Piecewise Linear Modeling and Analysis

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Publisher : Springer Science & Business Media
ISBN 13 : 1475761902
Total Pages : 202 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Piecewise Linear Modeling and Analysis by : Domine Leenaerts

Download or read book Piecewise Linear Modeling and Analysis written by Domine Leenaerts and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Piecewise Linear (PL) approximation of non-linear behaviour is a well-known technique in synthesis and analysis of electrical networks. However, the PL description should be efficient in data storage and the description should allow simple retrieval of the stored information. Furthermore, it would be useful if the model description could handle a large class of piecewise linear mappings. Piecewise Linear Modeling and Analysis explains in detail all possible model descriptions for efficiently storing piecewise linear functions, starting with the Chua descriptions. Detailed explanation on how the model parameter can be obtained for a given mapping is provided and demonstrated by examples. The models are ranked to compare them and to show which model can handle the largest class of PL mappings. All model descriptions are implicitly related to the Linear Complementarity Problem and most solution techniques for this problem, like Katzenelson and Lemke, are discussed according to examples that are explained in detail. To analyse PL electrical networks a simulator is mandatory. Piecewise Linear Modeling and Analysis provides a detailed outline of a possible PL simulator, including pseudo-programming code. Several simulation domains like transient, AC and distortion are discussed. The book explains the attractive features of PL simulators with respect to mixed-level and mixed-signal simulation while paying due regard also to hierarchical simulation. Piecewise Linear Modeling and Analysis shows in detail how many existing components in electrical networks can be modeled. These range from digital logic and analog basic elements such as transistors to complex systems like Phase-Locked Loops and detection systems. Simulation results are also provided. The book concludes with a discussion on how to find multiple solutions for PL functions or networks. Again, the most common techniques are outlined using clear examples. Piecewise Linear Modeling and Analysis is an indispensable guide for researchers and designers interested in network theory, network synthesis and network analysis.

Piecewise-linear Modelling and Analysis

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Publisher :
ISBN 13 : 9789020114539
Total Pages : 140 pages
Book Rating : 4.1/5 (145 download)

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Book Synopsis Piecewise-linear Modelling and Analysis by : Wilhelmus Maria Gezinus van Bokhoven

Download or read book Piecewise-linear Modelling and Analysis written by Wilhelmus Maria Gezinus van Bokhoven and published by . This book was released on 1981 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Piecewise Linear Control Systems

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Publisher : Springer
ISBN 13 : 3540368019
Total Pages : 212 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Piecewise Linear Control Systems by : Mikael K.-J. Johansson

Download or read book Piecewise Linear Control Systems written by Mikael K.-J. Johansson and published by Springer. This book was released on 2003-07-01 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 2. Piecewise Linear Modeling . . . . . . . . . . . . . . . . . . . . . 9 2. 1 Model Representation . . . . . . . . . . . . . . . . . . . . . 9 2. 2 Solution Concepts . . . . . . . . . . . . . . . . . . . . . . . 2. 3 Uncertainty Models . . . . . . . . . . . . . . . . . . . . . . 2. 4 Modularity and Interconnections . . . . . . . . . . . . . . 26 2. 5 Piecewise Linear Function Representations . . . . . . . . . 28 2. 6 Comments and References . . . . . . . . . . . . . . . . . . 30 3. Structural Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3. 1 Equilibrium Points and the Steady State Characteristic . . 32 3. 2 Constraint Verification and Invariance . . . . . . . . . . . 35 3. 3 Detecting Attractive Sliding Modes on Cell Boundaries 37 3. 4 Comments and References . . . . . . . . . . . . . . . . . . 39 4. Lyapunov Stability . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4. 1 Exponential Stability . . . . . . . . . . . . . . . . . . . . . . 41 4. 2 Quadratic Stability . . . . . . . . . . . . . . . . . . . . . . . 42 4. 3 Conservatism of Quadratic Stability . . . . . . . . . . . . . 46 4. 4 From Quadratic to Piecewise Quadratic . . . . . . . . . . . 48 4. 5 Interlude: Describing Partition Properties . . . . . . . . . 51 4. 6 Piecewise Quadratic Lyapunov Functions . . . . . . . . . 55 4. 7 Analysis of Piecewise Linear Differential Inclusions . . . . 61 4. 8 Analysis of Systems with Attractive Sliding Modes . . . . 63 4. 9 Improving Computational Efficiency . . . . . . . . . . . . 66 4. 10 Piecewise Linear Lyapunov Functions . . . . . . . . . . . 72 4. 11 A Unifying View . . . . . . . . . . . . . . . . . . . . . . . . 77 4. 12 Comments and References . . . . . . . . . . . . . . . . . . 82 5. Dissipativity Analysis . . . . . . . . . . . . . . . . . . . . . . . . 85 5. 1 Dissipativity Analysis via Convex Optimization . . . . . . 86 21 14 Contents Contents 5. 2 Computation of £2 induced Gain . . . . . . . . . . . . . . 88 5. 3 Estimation of Transient Energy . . . . . . . . . . . . . . . . 89 5. 4 Dissipative Systems with Quadratic Supply Rates . . . . . 91 5. 5 Comments and References . . . . . . . . . . . . . . . . . . 95 Controller Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 6. 1 Quadratic Stabilization of Piecewise Linear" Systems . . . 97 6. 2 Controller Synthesis based on Piecewise Quadratics . . . 98 6. 3 Comments and References . . . . . . . . . . . . . . . . . . 105 7. Selected Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 7. 1 Estimation of Regions of Attraction . . . . . . . . . . . . .

