Robust learning controller design for MIMO stochastic discrete-time systems: An H_∞-based approach

This paper is devoted to designing iterative learning control (ILC) for multiple-input multiple-output discrete-time systems that are subject to random disturbances varying from iteration to iteration. Using the super-vector approach to ILC, statistical expressions are presented for both expectation and variance of the tracking error, and time-domain conditions are developed to ensure their asymptotic stability and monotonic convergence. It shows that time-domain conditions can be tied together with an H_∞-based condition in the frequency domain by considering the properties of block Toeplitz matrices. This makes it possible to apply the linear matrix inequality technique to describe the convergence conditions and to obtain formulas for the control law design. Furthermore, the H_∞-based approach is shown applicable to ILC design regardless of the system relative degree, which can also be used to address issues of model uncertainty. For a class of systems with a relative degree of one, simulation tests are provided to illustrate the effectiveness of the H_∞-based approach to robust ILC design.