Aggregation of linear dynamic control systems. I

High dimension control systems whose vector-valued response depends on the syst em phase space are considered. Assuming that the response dimension is much lower than that of the system an aggregation problem is posed. To solve this is to find a system of lower dimension which is invariant or $\varepsilon$-invariant with the original system as far as the response curve is concerned. The problem is discussed in detail for a linear and autonomous system. The article is an extension of [1-4].