Brief Multiplier theory for stability analysis of anti-windup control systems

Authors:
Mayuresh V. Kothare;Manfred Morari
Affiliations:
Department of Chemical, Lehigh University, B315 Iacocca Hall, 111 Research Drive, Bethlehem, PA 18015, USA;Automatic Control Laboratory, Swiss Federal Institute of Technology (ETH), Physikstrasse 3, 8092 Zürich, Switzerland
Venue:
Automatica (Journal of IFAC)
Year:
1999

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Abstract

We apply the passivity theorem with appropriate choice of multipliers to develop a general framework for analyzing stability of anti-windup bumpless transfer (AWBT) schemes. For appropriate choices of the multipliers, we reduce the resulting sufficient conditions for stability to equivalent linear matrix inequalities (LMIs). We show that a number of previously reported attempts to analyze AWBT stability, using seemingly diverse techniques such as the Popov, circle and off-axis circle criteria, the optimally scaled small-gain theorem (generalized @m upper bound) and describing functions can all be generalized within the framework of this paper.