Stabilizing controllers for systems with inputs scaled by persistently exciting diagonal matrices

This paper addresses the stabilization problem for a class of multi-input linear systems with inputs that are scaled by time-varying, singular gains in the form of a diagonal matrix. The scaling gains on the input vector are assumed to satisfy persistency of excitation conditions. A new state-dependent control structure is proposed, in which a scalar low-pass filter is employed to achieve the stabilization objective. A salient feature of this result is that the states of the closed-loop system are shown satisfy exponential convergence properties. As an interesting practical application, the relative proximity problem of spacecraft is presented taking into account the on-off schedules, as well as the rise and fall times of thrusters to illustrate the effectiveness of the proposed approach.