Low frequency positive real control for delta operator systems

A strictly positive real control problem for delta operator systems in a low frequency range is presented by using the generalized Kalman–Yakubovic˘–Popov lemma. The objective of the strictly positive real control problem is to design a controller such that the transfer function is strictly positive real and the resulting closed-loop system is stable. Sufficient conditions for the low frequency strictly positive real controller of the closed-loop delta operator systems are presented in terms of solutions to a set of linear matrix inequalities. A numerical example is given to illustrate the effectiveness and potential for the developed techniques.