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Zeros and the output-zeroing problem in linear systems with time delay in control vector

Tokarzewski J.

Archives of Control Sciences

2009

Vol. 19, no. 1

23-41

The notion of zeros in linear time-invariant multi input multi output systems with delay in state or/and control input is not extensively discussed in the relevant literature. The concept of invariant zeros in a linear time-invariant MIMO 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 also addressed. 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. General formulas for output-zeroing inputs, the corresponding solutions and the zero dynamics are provided. The obtained results are illustrated by simple numerical examples.