A Novel Continuous Feedback Control for Rapidly Exponentially Stabilisation of Mechanical Systems

Abstract

In this paper, stabilization in accelerated time with continuous state feedback control is considered for mechanical systems. A general approach to construct Lyapunov functions that can be used to show rapidly exponential stability of the feedback controlled systems is developed. Furthermore, the continuous feedback control does not lead to chattering phenomena in the presence of measurement noise. The rapidly exponentially stabilization scheme given here generalizes this prior research to multiple degree-of-freedom mechanical comparison is carried out through numerical simulations on two classical nonlinear systems that are representative of a broad class of mechanical systems.