Initial Undershoot in Discrete-Time Input-Output Hammerstein Systems

作     者：Kim, Hyung Jun Kamaldar, Mohammadreza Bernstein, Dennis S. 

作者机构：Univ Michigan Dept Aerosp Engn Ann Arbor MI 48104 USA 

出 版 物：《IEEE OPEN JOURNAL OF CONTROL SYSTEMS》 (IEEE. Open. J. Control. Syst.)

年 卷 期：2025年第4卷

页      面：30-40页

核心收录：

基　　金：The authors thank the reviewers for numerous comments and suggestions that greatly improved the paper 

主　　题：Delays Nonlinear dynamical systems Sufficient conditions Linear systems Transient analysis Aerodynamics Terminology Stability analysis Poles and zeros Standards Nonlinear systems and control stability of nonlinear systems initial undershoot nonlinear zero dynamics discrete-time input-output Hammerstein system 

摘      要：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.