skip to content
Matrix diagonal stability in systems and computation Preview this item
ClosePreview this item
Checking...

Matrix diagonal stability in systems and computation

Author: Eugenius Kaszkurewicz; Amit Bhaya
Publisher: Boston : Birkhäuser, ©2000.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
"Matrix diagonal stability and the related diagonal-type Liapunov functions possess properties that make them attractive and very useful for applications. This new book addresses the matrix-stability concept and its applications to the analysis and design of several types of discrete-time and continuous-time dynamical systems." "The book provides an essential reference for new methods and analysis related to  Read more...
Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

 

Find a copy online

Links to this item

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Eugenius Kaszkurewicz; Amit Bhaya
ISBN: 0817640886 9780817640880 3764340886 9783764340889
OCLC Number: 41380381
Description: xiv, 267 pages : illustrations ; 24 cm
Contents: 1 Diagonally Stable Structures in Systems and Computation 1 --
1.2 Robust Stability of a Mechanical System 5 --
1.3 Lotka-Volterra Ecosystem Model 8 --
1.4 Convergence of Asynchronous Computations 11 --
1.5 Global Stability of Neural Networks 15 --
1.6 Variable Structure Systems 17 --
1.7 Existence of Diagonal-Type Liapunov Functions 21 --
2 Matrix Diagonal and D-Stability 25 --
2.1 Matrix Stability Concepts 25 --
2.1.1 Basic Notation and Terminology 28 --
2.1.2 Basic Results on Hurwitz Diagonal and D-Stability 31 --
2.2 Special Classes of Hurwitz Diagonally Stable Matrices 40 --
2.3 Similarity for Hurwitz Diagonally Stable Matrices 46 --
2.4 Persistence of Diagonal Stability under Perturbations 48 --
2.5 Basic Results on Schur Diagonal and D-Stability 50 --
2.6 A Matrix Polytopic View of Schur Diagonal and D-Stability 54 --
2.7 Special Classes of Schur Diagonally Stable Matrices 58 --
2.7.1 Schur Diagonal and D-Stability for Two-by-Two Matrices 63 --
2.7.2 Nonnegative Matrices 65 --
2.7.3 Qualitatively Schur Stable Matrices 72 --
2.8 Testing for Diagonal and D-Stability 75 --
2.10 Appendix Summary of the Theory of the Liapunov Equation 85 --
3 Mathematical Models Admitting Diagonal-Type Liapunov Functions 90 --
3.1 Classes of Nonlinearities and Diagonal-Type Liapunov Functions 90 --
3.2 Continuous-Time State-Space Models and Stability Results 92 --
3.3 Seeking Hurwitz Diagonal Stability: State-Space Realization Procedures 98 --
3.4 Discrete-Time State-Space Models and Stability Results 101 --
3.4.1 Discrete-Time Interval Systems 108 --
3.5 Models for Asynchronous Systems 115 --
3.6 Discrete-Time Systems with Delays 119 --
3.8 Appendix Summary of Liapunov Stability Theory 123 --
4 Convergence of Asynchronous Iterative Methods 128 --
4.1 What Are Asynchronous Iterative Methods? 128 --
4.2 A Mathematical Model for Asynchronous Block-Iterations 130 --
4.2.1 Convergence Conditions for the Asynchronous Case 133 --
4.2.2 Convergence Conditions for the Synchronous Case 136 --
4.3 Asynchronous Iterations to Solve Almost Linear Equations 138 --
4.4 Parallel Asynchronous Team Algorithms 144 --
5 Neural Networks, Circuits, and Systems 154 --
5.1 Continuous-Time Hopfield-Tank Neural Networks 154 --
5.1.1 A Global Stability Result 156 --
5.1.2 Refinements of the Global Stability Result 158 --
5.1.3 Persistence of Global Asymptotic Stability 164 --
5.2 Discrete-Time Neural Networks 166 --
5.3 Passive RLC Circuits 170 --
5.4 Digital Filters in State-Space Description 174 --
5.5 Two-Dimensional (2D) Dynamical Systems 177 --
5.6 Trophic Chains and Communities with Vertical Structure 184 --
6 Interconnected Systems: Stability and Stabilization 192 --
6.1 Diagonal Stability in the Large Scale Systems Approach 192 --
6.2 Absolute Stability of Interconnected Systems 199 --
6.3 Linearly Interconnected Lur'e Systems 203 --
6.4 Stabilization by Linear Feedback 210 --
6.5 Decentralized Power-Frequency Control of Power Systems 219 --
6.7 Appendix Summary of the Large Scale Systems Approach 227.
Responsibility: Eugenius Kaszkurewicz, Amit Bhaya.

Abstract:

A natural answer to these questions would be that the use of diagonal- type Liapunov functions is frequent because of their simplicity within the class of all possible Liapunov functions.  Read more...

Reviews

Editorial reviews

Publisher Synopsis

"The book provides an essential reference for new methods and analysis related to dynamical systems described by linear and nonlinear ordinary differential equations and difference equations. As Read more...

