Piecewise Linear Modeling And Analysis

Author : Domine Leenaerts,Wim M.G. van Bokhoven
Publisher : Springer Science & Business Media
Page : 202 pages
File Size : 47,9 Mb
Release : 2013-03-09
Category : Technology & Engineering
ISBN : 9781475761900

Get Book

Piecewise Linear Modeling and Analysis by Domine Leenaerts,Wim M.G. van Bokhoven Pdf

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 : Wilhelmus Maria Gezinus van Bokhoven
Publisher : Unknown
Page : 140 pages
File Size : 43,6 Mb
Release : 1981
Category : Electric circuits
ISBN : 9020114530

Get Book

Piecewise-linear Modelling and Analysis by Wilhelmus Maria Gezinus van Bokhoven Pdf

Author : Mikael K.-J. Johansson
Publisher : Springer
Page : 212 pages
File Size : 52,7 Mb
Release : 2003-07-01
Category : Technology & Engineering
ISBN : 9783540368014

Get Book

Piecewise Linear Control Systems by Mikael K.-J. Johansson Pdf

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 : Mikael K.-J. Johansson
Publisher : Springer
Page : 202 pages
File Size : 51,8 Mb
Release : 2014-03-12
Category : Technology & Engineering
ISBN : 366216955X

Get Book

Piecewise Linear Control Systems by Mikael K.-J. Johansson Pdf

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 : Garrett M. Fitzmaurice,Nan M. Laird,James H. Ware
Publisher : John Wiley & Sons
Page : 540 pages
File Size : 48,5 Mb
Release : 2004-07
Category : Mathematics
ISBN : 0471214876

Get Book

Applied Longitudinal Analysis by Garrett M. Fitzmaurice,Nan M. Laird,James H. Ware Pdf

Publisher Description

Author : Stephen W. Raudenbush,Anthony S. Bryk
Publisher : SAGE
Page : 520 pages
File Size : 48,7 Mb
Release : 2002
Category : Social Science
ISBN : 076191904X

Get Book

Hierarchical Linear Models by Stephen W. Raudenbush,Anthony S. Bryk Pdf

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 : Wai-Kai Chen
Publisher : CRC Press
Page : 455 pages
File Size : 43,5 Mb
Release : 2018-10-08
Category : Technology & Engineering
ISBN : 9781351835053

Get Book

Feedback, Nonlinear, and Distributed Circuits by Wai-Kai Chen Pdf

Upon its initial publication, the Handbook of Circuits and Filters broke new ground. It quickly became the resource for comprehensive coverage of issues and practical information that can be put to immediate use. Not content to rest on his laurels, editor Wai-kai Chen divided the second edition into volumes, making the information easily accessible and digestible. In the third edition, these volumes have been revised, updated, and expanded so that they continue to provide solid coverage of standard practices and enlightened perspectives on new and emerging techniques. Feedback, Nonlinear, and Distributed Circuits draws together international contributors who discuss feedback amplifier theory and then move on to explore feedback amplifier configurations. They develop Bode’s feedback theory as an example of general feedback theory. The coverage then moves on to the importance of complementing numerical analysis with qualitative analysis to get a global picture of a circuit’s performance. After reviewing a wide range of approximation techniques and circuit design styles for discreet and monolithic circuits, the book presents a comprehensive description of the use of piecewise-linear methods in modeling, analysis, and structural properties of nonlinear circuits highlighting the advantages. It describes the circuit modeling in the frequency domain of uniform MTL based on the Telegrapher’s equations and covers frequency and time domain experimental characterization techniques for uniform and nonuniform multiconductor structures. This volume will undoubtedly take its place as the engineer's first choice in looking for solutions to problems encountered in the analysis and behavior predictions of circuits and filters.

Author : An-Chang Deng
Publisher : Unknown
Page : 372 pages
File Size : 45,7 Mb
Release : 1986
Category : Electronic
ISBN : UCAL:C2927460

Get Book

Canonical Piecewise-linear Analysis and Modeling by An-Chang Deng Pdf

Author : Sandra E. Ryan
Publisher : Unknown
Page : 48 pages
File Size : 43,6 Mb
Release : 2007
Category : River sediments
ISBN : IND:30000117514665

Get Book

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

"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 : Nikos E Mastorakis
Publisher : World Scientific
Page : 438 pages
File Size : 49,9 Mb
Release : 1998-10-12
Category : Technology & Engineering
ISBN : 9789814544313

Get Book

Recent Advances In Circuits And Systems by Nikos E Mastorakis Pdf

Recent Advances in Circuits and Systems brings you a balanced, state-of-the-art presentation of the latest concepts, methods, algorithms, techniques, procedures and applications of the fascinating field of Circuits and Systems. Written by eminent, leading, international experts, the contributors provide up-to-date aspects of topics discussed and present fresh, original insights into their own experience with Circuits and Systems.The main aim of this book is to present most of the new trends and recent advances of the impressive evolution in the discipline of circuits and systems. Special emphasis is given in the interaction between the classic areas of systems theory (feedback control, circuits design, electronics, etc) and the modern techniques of computational intelligence (neural networks, genetic algorithms, fuzzy logic and expert systems) since this fertile interaction promises to open up new horizons in circuits and systems theory.This book is composed of four parts. Part I is devoted to Circuits and Electronics and also includes Power Systems. Part II refers to Systems Theory and Control (H infinity problems, feedback control, non-linear systems, robust stability and robust control, multivariable systems, hybrid systems and hydraulic systems). Part III presents the latest developments in the Robotics (theory and applications) while Part IV is devoted to Computational Intelligence in Systems Theory.

