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arXiv · 2610.30559

Exact Characterization of Admissible Bandwidths for Linear Disturbance Observers

Hamin Chang·Hyuntae Kim
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Abstract

This paper characterizes the entire set of admissible Q-filter bandwidths, equivalently parameterized by the time constant $τ$, that guarantee robust internal stability of a linear disturbance observer (DOB) under parametric plant uncertainties. Classical small-$τ$ stability results provide a rigorous foundation for Q-filter bandwidth design. Building on this foundation, we formulate the $τ$-dependent robust internal-stability problem as a semialgebraic feasibility problem in bivariate polynomials and prove that the complete admissible set is a finite union of open intervals under the standing assumptions. A constructive procedure with exact membership tests recovers all stabilizing intervals. A numerical example with an uncertain plant family containing non-minimum-phase members illustrates a disconnected admissible set.

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Hamin Chang, Hyuntae Kim. 2026-10-22. Exact Characterization of Admissible Bandwidths for Linear Disturbance Observers. https://arxiv.org/abs/2610.30559

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