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TECHNICAL PAPERS

A Non-Normality Measure of the Condition Number for Monitoring and Control

[+] Author and Article Information
Kunsoo Huh

Department of Precision Mechanical Engineering, Hanyang University, Seoul, Korea

Jeffrey L. Stein

Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, MI 48109-2125

J. Dyn. Sys., Meas., Control 119(2), 217-222 (Jun 01, 1997) (6 pages) doi:10.1115/1.2801236 History: Received July 12, 1994; Revised July 12, 1995; Online December 03, 2007

Abstract

Because the behavior of the condition number can have highly steep and multi-modal structure, optimal control and monitoring problems based on the condition number cannot be easily solved. In this paper, a minimization problem is formulated for κ2 (P), the condition number of an eigensystem (P) of a matrix in terms of the L2 norm. A new non-normality measure is shown to exist that guarantees small values for the condition number. In addition, this measure can be minimized by proper selection of controller and observer gains. Application to the design of well-conditioned controller and observer-based monitors is illustrated.

Copyright © 1997 by The American Society of Mechanical Engineers
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