Recently, the shape of the Nyquist plot has been proved invariant under frequency transformation in continuous-time linear systems. This letter deals with the discrete-time case where the frequency transformation is performed using an inner frequency transformation of the type z-1→ F(z). Dual results with respect to the continuous case are obtained, showing that the closed-loop stability for the class of transformed systems can be inferred from the order of the transformation and the Nyquist plot of the not transformed system, after calculating the number of unstable poles. Both single-input-single-output (SISO) and multi-input-multi-output (MIMO) systems are considered.

Nyquist Plots Under Frequency Transformations: The Discrete-Time Case

Bucolo M.;Buscarino A.;Fortuna L.;Frasca M.
2022

Abstract

Recently, the shape of the Nyquist plot has been proved invariant under frequency transformation in continuous-time linear systems. This letter deals with the discrete-time case where the frequency transformation is performed using an inner frequency transformation of the type z-1→ F(z). Dual results with respect to the continuous case are obtained, showing that the closed-loop stability for the class of transformed systems can be inferred from the order of the transformation and the Nyquist plot of the not transformed system, after calculating the number of unstable poles. Both single-input-single-output (SISO) and multi-input-multi-output (MIMO) systems are considered.
discrete-time systems
frequency transformations
inner systems
invariants
Nyquist plot
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11769/535261
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