His research has been conducted in the areas of optimum control of stochastic systems, stochastic games theory, infinite linear programming, and Markov processes. He has made significant contributions to all of these areas, but his work is most prominent in the area of stochastic control.

His work established a strong base for a subject matter known as "Adaptive control" of stochastic systems, and the large number and impact of his papers have earned him international recognition as creator of the "Mexican school of stochastic control”.

He was head of the departamento de matemáticas [department of mathematics] of the Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional (Cinvestav) [Center for Research and Advanced Studies of the National Polytechnic Institute]. Professor of Ciencia Básicas e Ingeniería [Basic Sciences and Engineering] of the Universidad Autónoma Metropolitana (UAM) [Autonomous Metropolitan University]. Professor at the Sección de Graduados [Graduate Section] of the Escuela Superior de Ingeniería Mecánica y Eléctrica (ESIME) [Upper School of Mechanical and Electrical Engineering] of the Instituto Politécnico Nacional (IPN) [National Polytechnic Institute]. He is a member of the Consejo Consultivo de Ciencias de la Presidencia de la República (CCC) [Science Consulting Council of the President’s Office].

He has received the Premio Nacional de Ciencias y Artes [National Award for Science and Arts] and was conferred a PhD Honoris Causa by the University of Sonora.

He has published over 100 research papers and 12 books and monographs. Dr. Hernández-Lerma is one of Mexico’s mathematicians with a very high number of citations of their work (some 800).

He has tutored 12 doctoral students (7 from the Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional (Cinvestav) [Center for Research and Advanced Studies of the National Polytechnic Institute], 3 from the Facultad de Ciencias [Faculty of Sciences] of the Universidad Nacional Autónoma de México (UNAM) [National Autonomous University of Mexico] and 2 from the Universidad Autónoma Metropolitana (UAM) [Autonomous Metropolitan University]). He has also supervised 28 masters and 3 undergraduate theses.