Schur stability radius bounds for robust iterative learning controller design

This paper computes bounds on the Schur stability radius for use in designing robust iterative learning controllers. The discrete Lyapunov equation is used to compute the Schur stability radius of the ILC system for the case of parametric or interval perturbations in the system Markov parameters. This paper is distinct from the existing ILC works in that the interval robustness concepts are integrated with asymptotic stability and monotonic convergence conditions to suggest design of the learning gain matrix that makes the system robust against interval model uncertainties up to a computable bound. After derivations of the analytical stability radius, optimization schemes are suggested to design the learning gain matrix. The proposed approach allows design of causal/noncausal time-varying learning matrix gains.