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...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IEEE
2025-01-01
|
| Series: | IEEE Open Journal of Control Systems |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/10824927/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832582296304091136 |
|---|---|
| author | Hyung Jun Kim Mohammadreza Kamaldar Dennis S. Bernstein |
| author_facet | Hyung Jun Kim Mohammadreza Kamaldar Dennis S. Bernstein |
| author_sort | Hyung Jun Kim |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-409170c282e04125a5f6934fc3077347 |
| institution | Kabale University |
| issn | 2694-085X |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Open Journal of Control Systems |
| spelling | doaj-art-409170c282e04125a5f6934fc30773472025-01-30T00:04:44ZengIEEEIEEE Open Journal of Control Systems2694-085X2025-01-014304010.1109/OJCSYS.2025.352598310824927Initial Undershoot in Discrete-Time Input–Output Hammerstein SystemsHyung Jun Kim0https://orcid.org/0009-0006-1837-4280Mohammadreza Kamaldar1https://orcid.org/0000-0002-4774-9794Dennis S. Bernstein2https://orcid.org/0000-0003-0399-3039Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI, USADepartment of Aerospace Engineering, University of Michigan, Ann Arbor, MI, USADepartment of Aerospace Engineering, University of Michigan, Ann Arbor, MI, USAThis 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.https://ieeexplore.ieee.org/document/10824927/Nonlinear systems and controlstability of nonlinear systemsinitial undershootnonlinear zero dynamicsdiscrete-time input-output Hammerstein system |
| spellingShingle | Hyung Jun Kim Mohammadreza Kamaldar Dennis S. Bernstein Initial Undershoot in Discrete-Time Input–Output Hammerstein Systems IEEE Open Journal of Control Systems Nonlinear systems and control stability of nonlinear systems initial undershoot nonlinear zero dynamics discrete-time input-output Hammerstein system |
| title | Initial Undershoot in Discrete-Time Input–Output Hammerstein Systems |
| title_full | Initial Undershoot in Discrete-Time Input–Output Hammerstein Systems |
| title_fullStr | Initial Undershoot in Discrete-Time Input–Output Hammerstein Systems |
| title_full_unstemmed | Initial Undershoot in Discrete-Time Input–Output Hammerstein Systems |
| title_short | Initial Undershoot in Discrete-Time Input–Output Hammerstein Systems |
| title_sort | initial undershoot in discrete time input x2013 output hammerstein systems |
| topic | Nonlinear systems and control stability of nonlinear systems initial undershoot nonlinear zero dynamics discrete-time input-output Hammerstein system |
| url | https://ieeexplore.ieee.org/document/10824927/ |
| work_keys_str_mv | AT hyungjunkim initialundershootindiscretetimeinputx2013outputhammersteinsystems AT mohammadrezakamaldar initialundershootindiscretetimeinputx2013outputhammersteinsystems AT dennissbernstein initialundershootindiscretetimeinputx2013outputhammersteinsystems |