A Nonlinear φ ₀ -Convexity Result for the Bilateral Minimal Time Function

For a nonlinear control system, we derive a

-convexity result for the epigraph of the bilateral minimal time function. This extends the main result in a previous publication of the second author [Proximal subdifferential of the bilateral minimal time function and some regularity applications, J. Convex Analysis 20 (2013) 1095–1112], which discussed the linear case.