Canonical Piecewise-linear Analysis and Modeling

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Publisher :
ISBN 13 :
Total Pages : 372 pages
Book Rating : 4.:/5 (29 download)

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Book Synopsis Canonical Piecewise-linear Analysis and Modeling by : An-Chang Deng

Download or read book Canonical Piecewise-linear Analysis and Modeling written by An-Chang Deng and published by . This book was released on 1986 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Piecewise Linear Control Systems

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Publisher : Springer
ISBN 13 : 9783662169551
Total Pages : 202 pages
Book Rating : 4.1/5 (695 download)

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Book Synopsis Piecewise Linear Control Systems by : Mikael K.-J. Johansson

Download or read book Piecewise Linear Control Systems written by Mikael K.-J. Johansson and published by Springer. This book was released on 2014-03-12 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: 2. Piecewise Linear Modeling . . . . . . . . . . . . . . . . . . . . . 9 2. 1 Model Representation . . . . . . . . . . . . . . . . . . . . . 9 2. 2 Solution Concepts . . . . . . . . . . . . . . . . . . . . . . . 2. 3 Uncertainty Models . . . . . . . . . . . . . . . . . . . . . . 2. 4 Modularity and Interconnections . . . . . . . . . . . . . . 26 2. 5 Piecewise Linear Function Representations . . . . . . . . . 28 2. 6 Comments and References . . . . . . . . . . . . . . . . . . 30 3. Structural Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3. 1 Equilibrium Points and the Steady State Characteristic . . 32 3. 2 Constraint Verification and Invariance . . . . . . . . . . . 35 3. 3 Detecting Attractive Sliding Modes on Cell Boundaries 37 3. 4 Comments and References . . . . . . . . . . . . . . . . . . 39 4. Lyapunov Stability . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4. 1 Exponential Stability . . . . . . . . . . . . . . . . . . . . . . 41 4. 2 Quadratic Stability . . . . . . . . . . . . . . . . . . . . . . . 42 4. 3 Conservatism of Quadratic Stability . . . . . . . . . . . . . 46 4. 4 From Quadratic to Piecewise Quadratic . . . . . . . . . . . 48 4. 5 Interlude: Describing Partition Properties . . . . . . . . . 51 4. 6 Piecewise Quadratic Lyapunov Functions . . . . . . . . . 55 4. 7 Analysis of Piecewise Linear Differential Inclusions . . . . 61 4. 8 Analysis of Systems with Attractive Sliding Modes . . . . 63 4. 9 Improving Computational Efficiency . . . . . . . . . . . . 66 4. 10 Piecewise Linear Lyapunov Functions . . . . . . . . . . . 72 4. 11 A Unifying View . . . . . . . . . . . . . . . . . . . . . . . . 77 4. 12 Comments and References . . . . . . . . . . . . . . . . . . 82 5. Dissipativity Analysis . . . . . . . . . . . . . . . . . . . . . . . . 85 5. 1 Dissipativity Analysis via Convex Optimization . . . . . . 86 21 14 Contents Contents 5. 2 Computation of £2 induced Gain . . . . . . . . . . . . . . 88 5. 3 Estimation of Transient Energy . . . . . . . . . . . . . . . . 89 5. 4 Dissipative Systems with Quadratic Supply Rates . . . . . 91 5. 5 Comments and References . . . . . . . . . . . . . . . . . . 95 Controller Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 6. 1 Quadratic Stabilization of Piecewise Linear" Systems . . . 97 6. 2 Controller Synthesis based on Piecewise Quadratics . . . 98 6. 3 Comments and References . . . . . . . . . . . . . . . . . . 105 7. Selected Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 7. 1 Estimation of Regions of Attraction . . . . . . . . . . . . .

