Uniform continuity and delay robustness of an adaptive controller for Lagrangian systems

Abstract

Abstract This paper presents a method based on a continuity argument for analysing the delay robustness of nonlinear control systems with uncertainties. In particular, a delay-dependent stability condition is established in the form of a norm inequality for an adaptive control system with a time delay in the control input. The continuous dependence of the condition on the delay is derived via the uniform continuity in the delay of the fundamental solution of a general linear time-varying delay-differential equation. Since the stability condition holds when the delay is zero, the condition must be true for a certain non-zero positive delay due to continuity. Numerical simulations show the performance and robustness of the control system in the presence of an input delay. Remarkably, the results also illustrate a close agreement with the dependence on control parameters of the transient performance bounds predicted by the theoretical analysis in this paper.