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Author: Domine Leenaerts
Publisher: Springer Science & Business Media
ISBN: 1475761902
Category : Technology & Engineering
Languages : en
Pages : 202
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Book Description
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.
Author: Domine Leenaerts
Publisher: Springer Science & Business Media
ISBN: 1475761902
Category : Technology & Engineering
Languages : en
Pages : 202
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Book Description
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.
Author: Mikael K.-J. Johansson
Publisher: Springer
ISBN: 3540368019
Category : Technology & Engineering
Languages : en
Pages : 212
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Book Description
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 . . . . . . . . . . . . .
Author: G. David Garson
Publisher: SAGE
ISBN: 1412998859
Category : Mathematics
Languages : en
Pages : 393
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Book Description
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.
Author: Sandra E. Ryan
Publisher:
ISBN:
Category : River sediments
Languages : en
Pages : 48
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Book Description
"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."
Author: Wai-Kai Chen
Publisher: CRC Press
ISBN: 9781420041408
Category : Computers
Languages : en
Pages : 3076
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Book Description
A bestseller in its first edition, The Circuits and Filters Handbook has been thoroughly updated to provide the most current, most comprehensive information available in both the classical and emerging fields of circuits and filters, both analog and digital. This edition contains 29 new chapters, with significant additions in the areas of computer-
Author: Wai-Kai Chen
Publisher: CRC Press
ISBN: 1000006573
Category : Technology & Engineering
Languages : en
Pages : 3364
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Book Description
Standard-setting, groundbreaking, authoritative, comprehensive—these often overused words perfectly describe The Circuits and Filters Handbook, Third Edition. This standard-setting resource has documented the momentous changes that have occurred in the field of electrical engineering, providing the most comprehensive coverage available. More than 150 contributing experts offer in-depth insights and enlightened perspectives into standard practices and effective techniques that will make this set the first—and most likely the only—tool you select to help you with problem solving. In its third edition, this groundbreaking bestseller surveys accomplishments in the field, providing researchers and designers with the comprehensive detail they need to optimize research and design. All five volumes include valuable information on the emerging fields of circuits and filters, both analog and digital. Coverage includes key mathematical formulas, concepts, definitions, and derivatives that must be mastered to perform cutting-edge research and design. The handbook avoids extensively detailed theory and instead concentrates on professional applications, with numerous examples provided throughout. The set includes more than 2500 illustrations and hundreds of references. Available as a comprehensive five-volume set, each of the subject-specific volumes can also be purchased separately.
Author: Luis Rodrigues
Publisher: SIAM
ISBN: 1611975905
Category : Mathematics
Languages : en
Pages : 243
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Book Description
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.
Author: Wai-Kai Chen
Publisher: CRC Press
ISBN: 1420037080
Category : Technology & Engineering
Languages : en
Pages : 352
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Book Description
Culled from the pages of CRC's highly successful, best-selling The Circuits and Filters Handbook, Second Edition, Nonlinear and Distributed Circuits presents a sharply focused, comprehensive review of the fundamental theory behind professional applications of these complex circuits. It supplies a concise, convenient reference to the key concepts, models, and equations necessary to analyze, design, and predict the behavior of nonlinear and distributed circuits, illustrated by frequent examples. Edited by a distinguished authority, this book emphasizes the theoretical concepts underlying the processes, behavior, and operation of these devices. More than 225 figures and tables illustrate the concepts, and where necessary, the theories, principles, and mathematics of some subjects are reviewed. Expert contributors discuss the analysis, synthesis, and design of nonlinear circuits; their representation, approximation, identification, and simulation; cellular neural networks; multiconductor transmission lines; and analysis and synthesis of distributed circuits. Nonlinear and Distributed Circuits builds a strong theoretical foundation for the design and analysis of both distributed and nonlinear circuits while serving as a handy reference for experienced engineers, making it a must-have for both beginners and seasoned experts.
Author: Stephen W. Raudenbush
Publisher: SAGE
ISBN: 9780761919049
Category : Mathematics
Languages : en
Pages : 520
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Book Description
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.
Author: Vincent Acary
Publisher: Springer Science & Business Media
ISBN: 9048196817
Category : Technology & Engineering
Languages : en
Pages : 295
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Book Description
Nonsmooth Modeling and Simulation for Switched Circuits concerns the modeling and the numerical simulation of switched circuits with the nonsmooth dynamical systems (NSDS) approach, using piecewise-linear and multivalued models of electronic devices like diodes, transistors, switches. Numerous examples (ranging from introductory academic circuits to various types of power converters) are analyzed and many simulation results obtained with the INRIA open-source SICONOS software package are presented. Comparisons with SPICE and hybrid methods demonstrate the power of the NSDS approach. Nonsmooth Modeling and Simulation for Switched Circuits is intended to researchers and engineers in the field of circuits simulation and design, but may also attract applied mathematicians interested by the numerical analysis for nonsmooth dynamical systems, as well as researchers from Systems and Control.
