Observer-based Iterative Learning Control for the Discrete-time Systems with Time Delay and Finite Frequency Domain Specifications

This paper investigates the problem of the observer-based iterative learning control law for a class of discrete-time linear systems with a single delay. Particularly, the design is composed of a stabilizing feedback controller in the time domain and a PD-type of feedforward controller in the iteration domain that guarantees the monotonic convergence of the resulting control scheme. Furthermore, sufficient conditions for the stability analysis and the design method of the iterative learning control law are given based on the repetitive process stability theory and a version of generalized Kalman-Yakubovich-Popov (KYP) lemma. As the result, the control law design problem is cast into the convex optimization problem over linear matrix inequalities (LMIs) and therefore it is amenable to effective algorithmic solution. Also, it allows designers to impose control performance requirements over specific frequency ranges and obtain the conditions which are dependent on the delay size. Finally, an example is given to verify the effectiveness of the proposed method.