Challenges of a Generalized System Theory

During the last five or six years a new general method has been discovered which allows one to transform system theoretical results and techniques into a non-stationary framework that were originally restricted to the analysis of time-variant systems and signals. Mathematically this approach involves complicated transitions from functions defining Toeplitz matrices to operators that appear as input-output maps of time-variant systems, from shifts to weighted shifts, from analytic functions to triangular operators, from Laplace and z-transforms to diagonal transforms and non-stationary evaluation maps. This breakthrough has stimulated various researchers to study and extend classical system theoretical problems in a non-stationary context. In its wake, a host of new results have been derived, many of which are documented in this book. In addition, the book provides comprehensive mathematical treatment of time varying systems, new methods for modelling and model reduction of systems, and applications to robust control. It should be of value to engineering and mathematical departments as well as research institutes.
 
During the last five or six years a new general method has been discovered which allows one to transform system theoretical results and techniques into a non-stationary framework that were originally restricted to the analysis of time-variant systems and signals. Mathematically this approach involves complicated transitions from functions defining Toeplitz matrices to operators that appear as input-output maps of time-variant systems, from shifts to weighted shifts, from analytic functions to triangular operators, from Laplace and z-transforms to diagonal transforms and non-stationary evaluation maps. This breakthrough has stimulated various researchers to study and extend classical system theoretical problems in a non-stationary context. In its wake, a host of new results have been derived, many of which are documented in this book. In addition, the book provides comprehensive mathematical treatment of time varying systems, new methods for modelling and model reduction of systems, and applications to robust control. It should be of value to engineering and mathematical departments as well as research institutes.