Recursiveness of zero structures for system matrices of interconnected linear systems via module theoretic tools

The importance of the zeros of multivariable linear systems is well-known in terms of measure obstructions to the controllability and the observability. In this paper, a recursive decomposition of interconnected systems is outlined by taking into account the sequential structure of the connections. The paper extends the coordinate, module-theoretic studies from the elementary algebraic systems theory to include the case of such linear interconnected systems which need not to be controllable or observable. Also, the properties of controllability and observability, the decoupling zeros and the signal bloking issues are characterized.