Composite inverse model ILC for discrete time linear systems: zero error in finite steps and uncertain initial conditions

This paper develops iterative learning control strategies for discrete-time linear systems. An explicit state-space formula for the inverse-model-based ILC algorithm is derived under general conditions, which simplifies further when matrices B and C are invertible, providing a foundation for MIMO non-square systems. Building upon this formulation, a class of composite inverse-model algorithms is proposed, ensuring zero tracking error after a finite number of iterations while maintaining approximately minimal transient errors, and serving as a flexible framework to integrate optimization or greedy strategies. Robustness analysis is conducted for the multi-iteration inverse-model algorithms under model uncertainties, demonstrating uniform convergence properties. Furthermore, the framework is extended to systems with uncertain initial conditions, achieving zero-error convergence without requiring the initial state to converge to a fixed value, overcoming limitations in existing literature. Numerical simulations validate the effectiveness and practicality of the proposed methods.