Finite-time stabilization of an integrator chain using only signs of the state variables

This paper considers the finite-time stabilization problem for an integrator chain in the context of uncertain measurement nonlinearities, such that the signs of the state variables are the only available information for feedback. The solutions of this problem are known for single, double, and triple integrators. The main result of the present paper is a higher-order sliding mode (HOSM) controller that stabilizes an integrator chain of arbitrary length. Computer simulations are provided to validate theoretical results.