 
User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.
Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


Primary Entity

<http://www.worldcat.org/oclc/41380381> # Matrix diagonal stability in systems and computation
    a schema:Book, schema:CreativeWork ;
   library:oclcnum "41380381" ;
   library:placeOfPublication <http://dbpedia.org/resource/Boston> ; # Boston
   library:placeOfPublication <http://id.loc.gov/vocabulary/countries/nyu> ;
   schema:about <http://dewey.info/class/515.352/e21/> ;
   schema:about <http://experiment.worldcat.org/entity/work/data/20888049#Topic/matrix_stabilitat_differenzierbares_dynamisches_system> ; # Matrix--Stabilität--Differenzierbares dynamisches System
   schema:about <http://id.worldcat.org/fast/1012399> ; # Matrices
   schema:about <http://experiment.worldcat.org/entity/work/data/20888049#Topic/differenzierbares_dynamisches_system_matrix_stabilitat> ; # Differenzierbares dynamisches System--Matrix--Stabilität
   schema:about <http://id.worldcat.org/fast/1131203> ; # Stability
   schema:about <http://id.worldcat.org/fast/893426> ; # Differentiable dynamical systems
   schema:about <http://experiment.worldcat.org/entity/work/data/20888049#Topic/stabilitat_matrix_differenzierbares_dynamisches_system> ; # Stabilität--Matrix--Differenzierbares dynamisches System
   schema:bookFormat bgn:PrintBook ;
   schema:contributor <http://viaf.org/viaf/67333146> ; # Amit Bhaya
   schema:copyrightYear "2000" ;
   schema:creator <http://viaf.org/viaf/74718974> ; # Eugenius Kaszkurewicz
   schema:datePublished "2000" ;
   schema:exampleOfWork <http://worldcat.org/entity/work/id/20888049> ;
   schema:inLanguage "en" ;
   schema:name "Matrix diagonal stability in systems and computation"@en ;
   schema:productID "41380381" ;
   schema:publication <http://www.worldcat.org/title/-/oclc/41380381#PublicationEvent/boston_birkhauser_2000> ;
   schema:publisher <http://experiment.worldcat.org/entity/work/data/20888049#Agent/birkhauser> ; # Birkhäuser
   schema:reviews <http://www.worldcat.org/title/-/oclc/41380381#Review/1205187628> ;
   schema:url <http://www.gbv.de/dms/ilmenau/toc/269887598.PDF> ;
   schema:workExample <http://worldcat.org/isbn/9780817640880> ;
   schema:workExample <http://worldcat.org/isbn/9783764340889> ;
   wdrs:describedby <http://www.worldcat.org/title/-/oclc/41380381> ;
    .


Related Entities

<http://dbpedia.org/resource/Boston> # Boston
    a schema:Place ;
   schema:name "Boston" ;
    .

<http://experiment.worldcat.org/entity/work/data/20888049#Topic/differenzierbares_dynamisches_system_matrix_stabilitat> # Differenzierbares dynamisches System--Matrix--Stabilität
    a schema:Intangible ;
   schema:name "Differenzierbares dynamisches System--Matrix--Stabilität"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/20888049#Topic/matrix_stabilitat_differenzierbares_dynamisches_system> # Matrix--Stabilität--Differenzierbares dynamisches System
    a schema:Intangible ;
   schema:name "Matrix--Stabilität--Differenzierbares dynamisches System"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/20888049#Topic/stabilitat_matrix_differenzierbares_dynamisches_system> # Stabilität--Matrix--Differenzierbares dynamisches System
    a schema:Intangible ;
   schema:name "Stabilität--Matrix--Differenzierbares dynamisches System"@en ;
    .

<http://id.worldcat.org/fast/1012399> # Matrices
    a schema:Intangible ;
   schema:name "Matrices"@en ;
    .

<http://id.worldcat.org/fast/1131203> # Stability
    a schema:Intangible ;
   schema:name "Stability"@en ;
    .

<http://id.worldcat.org/fast/893426> # Differentiable dynamical systems
    a schema:Intangible ;
   schema:name "Differentiable dynamical systems"@en ;
    .

<http://viaf.org/viaf/67333146> # Amit Bhaya
    a schema:Person ;
   schema:familyName "Bhaya" ;
   schema:givenName "Amit" ;
   schema:name "Amit Bhaya" ;
    .

<http://viaf.org/viaf/74718974> # Eugenius Kaszkurewicz
    a schema:Person ;
   schema:familyName "Kaszkurewicz" ;
   schema:givenName "Eugenius" ;
   schema:name "Eugenius Kaszkurewicz" ;
    .

<http://worldcat.org/isbn/9780817640880>
    a schema:ProductModel ;
   schema:isbn "0817640886" ;
   schema:isbn "9780817640880" ;
    .

<http://worldcat.org/isbn/9783764340889>
    a schema:ProductModel ;
   schema:isbn "3764340886" ;
   schema:isbn "9783764340889" ;
    .

<http://www.worldcat.org/title/-/oclc/41380381#Review/1205187628>
    a schema:Review ;
   schema:itemReviewed <http://www.worldcat.org/oclc/41380381> ; # Matrix diagonal stability in systems and computation
   schema:reviewBody ""Matrix diagonal stability and the related diagonal-type Liapunov functions possess properties that make them attractive and very useful for applications. This new book addresses the matrix-stability concept and its applications to the analysis and design of several types of discrete-time and continuous-time dynamical systems." "The book provides an essential reference for new methods and analysis related to dynamical systems described by linear and nonlinear ordinary differential equations and difference equations. Researchers, professionals, and graduates in applied mathematics, control engineering, stability of dynamical systems, and scientific computation will find the book a useful guide to current results and developments."--Jacket." ;
    .


Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.