster computing consists on evenly dividing at any moment of time the workload to be distributed among the nodes, in order to avoid load unbalance. Load unbalance can be resolved if nodes can migrate some of their work. Using a stability criterion to allow the analysis of stability in the cluster is a way to decide the migration tasks. The Routh-Hurwitz criterion applied to the equation feature allows knowing whether a system is stable or not. The aim of this work is to develop a mathematical model based on linear differential equations representing the load, execution, and migration of task on a cluster computing. With the model, it is possible to determine the stability of the cluster. If the workload on the nodes tends to their equilibrium, new migration tasks do not need to check the stability of the nodes to be executed. © 2013 IEEE.