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.

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.

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 book contains the plenary lectures presented at the Workshop 'Operators, Systems and Linear Algebra: Three Decades of Algebraic Systems Theory, ' held in Kaiserslautern, Germany, September 24-26, 1997. It is a Festschrift honoring the impact of the work of Paul Fuhrmann in operator and control theory. The book includes essays written by prominent scientists to present their views on some of the most recent developments in the area of mathematical systems theory and its applications. The papers cover a wide range of theoretical and applied topics, with emphasis on computational aspects and relations to engineering problems. The impact of Paul Fuhrmann's work can be traced through many parts of the volume. Polynomial models and shift realizations, the algebraic structure of linear state feedback, partial realization theory and the recursive inversion of Hanke! and Toeplitz operators, spectral factorization, and parametrizations of classes of rational functions are some of the topics in the book, where explicit references are made to his work. It is impossible to give in this short preface any substantial review of Paul Fuhr- mann's numerous and major contributions to finite and infinite dimensionallinear systems theory. Instead we like to emphasize that his work demonstrates in a clear way the underlying attempt to unreveal the basic unity of mathematics.