On positive filtering with H∞ performance for compartmental networks

Abstract

This article studies the reduced-order positive filtering problem with H performance of compartmental networks via a system augmentation approach. The filtering system is represented as a system augmentation form, which facilitates the parameterisation with structural constraints. By virtue of system augmentation, a new characterisation of the stability and H performance of the filtering system is established in terms of matrix inequalities. Based on this new characterisation, a necessary and sufficient condition for the existence of a desired filter is proposed, and an iterative algorithm is given to solve the condition. It is emphasised that the significance of the results presented in the article is not any extension of existing approaches or techniques to compartmental networks, but a new framework for filter synthesis. The effectiveness of the theoretical results is shown through some numerical examples.