Stabilization of underactuated nonlinear systems to non‐feasible curves

This paper focuses on the development of stability conditions for systems of nonlinear non‐autonomous ordinary differential equations and their applications to control problems. We present a novel approach for the study of asymptotic stability properties for nonlinear non‐autonomous systems based on considering a parameterized family of sets. The proposed approach allows to state asymptotic stability conditions for a family of sets representing the level sets of a time‐varying Lyapunov function and to estimate the rate of convergence of solutions to a prescribed neighbourhood of the given curve. The obtained stability results are applied to the trajectory tracking problem for a class of nonholonomic systems.