M. I. Zelikin was awarded the Chebyshev Award in 1987 and the Lyapunov Award in 2010.
He was elected a corresponding member of the Russian Academy of Sciences in 2011.
Apart from mathematics, M. I. Zelikin is also known due to his activity in ecology, in particular, criticism of the Northern river reversal.
He wrote and published a book of memoirs «History of Evergreen Life» (Russian: «История вечнозелёной жизни», — Moscow, 2001) about it.
Zelikin, M. I.; Borisov, V. F. Theory of chattering control. With applications to astronautics, robotics, economics, and engineering. Systems & Control: Foundations & Applications. Birkhäuser Boston, Inc., Boston, MA, 1994. xvi+242 pp. ISBN0-8176-3618-8.
Zelikin, M. I. Control theory and optimization. I. Homogeneous spaces and the Riccati equation in the calculus of variations. Encyclopaedia of Mathematical Sciences, 86. Springer-Verlag, Berlin, 2000. xii+284 pp. ISBN3-540-66741-5.
Zelikin, M. I. Optimal control and variational calculus. Editorial URSS, Moscow, 2004 (in Russian) & 2010 (in Spanish).