Foundations and Trends® in Systems and Control > Vol 2 > Issue 2

Switched Positive Linear Systems

Franco Blanchini, University of Udine, Italy, blanchini@uniud.it Patrizio Colaneri, DEIB-Politecnico di Milano and IEIIT-CNR, Italy, colaneri@elet.polimi.it Maria Elena Valcher, University of Padova, Italy, meme@dei.unipd.it
 
Suggested Citation
Franco Blanchini, Patrizio Colaneri and Maria Elena Valcher (2015), "Switched Positive Linear Systems", Foundations and Trends® in Systems and Control: Vol. 2: No. 2, pp 101-273. http://dx.doi.org/10.1561/2600000005

Published: 25 Nov 2015
© 2015 F. Blanchini, P. Colaneri and M. E. Valcher
 
Subjects
Systems Theory,  Optimal Control
 

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In this article:
1. Introduction
2. Motivating applications
3. Stability
4. Input-output performances
5. Stabilization
6. Performances optimization
References

Abstract

In this mongraph we consider the class of continuous-time positive switched systems. We discuss several problems, including stability, performance analysis, stabilization via switching control, and optimization. The monograph starts with a chapter where several application examples are provided, to motivate the interest in this class of systems. The rest of the monograph is dedicated to the theory of stability, stabilization and performance optimization of positive switched systems. The main existing results are recalled, but also new challenging problems are proposed and solved. Special attention has been devoted to point out those results that specifically pertain to positive (linear) switched systems and do not find a counterpart for the wider class of (nonpositive) linear switched systems.

DOI:10.1561/2600000005
ISBN: 978-1-68083-070-5
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ISBN: 978-1-68083-071-2
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Table of contents:
1. Introduction
2. Motivating applications
3. Stability
4. Input-output performances
5. Stabilization
6. Performances optimization
References

Switched Positive Linear Systems

Positive systems are an important class of systems that frequently arise in application areas, such as in the chemical process industry, electronic circuit design, communication networks, and biology. The study of the stability of such systems differs from standard systems in that the analysis focuses only on the trajectories generated under positivity constraints.

Switched positive systems also arise in a variety of applications. Examples can be found in TCP congestion control, in processes described by non-homogeneous Markov chains, in image processing, in biochemical networks, and so on. In comparison to general switched systems, that have received a lot of attention in the past years, the theory for positive switched systems is still in its infancy. Switched Positive Linear Systems studies the stability, performance evaluation, stabilization via switching control, and optimal control of (continuous-time and linear) positive switched systems. It provides a review of the results that have already been established in the literature. Other results, especially those related to norm computation and optimization, are new and are presented integrated with previous ones.

Switched Positive Linear Systems provides a comprehensive and timely introduction to the study of such systems. Readers who are new to the topic will find everything required to understand such systems in a concise and accessible form.

 
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