Dynamic position feedback stabilisation of multidegrees-of-freedom linear mechanical systems subject to nonsmooth impacts

The goal of the paper is to extend some previous results concerned with state feedback stabilisation of mechanical systems subject to nonsmooth impacts, to the case when only position measurements are available for feedback. Fully actuated n-degrees-of-freedom mechanical systems are considered (whereas earlier studies considered only one-degree-of-freedom systems) whose dynamics would be linear in the absence of the inequality constraint delimiting the admissible region. For such systems, a class of compensators that ensures exponential and BIBS stabilisation (without using velocity measurements, which were requested in earlier studies) is proposed and their efficacy is proven by means of Lyapunov techniques. Simulations and experimental results are included to show the effectiveness of the theory presented.