Time-Varying Lyapunov Functions for Tracking Control of Mechanical Systems With and Without Frictions

In this paper, the tracking control problem is investigated for time-varying nonlinear mechanical systems with and without frictions. A reduced-order dynamic and a traditional time-invariant Lyapunov design method is utilized for the case without frictions. Based on the traditional results, a new class of time-varying Lyapunov functions is provided for the case with time-varying frictions. It is shown that the tracking errors of the closed-loop system will converge to the neighborhood of the origin, which is determined by the feedback parameters. Numerical examples are presented for illustration.