Integrator Backstepping using Barrier Functions for Systems with Multiple State Constraints

The problem of stabilization for a class of feedback linearizable systems with multiple state constraints is addressed. The design procedure is constructive, and yields a continuous final control law which guarantees that all specified states remain within certain bounds for all time. The achieved bounds on the states are independent of the initial conditions. The procedure entails shaping the control Lyapunov function, and propagating hard-bounds imposed on the pertinent stabilising functions and associated error signals through the steps of the backstepping control design framework.