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Asymptotic stability of singularly perturbed systems that have marginally stable boundary-layer systems

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Dynamics and Control

Abstract

A class of linear singularly perturbed systems with singular perturbation parameter µ > 0 is considered. To assure asymptotic stability of the full-order system for sm > 0 sufficiently small, it is customary to require that both the reduced-order system (µ = 0) and the boundary-layer system are asymptotically stable. Here we relax the requirement on the boundary-layer system to stability (i.e., stability, but not necessarily asymptotic stability) and show that, subject to one additional condition, the full-order system is asymptotically stable for sufficiently small µ. The result is illustrated by an application in which we consider the stability robustness of a feedback-controlled mechanical system with respect to an unmodeled flexibility.

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Authors and Affiliations

  1. School of Aeronautics and Astronautics, Purdue University, 47907, W. Lafayette, IN

    Martin Corless

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  1. Martin Corless
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Recommended by M. Ardema

This article is based on research supported by the U.S. National Science Foundation under grant MSM-87-06927. 1 .IfM, N ∈ ℝm×m, the notationM < N meansx T Mx <x T Nx for allx ∈ ℝm,x ≠ 0.

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Corless, M. Asymptotic stability of singularly perturbed systems that have marginally stable boundary-layer systems. Dynamics and Control 1, 95–108 (1991). https://doi.org/10.1007/BF02169427

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  • DOI: https://doi.org/10.1007/BF02169427

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