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Journal of Control Science and Engineering
Volume 2011, Article ID 926712, 10 pages
Research Article

Generalized Quadratic Linearization of Machine Models

1Department of Electrical and Electronics Engineering Department, Hindustan of Science & Technology, Chennai 603103, India
2Department of Electrical and Electronics Engineering, SSN College of Engineering Kalavakkam 603110, India

Received 10 May 2011; Revised 17 August 2011; Accepted 26 August 2011

Academic Editor: Derong Liu

Copyright © 2011 Parvathy Ayalur Krishnamoorthy et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In the exact linearization of involutive nonlinear system models, the issue of singularity needs to be addressed in practical applications. The approximate linearization technique due to Krener, based on Taylor series expansion, apart from being applicable to noninvolutive systems, allows the singularity issue to be circumvented. But approximate linearization, while removing terms up to certain order, also introduces terms of higher order than those removed into the system. To overcome this problem, in the case of quadratic linearization, a new concept called “generalized quadratic linearization” is introduced in this paper, which seeks to remove quadratic terms without introducing third- and higher-order terms into the system. Also, solution of generalized quadratic linearization of a class of control affine systems is derived. Two machine models are shown to belong to this class and are reduced to only linear terms through coordinate and state feedback. The result is applicable to other machine models as well.