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Zeros of discrete-time linear periodic systems. (English) Zbl 0606.93036

The note deals with the concept of zero for the class of discrete-time SISO linear periodic systems. The definition is based on a suitable time- invariant MIMO representation of the original system. Precisely, the zeros of the periodic system are defined as the transmission zeros of such an equivalent representation.
It is shown that this definition is consistent, in that it enables one to extend the well-known transmission blocking property of the zeros valid in the time-invariant case.
It is also shown that the number of zeros of a SISO n-th order periodic system is n-1 at most, and the set of zeros is independent of the choice of the sampling instants leading to the time-invariant reformulation.
The authors believe that the issues discussed in this note might turn out useful in the analysis and design of periodic feedback control systems, with special reference to root-locus and pole-zero cancellation techniques.

MSC:

93B60 Eigenvalue problems
93C05 Linear systems in control theory
93C55 Discrete-time control/observation systems
34C25 Periodic solutions to ordinary differential equations
39A12 Discrete version of topics in analysis
15A18 Eigenvalues, singular values, and eigenvectors

Keywords:

time-dependent
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