Logo image
Back
Polynomial Internal Models for Finite-Horizon Robust Output Regulation with Unstructured Exogenous Signals
Journal article   Open access   Peer reviewed

Polynomial Internal Models for Finite-Horizon Robust Output Regulation with Unstructured Exogenous Signals

Venanzio Cichella, Ean Lovett, Michelangelo Bin, Nicola Mimmo and Lorenzo Marconi
IEEE control systems letters, Vol.10, pp.1303-1308
06/22/2026
DOI: 10.1109/LCSYS.2026.3706322
Appears in  UI Libraries Support Open Access
url
https://doi.org/10.1109/LCSYS.2026.3706322View
Published (Version of record) Open Access

Abstract

This paper addresses the robust output regulation problem for linear time-invariant (LTI) systems subject to sufficiently smooth, unstructured time-varying disturbances and reference signals. The proposed framework utilizes a polynomial basis to approximate these signals over a finite-time interval. First, we derive an internal model unit (IMU)-based controller which guarantees perfect regulation for polynomial signals of degree up to the selected order. We then extend this synthesis to exogenous signals satisfying suitable smoothness assumptions. By leveraging approximation theory and Input-to-State Stability (ISS) analysis, we prove that the regulation error remains within a neighborhood of zero over 0,t f , whose size is governed by the polynomial approximation error and the closed-loop amplification constants. For sufficiently smooth exogenous signals, this residual bound decreases with the polynomial approximation error as the internal-model order increases.
 Polynomials Regulation Closed loop systems Equations Internal model principle Matrices Modeling Poles and zeros Polynomial internal models Robust output regulation Steady-state Timing Tracking UIOWA OA Agreement

Details

Metrics

2 Record Views
Logo image