ILC algorithm for a class of linear singular systems with multiple time-delays

Aiming at a class of linear singular systems with multiple time-delays, the Proportional Integration Differential (PID) type iterative learning control algorithm is given and the convergence criterion of the algorithm is obtained. Binding the characteristics of singular systems, the state variables are transformed in some condition by introducing the generalized Drazin inverse of matrix and the convergence of the algorithm is wholly analyzed by using λ norm and inequality technique. The results show that the iterative learning control conclusion of ordinary systems can be extended and applied to singular systems as long as make full use of the characteristics of singular systems.