Hierarchical Linear Modeling

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Publisher : SAGE
ISBN 13 : 1412998859
Total Pages : 393 pages
Book Rating : 4.4/5 (129 download)

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Book Synopsis Hierarchical Linear Modeling by : G. David Garson

Download or read book Hierarchical Linear Modeling written by G. David Garson and published by SAGE. This book was released on 2013 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a brief, easy-to-read guide to implementing hierarchical linear modeling using three leading software platforms, followed by a set of original how-to applications articles following a standardard instructional format. The "guide" portion consists of five chapters by the editor, providing an overview of HLM, discussion of methodological assumptions, and parallel worked model examples in SPSS, SAS, and HLM software. The "applications" portion consists of ten contributions in which authors provide step by step presentations of how HLM is implemented and reported for introductory to intermediate applications.

Piecewise-linear Modelling And Analysis

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ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (14 download)

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Book Synopsis Piecewise-linear Modelling And Analysis by : Van W. Bokhoven

Download or read book Piecewise-linear Modelling And Analysis written by Van W. Bokhoven and published by . This book was released on with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Piecewise Linear Control Modeling and Analysis with Applications in Circuits and Automotive Systems

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Publisher :
ISBN 13 :
Total Pages : 422 pages
Book Rating : 4.:/5 (761 download)

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Book Synopsis Piecewise Linear Control Modeling and Analysis with Applications in Circuits and Automotive Systems by : Lawrence T. Woods

Download or read book Piecewise Linear Control Modeling and Analysis with Applications in Circuits and Automotive Systems written by Lawrence T. Woods and published by . This book was released on 2006 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Piecewise Linear Models for Switch-level Simulation

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Publisher :
ISBN 13 :
Total Pages : 302 pages
Book Rating : 4.:/5 (123 download)

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Book Synopsis Piecewise Linear Models for Switch-level Simulation by : Russell Kao

Download or read book Piecewise Linear Models for Switch-level Simulation written by Russell Kao and published by . This book was released on 1992 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Modelling of Piecewise Linear Systems for Geometrical Analysis

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ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (643 download)

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Book Synopsis The Modelling of Piecewise Linear Systems for Geometrical Analysis by : V. Besson

Download or read book The Modelling of Piecewise Linear Systems for Geometrical Analysis written by V. Besson and published by . This book was released on 1993 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Piecewise-smooth Dynamical Systems

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Publisher : Springer Science & Business Media
ISBN 13 : 1846287081
Total Pages : 497 pages
Book Rating : 4.8/5 (462 download)

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Book Synopsis Piecewise-smooth Dynamical Systems by : Mario Bernardo

Download or read book Piecewise-smooth Dynamical Systems written by Mario Bernardo and published by Springer Science & Business Media. This book was released on 2008-01-01 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a coherent framework for understanding the dynamics of piecewise-smooth and hybrid systems. An informal introduction expounds the ubiquity of such models via numerous. The results are presented in an informal style, and illustrated with many examples. The book is aimed at a wide audience of applied mathematicians, engineers and scientists at the beginning postgraduate level. Almost no mathematical background is assumed other than basic calculus and algebra.

Piecewise Linear Tree-structured Regression

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ISBN 13 :
Total Pages : 256 pages
Book Rating : 4.:/5 (89 download)

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Book Synopsis Piecewise Linear Tree-structured Regression by : Min Ching Huang

Download or read book Piecewise Linear Tree-structured Regression written by Min Ching Huang and published by . This book was released on 1989 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Piecewise Affine Control: Continuous-Time, Sampled-Data, and Networked Systems

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Publisher : SIAM
ISBN 13 : 1611975905
Total Pages : 224 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Piecewise Affine Control: Continuous-Time, Sampled-Data, and Networked Systems by : Luis Rodrigues

