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

Piecewise Linear Control Systems

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Publisher :
ISBN 13 :
Total Pages : 199 pages
Book Rating : 4.:/5 (186 download)

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Book Synopsis Piecewise Linear Control Systems by : Mikael Johansson

Download or read book Piecewise Linear Control Systems written by Mikael Johansson and published by . This book was released on 1999 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 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.

Control and Estimation of Piecewise Affine Systems

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Publisher : Elsevier
ISBN 13 : 1782421629
Total Pages : 253 pages
Book Rating : 4.7/5 (824 download)

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Book Synopsis Control and Estimation of Piecewise Affine Systems by : Jun Xu

Download or read book Control and Estimation of Piecewise Affine Systems written by Jun Xu and published by Elsevier. This book was released on 2014-04-21 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: As a powerful tool to study nonlinear systems and hybrid systems, piecewise affine (PWA) systems have been widely applied to mechanical systems. Control and Estimation of Piecewise Affine Systems presents several research findings relating to the control and estimation of PWA systems in one unified view. Chapters in this title discuss stability results of PWA systems, using piecewise quadratic Lyapunov functions and piecewise homogeneous polynomial Lyapunov functions. Explicit necessary and sufficient conditions for the controllability and reachability of a class of PWA systems are considered along with controller and estimator design methods for PWA systems using linear matrix inequality (LMI) and bilinear matrix inequality (BMI) techniques. A PWA approach to a class of Takagi-Sugeno fuzzy system is discussed in depth. The book uses a number of mechanical systems, such as disk servo systems to illustrate the advantages of the proposed methods. Provides new insights on properties of PWA systems, including stability, stabilizability, reachability and controllability Presents a unified framework for analysis and synthesis of both continuous-time and discrete-time PWA systems Presents novel approaches for stability analysis and control design based on the promising SOS techniques

A New Method for the Analysis of Piecewise Linear Control Systems, with Particular Application to Relay Controls

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Publisher :
ISBN 13 :
Total Pages : 14 pages
Book Rating : 4.:/5 (118 download)

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Book Synopsis A New Method for the Analysis of Piecewise Linear Control Systems, with Particular Application to Relay Controls by : Robert Hugh Macmillan

Download or read book A New Method for the Analysis of Piecewise Linear Control Systems, with Particular Application to Relay Controls written by Robert Hugh Macmillan and published by . This book was released on 1955 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Investigation of Nonlinear Control Systems: Piecewise linear methods and absolute stability

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Publisher :
ISBN 13 :
Total Pages : 170 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Investigation of Nonlinear Control Systems: Piecewise linear methods and absolute stability by : Nicolai Minorsky

Download or read book Investigation of Nonlinear Control Systems: Piecewise linear methods and absolute stability written by Nicolai Minorsky and published by . This book was released on 1960 with total page 170 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.

Stabilisation Studies for Piecewise Linear Control Systems

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Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (643 download)

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Book Synopsis Stabilisation Studies for Piecewise Linear Control Systems by : Christos Yfoulis

Download or read book Stabilisation Studies for Piecewise Linear Control Systems written by Christos Yfoulis and published by . This book was released on 2000 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Adaptive Control of Piecewise Linear Systems

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Publisher :
ISBN 13 :
Total Pages : 86 pages
Book Rating : 4.:/5 (186 download)

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Book Synopsis Adaptive Control of Piecewise Linear Systems by : Martin Balters

Download or read book Adaptive Control of Piecewise Linear Systems written by Martin Balters and published by . This book was released on 1992 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Stabilisation of Nonlinear Systems

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Publisher :
ISBN 13 :
Total Pages : 236 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Stabilisation of Nonlinear Systems by : Christos A. Yfoulis

Download or read book Stabilisation of Nonlinear Systems written by Christos A. Yfoulis and published by . This book was released on 2001 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: The control engineering community has shown an increased interest in development of advanced techniques for the analysis and design of highly complex and uncertain control systems that arise in industrial applications. This is verified by the development of areas such as Robust Control and Hybrid Systems. Advances in computer technology have facilitated the development of highly sophisticated simulation tools and software environments. However, new technologies cannot be promoted by advanced computer tools only: parallel advances of new theories are necessary.

Stability of Piecewise-linear and Rule-based Control Systems

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

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Book Synopsis Stability of Piecewise-linear and Rule-based Control Systems by : Dimitrios Maniotis

Download or read book Stability of Piecewise-linear and Rule-based Control Systems written by Dimitrios Maniotis and published by . This book was released on 2001 with total page 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:

The Structure and Control of Piecewise-linear Systems

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Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (271 download)

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Book Synopsis The Structure and Control of Piecewise-linear Systems by : Saadi A. Khathur

Download or read book The Structure and Control of Piecewise-linear Systems written by Saadi A. Khathur and published by . This book was released on 1990 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Optimal Control of Constrained Piecewise Affine Systems

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Publisher : Springer
ISBN 13 : 3540727019
Total Pages : 196 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Optimal Control of Constrained Piecewise Affine Systems by : Frank Christophersen

Download or read book Optimal Control of Constrained Piecewise Affine Systems written by Frank Christophersen and published by Springer. This book was released on 2007-09-11 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most important and challenging problems in control is the derivation of systematic tools for the computation of controllers for constrained nonlinear systems that can guarantee closed-loop stability, feasibility, and optimality with respect to some performance index. This book focuses on the efficient and systematic computation of closed-form optimal controllers for the powerful class of fast-sampled constrained piecewise affine systems. These systems may exhibit rather complex behavior and are equivalent to many other hybrid system formalisms (combining continuous-valued dynamics with logic rules) reported in the literature. Furthermore, piecewise affine systems are a useful modeling tool that can capture general nonlinearities (e.g. by local approximation), constraints, saturations, switches, and other hybrid modeling phenomena. The first part of the book presents an introduction to the mathematical and control theoretical background material needed for the full understanding of the book. The second part provides an in depth look at the computational and control theoretic properties of the controllers and part three presents different analysis and post-processing techniques.

Neighbouring Extremal Guidance Systems with Piecewise Linear Control

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Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (11 download)

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Book Synopsis Neighbouring Extremal Guidance Systems with Piecewise Linear Control by : D. Hull

Download or read book Neighbouring Extremal Guidance Systems with Piecewise Linear Control written by D. Hull and published by . This book was released on 1991 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: