Essentially negative news about positive systems

被引：8
|
作者：
Zappavigna, A. [1 ]
Colaneri, P. [1 ]
Kirkland, S. [2 ]
Shorten, R. [2 ]
机构：
[1] Politecn Milan, Dipartimento Elettron & Informaz, I-20133 Milan, Italy
[2] Natl Univ Ireland Maynooth, Hamilton Inst, Maynooth, Kildare, Ireland
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2012年 / 436卷 / 09期
基金：
爱尔兰科学基金会;
关键词：
Switching positive systems; Discretisation; Pade approximation; STABILITY; PADE;
D O I：
10.1016/j.laa.2011.12.021
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper the discretisation of switched and non-switched linear positive systems using Pade approximations is considered. Pade 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 all alternative approximation to the matrix exponential which preserves positivity, and linear and quadratic stability. (C) 2012 Published by Elsevier Inc.
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页码：3425 / 3442
页数：18
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