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Preliminary Results on the Stability of Switched Positive Linear Systems

2004
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Release : 2004
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Book Synopsis Preliminary Results on the Stability of Switched Positive Linear Systems by :

Download or read book Preliminary Results on the Stability of Switched Positive Linear Systems written by . This book was released on 2004. Available in PDF, EPUB and Kindle. Book excerpt: It was recently conjectured that the Hurwitz stability of a polytope of Metzler matrices is a necessary and sufficient condition for the stability of the associated switched linear system for arbitrary switching sequences. In this paper we show: (i) that this conjecture is true for a polytope constructed from a pair of second order Metzler matrices; (ii) that the conjecture is true for general polytopes of a finite number of second order Metzler matrices; and (iii) that the conjecture is in general false for higher order systems. The implications of our results, both for the design of switched positive linear systems, and for research directions that arise as a result of our work, are discussed toward the end of the paper.

Switched Positive Linear Systems

2015-10-19 Computers
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Release : 2015-10-19
Genre : Computers
Kind : eBook
Book Rating : 705/5 ( reviews)

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Book Synopsis Switched Positive Linear Systems by : Franco Blanchini

Download or read book Switched Positive Linear Systems written by Franco Blanchini. This book was released on 2015-10-19. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Switched Positive Linear Systems

2015 Linear control systems
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Author :
Release : 2015
Genre : Linear control systems
Kind : eBook
Book Rating : 712/5 ( reviews)

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Book Synopsis Switched Positive Linear Systems by : Franco Blanchini

Download or read book Switched Positive Linear Systems written by Franco Blanchini. This book was released on 2015. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Switched Linear Systems

2005-04-13 Technology & Engineering
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Release : 2005-04-13
Genre : Technology & Engineering
Kind : eBook
Book Rating : 930/5 ( reviews)

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Book Synopsis Switched Linear Systems by : Zhendong Sun

Download or read book Switched Linear Systems written by Zhendong Sun. This book was released on 2005-04-13. Available in PDF, EPUB and Kindle. Book excerpt: Switched linear systems have enjoyed a particular growth in interest since the 1990s. The large amount of data and ideas thus generated have, until now, lacked a co-ordinating framework to focus them effectively on some of the fundamental issues such as the problems of robust stabilizing switching design, feedback stabilization and optimal switching. This deficiency is resolved by this book which features: nucleus of constructive design approaches based on canonical decomposition and forming a sound basis for the systematic treatment of secondary results; theoretical exploration and logical association of several independent but pivotal concerns in control design as they pertain to switched linear systems: controllability and observability, feedback stabilization, optimization and periodic switching; a reliable foundation for further theoretical research as well as design guidance for real life engineering applications through the integration of novel ideas, fresh insights and rigorous results.

Stability Theory of Switched Dynamical Systems

2011-01-06 Technology & Engineering
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Release : 2011-01-06
Genre : Technology & Engineering
Kind : eBook
Book Rating : 560/5 ( reviews)

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Book Synopsis Stability Theory of Switched Dynamical Systems by : Zhendong Sun

Download or read book Stability Theory of Switched Dynamical Systems written by Zhendong Sun. This book was released on 2011-01-06. Available in PDF, EPUB and Kindle. Book excerpt: There are plenty of challenging and interesting problems open for investigation in the field of switched systems. Stability issues help to generate many complex nonlinear dynamic behaviors within switched systems. The authors present a thorough investigation of stability effects on three broad classes of switching mechanism: arbitrary switching where stability represents robustness to unpredictable and undesirable perturbation, constrained switching, including random (within a known stochastic distribution), dwell-time (with a known minimum duration for each subsystem) and autonomously-generated (with a pre-assigned mechanism) switching; and designed switching in which a measurable and freely-assigned switching mechanism contributes to stability by acting as a control input. For each of these classes this book propounds: detailed stability analysis and/or design, related robustness and performance issues, connections to other control problems and many motivating and illustrative examples.

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