Saturated repetitive control for a class of nonlinear systems: A contraction mapping method

Contraction mapping methods do not need to know about the concrete form of plant models like the Lyapunov method. This is the biggest advantage over other methods in the field of iterative learning control for example. However, it is difficult to use such a tool to analyze repetitive control systems. This paper proposes a contraction mapping method based on spectral theory to design a saturated repetitive controller for a class of nonlinear systems, where the derived necessary and sufficient condition on the spectral radius can reduce the conservatism as much as possible. The feasibility of our work is demonstrated through a robotic manipulator tracking example.