Brief paper: Positivity-preserving H∞ model reduction for positive systems

Authors:
Ping Li;James Lam;Zidong Wang;Paresh Date
Affiliations:
Department of Mechanical Engineering, The University of Hong Kong, Hong Kong;Department of Mechanical Engineering, The University of Hong Kong, Hong Kong;Department of Information Systems and Computing, Brunel University, Uxbridge, Middlesex, UB8 3PH, UK;Department of Mathematical Sciences, Brunel University, Uxbridge, Middlesex, UB8 3PH, UK
Venue:
Automatica (Journal of IFAC)
Year:
2011

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Abstract

This paper is concerned with the model reduction of positive systems. For a given stable positive system, our attention is focused on the construction of a reduced-order model in such a way that the positivity of the original system is preserved and the error system is stable with a prescribed H"~ performance. Based upon a system augmentation approach, a novel characterization on the stability with H"~ performance of the error system is first obtained in terms of linear matrix inequality (LMI). Then, a necessary and sufficient condition for the existence of a desired reduced-order model is derived accordingly. Furthermore, iterative LMI approaches with primal and dual forms are developed to solve the positivity-preserving H"~ model reduction problem. Finally, a compartmental network is provided to show the effectiveness of the proposed techniques.