Iterative learning control of linear continuous systems with variable initial states based on 2-D system theory

This paper is concerned with the variable initial states problem in iterative learning control (ILC) for linear continuous systems. Firstly, the properties of the trajectory of 2-D continuous-discrete Roesser model are analyzed by using Lyapunov´s method. Then, for any variable initial states which absolutely converge to the desired initial state, some sufficient conditions in the form of linear matrix inequalities (LMI) are given to ensure the convergence of the PD-type ILC rules. It implies that the ILC rules can be used to achieve the perfect tacking for variable initial states, even if the system dynamic is unknown. Finally, two numerical examples are given to illustrate the perfect tracking performance with exponentially convergent initial states.