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Subzeros in Feedback Transmission

This paper introduces the new concept of transmission subzeros for linear, time-invariant, finite-dimensional, causal, dynamical systems. Unlike the customary transmission zeros of multi-input, multi-output systems, transmission subzeros may be placed by certain types of output feedback. This dependence of subzeros upon feedback gains is characterized naturally by means of classical adjoint representations. For design purposes, it is shown how to reconstruct an (essentially) unique matrix from its adjoint, for both singular and nonsingular cases. Specifically, the zeros of (m-1)×(m-1) closed-loop subtransmissions may be directly shifted by a single-loop feedback closure around m×m plants. For computational purposes, these definitions are set up at the Rosenbrock System Matrix level. Example calculations for a tactical aircraft in planar motion are presented.