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 . . . . . . . . . . . . .

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 . . . . . . . . . . . . .

Applied Longitudinal Analysis

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Publisher : John Wiley & Sons
ISBN 13 : 9780471214878
Total Pages : 540 pages
Book Rating : 4.2/5 (148 download)

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Book Synopsis Applied Longitudinal Analysis by : Garrett M. Fitzmaurice

Download or read book Applied Longitudinal Analysis written by Garrett M. Fitzmaurice and published by John Wiley & Sons. This book was released on 2004-07 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher Description

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.

Feedback, Nonlinear, and Distributed Circuits

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Publisher : CRC Press
ISBN 13 : 135183505X
Total Pages : 455 pages
Book Rating : 4.3/5 (518 download)

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Book Synopsis Feedback, Nonlinear, and Distributed Circuits by : Wai-Kai Chen

Download or read book Feedback, Nonlinear, and Distributed Circuits written by Wai-Kai Chen and published by CRC Press. This book was released on 2018-10-08 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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:

Analysis of Piecewise Linear Dynamical Systems

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Publisher : Wiley-Blackwell
ISBN 13 :
Total Pages : 272 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Analysis of Piecewise Linear Dynamical Systems by : Njal Brian Opicho Lenzing Pettit

Download or read book Analysis of Piecewise Linear Dynamical Systems written by Njal Brian Opicho Lenzing Pettit and published by Wiley-Blackwell. This book was released on 1995 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Recent Advances In Circuits And Systems

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Publisher : World Scientific
ISBN 13 : 9814544310
Total Pages : 438 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Recent Advances In Circuits And Systems by : Nikos E Mastorakis

Download or read book Recent Advances In Circuits And Systems written by Nikos E Mastorakis and published by World Scientific. This book was released on 1998-10-12 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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.

Nonlinear Dynamics of Piecewise Constant Systems and Implementation of Piecewise Constant Arguments

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Publisher : World Scientific
ISBN 13 : 9812818502
Total Pages : 345 pages
Book Rating : 4.8/5 (128 download)

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Book Synopsis Nonlinear Dynamics of Piecewise Constant Systems and Implementation of Piecewise Constant Arguments by : Liming Dai

Download or read book Nonlinear Dynamics of Piecewise Constant Systems and Implementation of Piecewise Constant Arguments written by Liming Dai and published by World Scientific. This book was released on 2008 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: Piecewise constant systems exist in widely expanded areas such as engineering, physics, and mathematics. Extraordinary and complex characteristics of piecewise constant systems have been reported in recent years. This book provides the methodologies for analyzing and assessing nonlinear piecewise constant systems on a theoretically and practically sound basis. Recently developed approaches for theoretically analyzing and numerically solving the nonlinear piecewise constant dynamic systems are reviewed. A new greatest integer argument with a piecewise constant function is utilized for nonlinear dynamic analyses and for establishing a novel criterion in diagnosing irregular and chaotic solutions from the regular solutions of a nonlinear dynamic system. The newly established piecewise constantization methodology and its implementation in analytically solving for nonlinear dynamic problems are also presented.

Generalized Linear Models with Random Effects

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Publisher : CRC Press
ISBN 13 : 1420011340
Total Pages : 411 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Generalized Linear Models with Random Effects by : Youngjo Lee

Download or read book Generalized Linear Models with Random Effects written by Youngjo Lee and published by CRC Press. This book was released on 2006-07-13 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Analysis of Periodically Time-Varying Systems

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Publisher : Springer Science & Business Media
ISBN 13 : 3642818730
Total Pages : 186 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Analysis of Periodically Time-Varying Systems by : John A. Richards

Download or read book Analysis of Periodically Time-Varying Systems written by John A. Richards and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Generalized Linear Models

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Publisher : CRC Press
ISBN 13 : 1482293455
Total Pages : 442 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Generalized Linear Models by : Dipak K. Dey

Download or read book Generalized Linear Models written by Dipak K. Dey and published by CRC Press. This book was released on 2000-05-25 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Artificial Intelligence in Real-Time Control 1992

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Publisher : Elsevier
ISBN 13 : 1483299023
Total Pages : 549 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Artificial Intelligence in Real-Time Control 1992 by : M.G. Rodd

Download or read book Artificial Intelligence in Real-Time Control 1992 written by M.G. Rodd and published by Elsevier. This book was released on 2014-06-28 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.