The past few decades have witnessed an increasing interest in the field of multidimensional systems theory. This is concerned with systems whose trajectories depend not on one single variable (usually interpreted as time or frequency), but on several independent variables, such as the coordinates of an image. The behavioural approach introduced by J. C. Willems provides a particularly suitable framework for developing a linear systems theory in several variables. The book deals with the classical concepts of autonomy, controllability, observability, and stabilizability. All the tests and criteria given are constructive in the sense that algorithmic versions may be implemented in modern computer algebra systems, using Gröbner basis techniques. There is a close connection between multidimensional systems theory and robust control of one-dimensional systems with several uncertain parameters. The central link consists in the basic tool of linear fractional transformations. The book concludes with examples from the theory of electrical networks.

Advanced Topics in Control Systems Theory contains selected contributions written by lecturers at the second (annual) Formation d’Automatique de Paris (FAP) (Graduate Control School in Paris). It is addressed to graduate students and researchers in control theory with topics touching on a variety of areas of interest to the control community such as cascaded systems, flatness, optimal control, and Hamiltonian and infinite-dimensional systems. The reader is provided with a well-integrated synthesis of the latest thinking in these subjects without the need for an exhaustive literature review. The internationally known contributors to this volume represent many of the most reputable control centers in Europe. Advanced Topics in Control Systems Theory can be used to support either a one-term general advanced course on nonlinear control theory, devoting a few lectures to each chapter, or for more focused and intensive courses at graduate level. The book’s concise but pedagogical manner will give an ideal start to researchers wishing to broaden their knowledge in aspects of modern control theory outside their own expertise.

The Second Edition of this book includes an abundance of examples to illustrate advanced concepts and brings out in a text book setting the algorithms for bivariate polynomial matrix factorization results that form the basis of two-dimensional systems theory. Algorithms and their implementation using symbolic algebra are emphasized.

Revised and updated, this concise new edition of the pioneering book on multidimensional signal processing is ideal for a new generation of students. Multidimensional systems or m-D systems are the necessary mathematical background for modern digital image processing with applications in biomedicine, X-ray technology and satellite communications. Serving as a firm basis for graduate engineering students and researchers seeking applications in mathematical theories, this edition eschews detailed mathematical theory not useful to students. Presentation of the theory has been revised to make it more readable for students, and introduce some new topics that are emerging as multidimensional DSP topics in the interdisciplinary fields of image processing. New topics include Groebner bases, wavelets, and filter banks.

This research report brings together present trends in advanced welding robots, robotic welding, artificial intelligent and automatic welding. It includes important technical subjects on welding robots such as intelligent technologies and systems, and design and analysis. Modeling, identification and control of the welding process are presented, as well as knowledge-based systems for welding and tele-robotic welding. Other topics covered are sensing and data fusion, computer vision and virtual-reality applications of the welding process. An overview of intelligent and flexible manufacturing systems is given in addition to artificial intelligent technologies for industrial processes.

This book is based on a workshop entitled "Robust Control workshop 2000". The workshop was held in Newcastle, Australia, from the 6th to the 8th December 2000. Chapters of the book are written by some of the leading researchers in the field of Robust Control. They cover a variety of topics all related to Robust Control and analysis of uncertain systems.

This book aims at reviewing recent progress in the direction of algebraic and symbolic computation methods for functional systems, e.g. ODE systems, differential time-delay equations, difference equations and integro-differential equations. In the nineties, modern algebraic theories were introduced in mathematical systems theory and in control theory. Combined with real algebraic geometry, which was previously introduced in control theory, the past years have seen a flourishing development of algebraic methods in control theory. One of the strengths of algebraic methods lies in their close connections to computations. The use of the above-mentioned algebraic theories in control theory has been an important source of motivation to develop effective versions of these theories (when possible). With the development of computer algebra and computer algebra systems, symbolic methods for control theory have been developed over the past years. The goal of this book is to propose a partial state of the art in this direction. To make recent results more easily accessible to a large audience, the chapters include materials which survey the main mathematical methods and results and which are illustrated with explicit examples.

This volume is based on the course notes of the 2nd NCN Pedagogical School, the second in the series of Pedagogical Schools in the frame work of the European TMR project, "Breakthrough in the control of nonlinear systems (Nonlinear Control Network)". The school consists of four courses that have been chosen to give a broad range of techniques for the analysis and synthesis of nonlinear control systems, and have been developed by leading experts in the field. The topics covered are: Differential Algebraic Methods in Nonlinear Systems; Nonlinear QFT; Hybrid Systems; Physics in Control. The book has a pedagogical character, and is specially directed to postgraduates in most areas of engineering and applied sciences like mathematics and physics. It will also be of interest to researchers and practitioners needing a solid introduction to the above topics.

This book keeps an eye in the direction of applications of advanced and high performance scientific computing in describing the behavior of natural and constructed systems, e.g. chaos, bifurcation, fractal, Lyapunov exponent, period doubling, Poincaré map, strange attractor etc. With the aid of powerful computers the modem theory of chaos and its geometry, the fractals, and attractors are developed. The concepts of object oriented computing are introduced early in the text and steadily expanded as one progresses through the chapters. The beginning of each chapter is of an introductory nature, followed by practical applications, the discussion of numerical results, theoretical investigations on nonlinear stability and convergence. This is the first complete introduction to process modelling and computing that fully integrates software tools — enabling professionals and students to master critical techniques hands on through computer simulations based on the popular MATLAB environment. The book offers a simple tool for all those oscillations that are travelling through the world, helping them discover its hidden beauty. Many applications as well as results of computer simulations are presented. The center of concern is set on existing as well as emerging continuous methods of investigations useful for researchers, engineers and practitioners active in many and often interdisciplinary fields, where physics, electrochemistry, biology and medicine play a key role. Coverage includes: • Dynamic behavior of nonlinear systems, • Fundamental descriptions of processes exhibiting nonlinear oscillations, • Mechanism and function of structures of nonlinear oscillations’ patterns, • Analysis of dynamical oscillations in electric circuits and systems, • Artificial intelligence models of natural systems, • Nonlinear oscillations in chemistry, biology and medicine, • Oscillations in mechanics and transport systems, • Oscillations in fractional-order systems, • Energy harvesting systems from the surrounding environment. With an insatiable appetite for exploring the surrounding world and doing research, this book can help readers quickly find ways to use new computers and facilitate the quest for greater knowledge and understanding of reality. The reach of novelty of the book ranges from new mathematical ideas to motivating questions and science issues in many subject areas.

This book aims to present a survey of a large class of nonlinear dynamical systems exhibiting mixed-mode oscillations (MMOs). It is a sort of a guide to systems related to MMOs that features material from original research papers, including the author’s own studies. The material is presented in seven chapters divided into sections. Usually, the first sections are of an introductory nature, explain phenomena, and exhibit numerical results. More advanced investigations are presented in the subsequent sections. Coverage includes * Dynamic behavior of nonlinear systems, * Fundamentals of processes exhibiting MMOs,* Mechanism and function of an structure of MMOs patterns, * Analysis of MMOs in electric circuits and systems, * MMOs in chemistry, biology, and medicine, * MMOs in mechanics and transport vehicles, * MMOs in fractional order systems. This is the first extensive description of these topics and the interpretation of analytical results and those obtained from computer simulations with the MATLAB environment. The book provides the readers with better understanding of the nature of MMOs, richness of their behaviors, and interesting applications.