An improved method for calculating iterative learning control convergence rate

In Iterative Learning Control (ILC). the lifted system is often used in design and analysis to determine convergence rate of the learning algorithm. Computation of the convergence rate in the lifted setting requires construction of large NxN matrices, where N is the number of data points in an iteration. The convergece rate computation is O(N²) and is typically limited to short iteration lengths because of computational memory constraints. In this article, we present an alternative method for calculating the convergence rate without the need of large matrix calculations. This method uses the implicitly restarted Arnoldi method and dynamic simulations to calculate the ILC norm, reducing the calculatin to O(N). In addition to faster computation, we are able to calculate the convergence rate for long iteration lengths. This method is presented for multi-input multi-output, linear time-varying discrete-time systems.