Zeros in linear systems with input delay

The concept of invariant zeros in a linear time-invariant system with delay in control vector is considered. In the state-space framework the invariant zeros are treated as the triples: complex number, nonzero state-zero direction, input-zero direction. Such treatment is strictly related to the output-zeroing problem and in that spirit the zeros can be easily interpreted. The problem of zeroing the system output is discussed. For systems of uniform rank the first nonzero Markov parameter comprises a certain amount of information concerning invariant zeros, output-zeroing inputs and the zero dynamics.