Initial Undershoot in Discrete-Time Input–Output Hammerstein Systems
This paper considers initial undershoot in the step response of discrete-time, input-output Hammerstein (DIH) systems, which have linear unforced dynamics and nonlinear zero dynamics (ZD). Initial undershoot occurs when the step response of a system moves initially in a direction that is opposite to...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
IEEE
2025-01-01
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| Series: | IEEE Open Journal of Control Systems |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/10824927/ |
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| Summary: | This paper considers initial undershoot in the step response of discrete-time, input-output Hammerstein (DIH) systems, which have linear unforced dynamics and nonlinear zero dynamics (ZD). Initial undershoot occurs when the step response of a system moves initially in a direction that is opposite to the direction of the asymptotic response. For DIH systems, the paper investigates the relationship among the existence of initial undershoot, the step height, the height-dependent delay, and the stability of the ZD. For linear, time-invariant systems, the height-dependent delay specializes to the relative degree. The main result of the paper provides conditions under which, for all sufficiently small step heights, initial undershoot in the step response of a DIH system implies instability of the ZD. Several examples of DIH systems are presented to illustrate these results. |
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| ISSN: | 2694-085X |