An example of robust internal model control under variable and uncertain delay

This paper proposes a particular study of the classic internal model control algorithm for a sampled-data system in a generalized context of uncertainty. Besides the usually considered model mismatch, the particularity of the case under consideration is that the measurements available to the control algorithm suffer from large, varying and uncertain delays. The presented study considers a simple SISO nonlinear system. The control algorithm is a sampled nonlinear model-based controller with successive model inversion and bias correction. The main contribution of this article is its proof of global convergence and robustness despite time-varying delays and uncertain measurement dating. In particular, the model error, the varying delays and measurements dating error are treated using monotonicity of the system and a detailed analysis of the closed-loop behaviour of the sampled dynamics, in an appropriate norm.