On minimal realizations and minimal partial realizations of linear time-invariant systems subject to point incommensurate delays

Abstract

This paper investigates key aspects of realization and partial realization theories for linear time-invariant systems being subject to a set of incommensurate internal and external point delays. The results are obtained based on the use of formal Laurent expansions whose coefficients are polynomial matrices of appropriate orders and which are also appropriately related to truncated and infinite block Hankel matrices. The above-mentioned polynomial matrices arise in a natural way from the transcendent equations associated with the delayed dynamics. The results are linked to the properties of controllability and observability of dynamic systems. Some related overview is given related to robustness concerned with keeping the realization properties under mismatching between a current transfer matrix and a nominal one