Author : Njal Brian Opicho Lenzing Pettit
Publisher : Wiley-Blackwell
Page : 272 pages
File Size : 44,6 Mb
Release : 1995
Category : Science
ISBN : UOM:39015034541139

Get Book

Analysis of Piecewise Linear Dynamical Systems by Njal Brian Opicho Lenzing Pettit Pdf

A first edition, Insiders' Guide to El Paso is the essential source for in-depth travel and relocation information to this legendary Texas panhandle area with wild west charm. Written by a local (and true insider), this guide offers a personal and practical perspective of El Paso and its surrounding environs.

Author : Youngjo Lee,John A. Nelder,Yudi Pawitan
Publisher : CRC Press
Page : 411 pages
File Size : 49,5 Mb
Release : 2006-07-13
Category : Mathematics
ISBN : 9781420011340

Get Book

Generalized Linear Models with Random Effects by Youngjo Lee,John A. Nelder,Yudi Pawitan Pdf

Since their introduction in 1972, generalized linear models (GLMs) have proven useful in the generalization of classical normal models. Presenting methods for fitting GLMs with random effects to data, Generalized Linear Models with Random Effects: Unified Analysis via H-likelihood explores a wide range of applications, including combining information over trials (meta-analysis), analysis of frailty models for survival data, genetic epidemiology, and analysis of spatial and temporal models with correlated errors. Written by pioneering authorities in the field, this reference provides an introduction to various theories and examines likelihood inference and GLMs. The authors show how to extend the class of GLMs while retaining as much simplicity as possible. By maximizing and deriving other quantities from h-likelihood, they also demonstrate how to use a single algorithm for all members of the class, resulting in a faster algorithm as compared to existing alternatives. Complementing theory with examples, many of which can be run by using the code supplied on the accompanying CD, this book is beneficial to statisticians and researchers involved in the above applications as well as quality-improvement experiments and missing-data analysis.

Author : John A. Richards
Publisher : Springer Science & Business Media
Page : 186 pages
File Size : 42,8 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9783642818738

Get Book

Analysis of Periodically Time-Varying Systems by John A. Richards Pdf

Many of the practical techniques developed for treating systems described by periodic differential equations have arisen in different fields of application; con sequently some procedures have not always been known to workers in areas that might benefit substantially from them. Furthermore, recent analytical methods are computationally based so that it now seems an opportune time for an applications-oriented book to be made available that, in a sense, bridges the fields in which equations with periodic coefficients arise and which draws together analytical methods that are implemented readily. This book seeks to ftll that role, from a user's and not a theoretician's view. The complexities of periodic systems often demand a computational approach. Matrix treatments therefore are emphasized here although algebraic methods have been included where they are useful in their own right or where they establish properties that can be exploited by the matrix approach. The matrix development given calls upon the nomenclature and treatment of H. D'Angelo, Linear Time Varying Systems: Analysis and Synthesis (Boston: Allyn and Bacon 1970) which deals with time-varying systems in general. It is recommended for its modernity and comprehensive approach to systems analysis by matrix methods. Since the present work is applications-oriented no attempt has been made to be complete theoretically by way of presenting all proofs, existence theorems and so on. These can be found in D'Angelo and classic and well-developed treatises such as McLachlan, N. W. : Theory and application of Mathieu functions.

Author : Dipak K. Dey,Sujit K. Ghosh,Bani K. Mallick
Publisher : CRC Press
Page : 442 pages
File Size : 49,6 Mb
Release : 2000-05-25
Category : Mathematics
ISBN : 9781482293456

Get Book

Generalized Linear Models by Dipak K. Dey,Sujit K. Ghosh,Bani K. Mallick Pdf

This volume describes how to conceptualize, perform, and critique traditional generalized linear models (GLMs) from a Bayesian perspective and how to use modern computational methods to summarize inferences using simulation. Introducing dynamic modeling for GLMs and containing over 1000 references and equations, Generalized Linear Models considers

Author : M.G. Rodd,H.B. Verbruggen
Publisher : Elsevier
Page : 549 pages
File Size : 45,5 Mb
Release : 2014-06-28
Category : Technology & Engineering
ISBN : 9781483299020

Get Book

Artificial Intelligence in Real-Time Control 1992 by M.G. Rodd,H.B. Verbruggen Pdf

The symposium had two main aims, to investigate the state-of-the-art in the application of artificial intelligence techniques in real-time control, and to bring together control system specialists, artificial intelligence specialists and end-users. Many professional engineers working in industry feel that the gap between theory and practice in applying control and systems theory is widening, despite efforts to develop control algorithms. Papers presented at the meeting ranged from the theoretical aspects to the practical applications of artificial intelligence in real-time control. Themes were: the methodology of artificial intelligence techniques in control engineering; the application of artificial intelligence techniques in different areas of control; and hardware and software requirements. This symposium showed that there exist alternative possibilities for control based on artificial intelligence techniques.