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On guaranteed stability of uncertain linear systems via linear control

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Abstract

This paper addresses the problem of stabilizing an uncertain linear system. The uncertaintyq(·) which enters the dynamics is nonstistical in nature. That is, noa priori statistics forq(·) are assumed; only boundsQ on the admissible variations ofq(·) are taken as given. The results given here applied to so-called matched systems differ from previous results in two ways. Firstly, the stabilizing control in this paper is linear; for this same class of problems, many of the existing results would require a nonlinear control. Furthermore, those results which do in fact yield linear controls are only valid when a certain matrix Ω(q) (formed using the given data) is negative definite for allq ∈Q. In contrast, the theory given here only requires compactness of the bounding setQ. Secondly, we show that the so-called matching conditions (used in earlier work) can be generalized so as to encompass a larger class of dynamical systems.

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Authors and Affiliations

  1. School of Electrical Engineering, Cornell University, Ithaca, New York

    J. S. Thorp (Professor)

  2. Department of Electrical Engineering, University of Rochester, Rochester, New York

    B. R. Barmish (Associate Professor)

Authors
  1. J. S. Thorp
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  2. B. R. Barmish
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Additional information

Communicated by G. Leitmann

This research was supported by the US Department of Energy under Contract No. ET-78-S-01-3390.

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Thorp, J.S., Barmish, B.R. On guaranteed stability of uncertain linear systems via linear control. J Optim Theory Appl 35, 559–579 (1981). https://doi.org/10.1007/BF00934932

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