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Published August 8, 1996 | public
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Multiplier theory for stability analysis of anti-windup control systems

Abstract

We apply the passivity theorem with appropriate choice of multipliers to develop sufficient conditions for stability of the general anti-windup bumpless transfer (AWBT) framework presented in [24]. For appropriate choices of the multipliers, we show that these tests can be performed using convex optimization over linear matrix inequalities (LMIs). We show that a number of previously reported attempts to analyze stability of AWBT control systems, using such well-known and seemingly diverse techniques as the Popov, Circle and Off-Axis Circle criteria, the optimally scaled small-gain theorem (generalized μ upper bound) and describing functions, are all special cases of the general conditions developed in this paper. The sufficient conditions are complemented by necessary conditions for internal stability of the AWBT compensated system. Using an example, we show how these tests can be used to analyze the stability properties of a typical anti-windup control scheme.

Additional Information

Submitted to Automatica. Also presented at the 34th IEEE Conference on Decision and Control, New Orleans, LA, December 1995. Partial financial support from the U.S. National Science Foundation and the Swiss Federal Institute of Technology (ETH), Zürich, Switzerland, is gratefully acknowledged. We would like to thank Prof. B. D. O. Anderson for several helpful comments.

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Created:
August 19, 2023
Modified:
October 24, 2023