Yuri Ledyaev's main research interests lie in control theory (in particular, stabilization, optimal control, differential games), theory of differential inclusions, nonlinear functional and nonsmooth analysis (in particular, nonsmooth analysis' applications in control theory).

He received his Ph.D. degree from Moscow Institute for Physics and Technology in 1980 and his Dr.Sc. degree from Steklov Institute of Mathematics in 1990. He was with Department of Mathematics of Moscow Institute for Physics and Technology during 1980-1984, since 1984 he has been with Steklov Institute of Mathematics of Russian Academy of Sciences where he is a Principal Researcher at the Department of Differential Equations founded by L.S.Pontryagin. He is a Full Professor at the Department of Mathematics , Western Michigan University since 2000.

He authored about 40 papers in above mentioned areas. He is a coauthor with F.H.Clarke, R.J.Stern and P.R.Wolenski of the textbook " Nonsmooth Analysis and Control Theory" published by Springer- Verlag in 1998.

He is a member of the Editorial Boards of "Journal of Dynamical and Control Systems" and "Nonlinear Analysis". His most recently supervised Ph.D.students have been: M.Radulescu (1996, Math, Universite de Montreal) and E.Devdariani (1996, Math, Queen's University, Kingston, Canada).