Abstract The averaging method is one of the most used tools to study dynamicalsystems. With the development of the theory of differential inclusions,a respective generalization of the averaging method followed the steps outlinedin the theory of differential equations. Presently, it has been successfully appliedto a wide range of problems involving differential inclusions, simplifyingthe study of the systems under consideration. In this work, the main developmenttrends and methods in the application of the averaging method to thestudy of stability and optimality of solutions to differential inclusions are surveyed.A detailed list of references is given and some examples of applicationsare presented.
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