Exact Characterization of Admissible Bandwidths for Linear Disturbance Observers

arXiv:2610.30559v1 Announce Type: new Abstract: This paper characterizes the entire set of admissible Q-filter bandwidths, equivalently parameterized by the time constant $\tau$, that guarantee robust internal stability of a linear disturbance observer (DOB) under parametric plant uncertainties. Classical small-$\tau$ stability results provide a rigorous foundation for Q-filter bandwidth design. Building on this foundation, we formulate the $\tau$-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.