On the input and output reducibility of multivariable linear systems

By introducing into a constant linear system (F, G, H) with input vectoruand output vectoryan open-loop controlu = Pvand observerz = Qy, a new constant linear system (F, GP, QH) results which has input vectorupsilonand output vectorz. The problem investigated is one of constructing (F, GP, QH) so thatupsilonandzhave minimal dimension, subject to the condition that the controllability and observability properties of (F, G, H) are preserved. It is shown that when the scalar fieldF(over which the system is defined) is infinite, the minimal dimensions ofupsilonandzare essentially independent of the specific values of the input and output matricesGandH. It is also shown that this is not the case whenFis finite. Furthermore, an algorithm is presented for the construction of the minimal input (minimal output) (F, GP, QH), which is directly represented in a useful canonical form.