On the input and output reducibility of multivariable linear systems

By introducing into a constant linear system ( ) with input vector and output vector an open-loop control and observer , a new constant linear system ( ) results which has input vector and output vector . The problem investigated is one of constructing ( ) so that and have minimal dimension, subject to the condition that the controllability and observability properties of ( ) are preserved. It is shown that when the scalar field (over which the system is defined) is infinite, the minimal dimensions of and are essentially independent of the specific values of the input and output matrices and . It is also shown that this is not the case when is finite. Furthermore, an algorithm is presented for the construction of the minimal input (minimal output) ( ), which is directly represented in a useful canonical form.