Nonlinear noninteger order circuits and systems : an introduction / P. Arena ... [et al.].

Format:

Book

Contributor:

Arena, Paolo, 1966-

Series:

World Scientific Series on Nonlinear Science Series A

World Scientific series on nonlinear science, Series A, Monographs and treatises ; v. 38

Language:

English

Subjects (All):

Nonlinear systems.

System theory.

Physical Description:

1 online resource (213 p.)

Place of Publication:

Singapore ; River Edge, NJ : World Scientific, c2000.

Language Note:

English

Summary:

In this book, the reader will find a theoretical introduction to noninteger order systems, as well as several applications showing their features and peculiarities. The main definitions and results of research on noninteger order systems and modelling of physical noninteger phenomena are reported together with problems of their approximation. Control applications, noninteger order CNNs and circuit realizations of noninteger order systems are also presented.The book is intended for students and researchers involved in the simulation and control of nonlinear noninteger order systems, with partic

Contents:

CONTENTS; Preface; Chapter 1 Non Integer Order Circuits and Systems; 1.1 Introduction: Non Integer Order Physical Laws; 1.2 Non Inductive Transmission Lines; 1.3 1/f Noise Spectra; 1.4 Polarization Phenomena; 1.5 Diffusion Phenomena; 1.6 Acoustic Phenomena; 1.7 Frequency Modulation and Bessel Function of the First Kind; Chapter 2 Main Results on Non Integer Order Systems; 2.1 Non Integer Order Integration: Historical Notes; 2.2 Preliminaries and Definitions; 2.3 Laplace Transforms and System's Representation; 2.4 General Properties of Fractional Systems

2.5 Impulse Response of a General Fractional System2.6 Numerical Differintegration; Chapter 3 Approximation of Non Integer Order Systems via Integer Order Systems; 3.1 Infinite Order and Non Integer Order; 3.2 Frequency Domain Approximation; 3.3 Inverse Method: Non Integer Order Modeling; 3.4 An Example of Time Domain Approximation; 3.5 Genetic Algorithms to Approximate Non Integer Order System; 3.5.1 Response Approximation; 3.5.2 Genetic Algorithms (GAs); 3.5.3 Self Similarity; Chapter 4 Control Problem: Non Integer Order Feedback Controllers; 4.1 Controller Design: a Brief Review

4.2 Non Integer Order Correction4.3 The CRONE Control; 4.4 Complex Integration and Evolution of the CRONE; 4.5 Non Integer Derivative Control of the Steady State in Chua's Circuit; 4.5.1 β Parameter and Piecewise Linear Resistor; 4.6 PIλDμ Non Integer Order Controller; 4.7 Non Linear System Control via PIλDμ Controller; Chapter 5 Non Integer Order Cellular Neural Network Systems; 5.1 Standard and Non Integer Order CNNs; 5.1.1 From Integer to Non Integer Order CCNs; 5.2 Image Processing Applications; 5.3 Autowaves in Non Integer Order CNNs; 5.3.1 The Non Integer Order CNN Simulator

5.3.2 Simulation of the Complex PhenomenaChapter 6 Circuit Design of Non Integer Order Chaotic Systems; 6.1 Non Integer Order and Chaos; 6.2 The Duffing System; 6.3 Non Integer Order CNNs and Chaos; 6.3.1 Numerical Example; 6.4 The Two-Cell CNN Circuit; Chapter 7 Conclusion; 7.1 The Status of the Non Integer Order System Research; 7.2 What It Needs to be Done; 7.3 Scheme of the book; References; Chapter I; Chapter II; Chapter III; Chapter IV; Chapter V; Chapter VI; APPENDIX; MATLAB FUNCTION FOR INTEGRATION; MATLAB FUNCTION FOR THE STUDY OF NON INTEGER ORDER SYSTEMS

MATLAB FUNCTION FOR THE REALIZATION OF THE SINGULARITY FUNCTION METHODDESCRIPTION OF THE SIMULATOR FOR THE NON INTEGER ORDER CNN (QCNNSIM).; NON INTEGER ORDER PLANT AND PD CONTROLLER; INDEX

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 151-157) and index.

ISBN:

9789812791856

981279185X