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IMA Journal of Mathematical Control and Information Advance Access published online on September 5, 2007
IMA Journal of Mathematical Control and Information, doi:10.1093/imamci/dnm021
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© The author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Generalized PI observer design for linear systems

Ai-Guo Wu{dagger}

Center for Control Theory and Guidance Technology, Harbin Institute of Technology, PO Box 416, Harbin 150001, People's Republic of China
Information and Control Research Center, Shenzhen Graduate School, Harbin Institute of Technology, HIT Campus, Shenzhen University Town, Shenzhen 518055, People's Republic of China

Guang-Ren Duan

Center for Control Theory and Guidance Technology, Harbin Institute of Technology, PO Box 416, Harbin 150001, People's Republic of China

{dagger} Email: ag.wu{at}163.com

Received on 1 November 2005; Revision received 25 January 2007. Accepted on 2 May 2007


  Abstract

A parametric design approach for generalized proportional–integral (PI) observers of linear systems is proposed. Based on an explicit parametric general solution to a type of Sylvester matrix equations, complete parameterizations for all observer gains are presented. Moreover, the parametric expression of the left eigenvector matrix of the observer system is also established. The proposed design method can offer all the degrees of design freedom which can be utilized to achieve various desirable system specifications and performances. Also, a numerical example is given to show the design procedure and illustrate the effect of the proposed approach.

Keywords: generalized PI observers; degree of design freedom; linear systems; parametric approach.


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