Almost sure and mean square convergence of ILC for linear systems with randomly varying iteration lengths

This note proposes convergence analysis for iterative learning control (ILC) design problem for discrete-time linear systems with randomly varying iteration length. No prior information on the probability distribution of stochastic iteration length is required. The simple P-type update algorithm is adopted in this note with Arimoto-like gain and/or causal gain. A novel switching system approach is introduced to prove the convergence both in almost sure and mean square senses. Further extensions to linear time-varying systems, randomly initial state condition, and stochastic linear systems are also provided.