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Bounded real lemmas for positive descriptor systems

Zhang, Qingling, Zhang, Youmei, Tanaka, Tamaki, Yan, Xinggang (2015) Bounded real lemmas for positive descriptor systems. Journal of the Franklin Institute, 352 (1). pp. 346-368. ISSN 0016-0032. (doi:10.1016/j.jfranklin.2014.10.019)


A well known result in the theory of linear positive systems is the existence of positive definite diagonal matrix (PDDM) solutions to some well known linear matrix inequalities (LMIs). In this paper, based on the positivity characterization, a novel bounded real lemma for continuous positive descriptor systems in terms of strict LMI is first established by the separating hyperplane theorem. The result developed here provides a necessary and sufficient condition for systems to possess H?H? norm less than ? and shows the existence of PDDM solution. Moreover, under certain condition, a simple model reduction method is introduced, which can preserve positivity, stability and H?H? norm of the original systems. An advantage of such method is that systems? matrices of the reduced order systems do not involve solving of LMIs conditions. Then, the obtained results are extended to discrete case. Finally, a numerical example is given to illustrate the effectiveness of the obtained results.

Item Type: Article
DOI/Identification number: 10.1016/j.jfranklin.2014.10.019
Subjects: T Technology
Divisions: Faculties > Sciences > School of Engineering and Digital Arts
Faculties > Sciences > School of Engineering and Digital Arts > Instrumentation, Control and Embedded Systems
Depositing User: Tina Thompson
Date Deposited: 01 Sep 2015 15:42 UTC
Last Modified: 01 Aug 2019 10:39 UTC
Resource URI: (The current URI for this page, for reference purposes)
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