Another Form of System Matrix Associated with Delay-Differential Systems

摘要

Various kinds of controllability as well as necessary and sufficient conditions for these types of controllability are defined for a form of system matrix over the set of real numbers, corresponding to a delay differential system. Various types of observability are also defined. To what extent controllability and observability depend on the decoupling factors and zeros of a system matrix of this form is discussed. Of particular interest are system matrices which have delay only in the state as well as system matrices which have delay only in the control term in the input state relationship. Finally, conditions under which associated forms of transformations of similarity exist between these types of system matrices are determined.