On the input and output reducibility of multivariable linear systems

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Abstract
By introducing into a constant linear system ( F, G, H ) with input vector u and output vector y an open-loop control u = Pv and observer z = Qy , a new constant linear system ( F, GP, QH ) results which has input vector upsilon and output vector z . The problem investigated is one of constructing ( F, GP, QH ) so that upsilon and z have 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 field F (over which the system is defined) is infinite, the minimal dimensions of upsilon and z are essentially independent of the specific values of the input and output matrices G and H . It is also shown that this is not the case when F is 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.

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