Download or read book Piecewise Affine Control: Continuous-Time, Sampled-Data, and Networked Systems written by Luis Rodrigues and published by SIAM. This book was released on 2019-11-06 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Engineering systems operate through actuators, most of which will exhibit phenomena such as saturation or zones of no operation, commonly known as dead zones. These are examples of piecewise-affine characteristics, and they can have a considerable impact on the stability and performance of engineering systems. This book targets controller design for piecewise affine systems, fulfilling both stability and performance requirements. The authors present a unified computational methodology for the analysis and synthesis of piecewise affine controllers, taking an approach that is capable of handling sliding modes, sampled-data, and networked systems. They introduce algorithms that will be applicable to nonlinear systems approximated by piecewise affine systems, and they feature several examples from areas such as switching electronic circuits, autonomous vehicles, neural networks, and aerospace applications. Piecewise Affine Control: Continuous-Time, Sampled-Data, and Networked Systems is intended for graduate students, advanced senior undergraduate students, and researchers in academia and industry. It is also appropriate for engineers working on applications where switched linear and affine models are important.

Fitting Models to Biological Data Using Linear and Nonlinear Regression

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Publisher : Oxford University Press
ISBN 13 : 9780198038344
Total Pages : 352 pages
Book Rating : 4.0/5 (383 download)

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Book Synopsis Fitting Models to Biological Data Using Linear and Nonlinear Regression by : Harvey Motulsky

Download or read book Fitting Models to Biological Data Using Linear and Nonlinear Regression written by Harvey Motulsky and published by Oxford University Press. This book was released on 2004-05-27 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most biologists use nonlinear regression more than any other statistical technique, but there are very few places to learn about curve-fitting. This book, by the author of the very successful Intuitive Biostatistics, addresses this relatively focused need of an extraordinarily broad range of scientists.

Linear Regression Analysis

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Publisher : World Scientific
ISBN 13 : 9812834109
Total Pages : 349 pages
Book Rating : 4.8/5 (128 download)

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Book Synopsis Linear Regression Analysis by : Xin Yan

Download or read book Linear Regression Analysis written by Xin Yan and published by World Scientific. This book was released on 2009 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This volume presents in detail the fundamental theories of linear regression analysis and diagnosis, as well as the relevant statistical computing techniques so that readers are able to actually model the data using the techniques described in the book. This book is suitable for graduate students who are either majoring in statistics/biostatistics or using linear regression analysis substantially in their subject area." --Book Jacket.

A Tutorial on the Piecewise Regression Approach Applied to Bedload Transport Data

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Publisher :
ISBN 13 :
Total Pages : 48 pages
Book Rating : 4.3/5 ( download)

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Book Synopsis A Tutorial on the Piecewise Regression Approach Applied to Bedload Transport Data by : Sandra E. Ryan

Download or read book A Tutorial on the Piecewise Regression Approach Applied to Bedload Transport Data written by Sandra E. Ryan and published by . This book was released on 2007 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This tutorial demonstrates the application of piecewise regression to bedload data to define a shift in phase of transport so that the reader may perform similar analyses on available data. The use of piecewise regression analysis implicitly recognizes different functions fit to bedload data over varying ranges of flow. The transition from primarily low rates of sand transport (Phase I) to higher rates of sand and coarse gravel transport (Phase II) is termed "breakpoint" and is defined as the flow where the fitted functions intersect. The form of the model used here fits linear segments to different ranges of data, though other types of functions may be used. Identifying the transition in phases is one approach used for defining flow regimes that are essential for self-maintenance of alluvial gravel bed channels. First, the statistical theory behind piecewise regression analysis and its procedural approaches are presented. The reader is then guided through an example procedure and the code for generating an analysis in SAS is outlined. The results from piecewise regression analysis from a number of additional bedload datasets are presented to help the reader understand the range of estimated values and confidence limits on the breakpoint that the analysis provides. The identification and resolution of problems encountered in bedload datasets are also discussed. Finally, recommendations on a minimal number of samples required for the analysis are proposed."

Hierarchical Linear Models

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Publisher : SAGE
ISBN 13 : 9780761919049
Total Pages : 520 pages
Book Rating : 4.9/5 (19 download)

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Book Synopsis Hierarchical Linear Models by : Stephen W. Raudenbush

Download or read book Hierarchical Linear Models written by Stephen W. Raudenbush and published by SAGE. This book was released on 2002 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: New edition of a text in which Raudenbush (U. of Michigan) and Bryk (sociology, U. of Chicago) provide examples, explanations, and illustrations of the theory and use of hierarchical linear models (HLM). New material in Part I (Logic) includes information on multivariate growth models and other topics.