Relative Controllability for Delayed Linear Discrete System with Second-Order Differences

Solution to delayed linear discrete system with constant coefficients and second‐order differences and application to iterative learning control

“…It is remarkable that Khusainov and Shuklin first develop the idea of Duhamel's principle in the classical linear ordinary differential equations for seeking the explicit representation of solutions 18 to delay discrete/differential systems. Thereafter, References 19–22 succeeded to introduce the notations of discrete matrix delayed exponential functions to give the representation of solutions, and obtained the controllability and stability results in References 23–29. Further, our group 30–33 derived the convergence results with the help of a representation of a solution involving a notation of delayed discrete matrix function, where we emphasized that we did not turn an original iterative learning control problem for linear delayed discrete system to a Roesser model and the delayed exponential matrices played an important role in computing the output of each iterative time on the finite time interval.…”