Robust Semi-Global Output Regulation of Uncertain Two-Time-Scale Systems With Input Saturation

This paper investigates the robust semi-global output regulation of uncertain linear systems with input saturation. In this setup, one cannot apply off-the-shelf techniques to reject structural uncertainties due to numerical issues caused by the two time scales but also due to technical issues generated by the input saturation. To solve this problem, we combine internal model principle with low gain technique and singular perturbation theory. Explicitly, the regulator design is based on the computation of the solutions of a Sylvester equation, which can be ill-conditioned in the two-time scales setting. To overcome this, we propose an easily solvable equation, and the existence and uniqueness of its solution are guaranteed under some standard assumptions. Accordingly, an internal model-based controller is designed such that the semi-global robust output regulation problem can be solved. In order to cope with the input saturation, we impose that the ultimate upper bound of the infinity norm of the exosystem state is limited and satisfies certain constraints. Finally, three examples are provided to illustrate the effectiveness of the results.