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Multiplier theory for stability analysis of anti-windup control systems

Kothare, Mayuresh V. and Morari, Manfred (1996) Multiplier theory for stability analysis of anti-windup control systems. California Institute of Technology , Pasadena, CA. (Unpublished)

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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.

Item Type:Report or Paper (Technical Report)
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.
Group:Control and Dynamical Systems Technical Reports
Subject Keywords:Control input nonlinearity, constrained system, nonlinear system, stability analysis, anti-windup, bumpless transfer, passivity theorem, linear matrix inequality, multiplier theory, absolute stability.
Record Number:CaltechCDSTR:1996.012
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Usage Policy:You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.
ID Code:28121
Deposited By: Imported from CaltechCDSTR
Deposited On:14 Dec 2007
Last Modified:03 Oct 2019 03:29

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