Abstract
Recently. Rosenbrock (1974) has defined the order, degree and complexity of a linear time-invariant dynamical system S. These numbers play an important role in the hierarchical structure of a system as discussed by Rosenbrock and Pugh (1974). The present paper gives a complete description of the interrelation between such numerical invariants associated with a system S and its subsystems Si. Some new results in the hierarchical theory of systems are then obtained.

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