[1][2] In his dissertation, Krener showed that the Lie bracket played a role in nonlinear controllability by proving a version of Chow's theorem.

[3] Krener retired from Davis as a distinguished professor in 2006 and joined the department of applied mathematics at the Naval Postgraduate School in Monterey, California.

His research interests are in developing methods for the control and estimation of nonlinear dynamical systems and stochastic processes.

With Isidori, Gori-Giorgi and Monaco,[6] he gave conditions for the existence and construction of decoupling and noninteracting control laws for nonlinear systems.

It also led to the concept of the zero of a nonlinear system, which was subsequently developed by Byrnes and Isidori and extended to the backstepping technique of control by Kokotovic, Krstic and many others.