On the local stability of the solution to optimal control problems

New conditions for the local stability of optimal control problems are presented. The conditions are an extension of the results of a previous study focusing on the solution to problems solvable using calculus of variations. A comparison is made between the conditions introduced here and those presented in the literature. It is shown that our condition is roughly as powerful as the one presented by Sorger (J. Math. Anal. Appl. 148 (1990) 191) but it is easier to check.