Arbitrary pole and zero assignment with N-delay input control using stable controllers

It was shown by T. Mita and Y. Chida (1988) that with a two-delay input control scheme it is possible to assign all the poles and zeros of a closed-loop system using state feedback. This result is generalized to the case of N-delay input control. In such a scheme the input to the continuous system is changed N times more often than the output is sampled. Using such a scheme, it is shown how to design output feedback controllers for SISO systems that ensure arbitrary placement of all the poles and zeros of the closed-loop system while maintaining internal stability. The design uses stable compensators whose denominators have order p⩾(n-N)/(N -1), where n is the order of the continuous-time system. It is also shown that a hidden cost associated with the use of N-delay input control is a degradation in the intersample behavior. This is demonstrated by simulation, and some analysis which helps explain why this degradation arises is presented