Three Decades of Mathematical System Theory: A Collection of Surveys at the Occasion of the 50th Birthday of Jan C. Willems

ISBN-13: 9783540516057 / Angielski / Miękka / 1989 / 567 str.

Hendrik Nijmeijer; Johannes M. Schumacher

Opis

The field of modern mathematical system theory has its origins in the work of R.E. Kalman in the late fifties. It came to a rapid development in the early sixties, and has seen a continuing and still growing stream of contributions in the years that followed. Today, it stands as a well-established discipline. The volume Three Decades of Mathematical System Theory surveys the developments in this field by presenting 21 articles covering the broad area of system and control theory. All articles have been written by well-known authors, who were invited to give their personal expert view on a particular direction of research. Together, the contributions in this volume review the wide range of mathematical methods that are being applied in modern system and control theory. The mathematical fields that are involved included differential and algebraic geometry, linear and commutative algebra, and functional and stochastic analysis.

Spis treści

The cascade structure in system theory.- Smooth dynamical systems which realize arithmetical and logical operations.- Pole assignment by output feedback.- Zeros, poles and modules in linear system theory.- Representations of infinite-dimensional systems.- Symmetric modeling in system identification.- Elements of factorization theory from a polynomial point of view.- A state space approach to H ? optimal control.- Decentralized control of large scale systems.- State space approach to the classical interpolation problem and its applications.- Generalized state-space systems and proper stable matrix fractions.- Scattering theory, unitary dilations and Gaussian processes.- On the theory of nonlinear control systems.- Aggregation of linear systems in a completely deterministic framework.- Linear system representations.- Optimal Control.- System theory and mechanics.- The impact of the singular value decomposition in system theory, signal processing, and circuit theory.- Stochastic realization problems.- Robust stabilization of uncertain dynamic systems.- On the control of discrete-event systems.