Lyapunov-Based Control of an Uncertain Euler-Lagrange System with Uncertain Time-Varying Input Delays without Delay Rate Constraints

A tracking controller is developed for a class of uncertain Euler-Lagrange systems with bounded external disturbances and an uncertain time-varying input delay. A novel filtered tracking error signal is designed to obtain a delay-free input signal in the closed-loop error system to facilitate the control design and analysis. The designed novel filtered tracking error consists of a finite integral over a constant estimated delay interval of the past control inputs as a means to compensate for the input delay. The maximum tolerable error between unknown time-varying delay and a constant estimate of the delay can be determined based on the selection of the control gains to provide uniformly ultimately bounded convergence of the tracking error to the origin. Lyapunov-Krasovskii functionals are used in the Lyapunov-based stability analysis