Essentially negative news about positive systems

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• 作者：A. Zappavigna^a ; ^{zappavigna@elet.polimi.it} ; P. Colaneri^a ; ^{colaneri@elet.polimi.it} ; S. Kirkland^b ; ^{stephen.kirkland@nuim.ie} ; R. Shorten^b ; ¹ ; ^{robert.shorten@nuim.ie}
• 关键词：Switching positive systems ; Discretisation ; Padé ; approximation
• 刊名：Linear Algebra and its Applications
• 出版年：2012
• 期刊代码：38_00243795
• 类别：mt
• 出版时间：1 May, 2012
• 卷：436
• 期：9
• 页码：3425-3442
• 文件大小：353 K

摘要

In this paper the discretisation of switched and non-switched linear positive systems using Pad茅 approximations is considered. Pad茅 approximations to the matrix exponential are sometimes used by control engineers for discretising continuous time systems and for control system design. We observe that this method of approximation is not suited for the discretisation of positive dynamic systems, for two key reasons. First, certain types of Lyapunov stability are not, in general, preserved. Secondly, and more seriously, positivity need not be preserved, even when stability is. Finally we present an alternative approximation to the matrix exponential which preserves positivity, and linear and quadratic stability.