Piecewise Linear Modeling And Analysis
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| Author | : Domine Leenaerts |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 202 |
| Release | : 2013-03-09 |
| Genre | : Technology & Engineering |
| ISBN | : 1475761902 |
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 |
| Total Pages | : 212 |
| Release | : 2003-07-01 |
| Genre | : Technology & Engineering |
| ISBN | : 3540368019 |
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 |
| Total Pages | : 393 |
| Release | : 2013 |
| Genre | : Mathematics |
| ISBN | : 1412998859 |
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 | : Michael H. Kutner |
| Publisher | : McGraw-Hill/Irwin |
| Total Pages | : 1396 |
| Release | : 2005 |
| Genre | : Mathematics |
| ISBN | : 9780072386882 |
Linear regression with one predictor variable; Inferences in regression and correlation analysis; Diagnosticis and remedial measures; Simultaneous inferences and other topics in regression analysis; Matrix approach to simple linear regression analysis; Multiple linear regression; Nonlinear regression; Design and analysis of single-factor studies; Multi-factor studies; Specialized study designs.
| Author | : Luis Rodrigues |
| Publisher | : SIAM |
| Total Pages | : 243 |
| Release | : 2019-11-06 |
| Genre | : Mathematics |
| ISBN | : 1611975905 |
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 | : An-Chang Deng |
| Publisher | : |
| Total Pages | : 372 |
| Release | : 1986 |
| Genre | : |
| ISBN | : |
| Author | : Wai-Kai Chen |
| Publisher | : CRC Press |
| Total Pages | : 3076 |
| Release | : 2002-12-23 |
| Genre | : Computers |
| ISBN | : 9781420041408 |
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 | : Stephen W. Raudenbush |
| Publisher | : SAGE |
| Total Pages | : 520 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 9780761919049 |
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 | : Xin Yan |
| Publisher | : World Scientific |
| Total Pages | : 349 |
| Release | : 2009 |
| Genre | : Mathematics |
| ISBN | : 9812834109 |
"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.
| Author | : José C. Pinheiro |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 538 |
| Release | : 2009-04-15 |
| Genre | : Computers |
| ISBN | : 1441903178 |
R, linear models, random, fixed, data, analysis, fit.
