RESEARCH PAPERS: Design and Synthesis

Linear, Multivariable Robust Control With a μ Perspective

[+] Author and Article Information
Andy Packard

Mechanical Engineering, University of California, Berkeley, CA

John Doyle

Electrical Engineering, Caltech, Pasadena, CA

Gary Balas

Aerospace Engineering, University of Minnesota, Minneapolis, MN

J. Dyn. Sys., Meas., Control 115(2B), 426-438 (Jun 01, 1993) (13 pages) doi:10.1115/1.2899083 History: Received January 20, 1993; Online March 17, 2008


The structured singular value is a linear algebra tool developed to study a particular class of matrix perturbation problems arising in robust feedback control of multivariable systems. These perturbations are called linear fractional, and are a natural way to model many types of uncertainty in linear systems, including state-space parameter uncertainty, multiplicative and additive unmodeled dynamics uncertainty, and coprime factor and gap metric uncertainty. The structured singular value theory provides a natural extension of classical SISO robustness measures and concepts to MIMO systems. The structured singular value analysis, coupled with approximate synthesis methods, make it possible to study the tradeoff between performance and uncertainty that occurs in all feedback systems. In MIMO systems, the complexity of the spatial interactions in the loop gains make it difficult to heuristically quantify the tradeoffs that must occur. This paper will look at the role played by the structured singular value (and its computable bounds) in answering these questions, as well as its role in the general robust, multivariable control analysis and design problem.

Copyright © 1993 by The American Society of Mechanical Engineers
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