Finite difference based iterative learning control with initial state learning for a class of fractional order two-dimensional continuous-discrete linear systems

This article presents a PI-type iterative learning control (ILC) law with initial state learning for a class of alpha$$ \alpha $$ (0<alpha <= 1$$ 0) fractional order two-dimensional (2D) linear systems. First, by using backward difference method, the finite difference approximation of the fractional order derivative is obtained, which leads to globally 2-alpha$$ 2-\alpha $$ order accuracy. Then, a PI-ILC law is constructed at the nodes and the convergence analysis of the iterative scheme is proved. A linear matrix inequality-based sufficient condition is derived to guarantee that the tracking error is asymptotically convergent. The obtained convergence condition is fractional order dependent. Most of the classical ILC conditions for fractional order one-dimensional linear systems fall into the special cases of this article. Finally, the simulation results show the effectiveness of the proposed control method.