A trajectory‐based method for constructing null controllable regions

Summary The problem of determining a system's set of stabilizable states, the null controllable region (NCR), is intricately related to the problem of determining control Lyapunov functions. In this paper, we address the problem of construction of the NCR for control‐affine nonlinear systems with input constraints. To this end, we explain how the boundary of the NCR is covered by time‐optimal trajectories. To construct the NCR, we employ an algorithm based on Pontryagin's minimum principle, which integrates optimal trajectories of a special smooth system in reverse time from the boundary of an initial NCR estimate. We illustrate this algorithm with linear and nonlinear system examples.