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Pole-placement problem for discrete-time linear periodic systems. (English) Zbl 0684.93039

Summary: The pole-placement problem for the monodromy matrix of a discrete-time linear periodic system is considered. Given a partition of the complex plane into a ‘good’ part \({\mathbb{C}}_ g\) and a ‘bad’ part \({\mathbb{C}}_ b\), the result obtained by W. M. Wonham [Linear multivariable control: A geometric approach, 2nd ed. (1979; Zbl 0424.93001)] is extended to the periodic case.
This extension is based on the decomposition of a completely controllable periodic system into two subsystems, such that the first subsystem is completely reachable and the eigenvalues of the monodromy matrix of the second one are equal to zero.

MSC:

93B55 Pole and zero placement problems
93C05 Linear systems in control theory
93C55 Discrete-time control/observation systems

Citations:

Zbl 0424.93001
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References:

[1] DOI: 10.1080/00207178408933268 · Zbl 0546.93010 · doi:10.1080/00207178408933268
[2] DOI: 10.1080/00207178708933923 · Zbl 0616.93033 · doi:10.1080/00207178708933923
[3] DOI: 10.1080/00207178008922850 · Zbl 0443.93044 · doi:10.1080/00207178008922850
[4] DOI: 10.1016/0024-3795(68)90047-5 · Zbl 0155.06603 · doi:10.1016/0024-3795(68)90047-5
[5] Wonham W. M., Linear Multivariale Control (1979)
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