Realization Theory Of Continuous Time Dynamical Systems

System Theory of Continuous Time Finite Dimensional Dynamical Systems

This book discusses the realization and control problems of finite-dimensional dynamical systems which contain linear and nonlinear systems. The author focuses on algebraic methods for the discussion of control problems of linear and non-linear dynamical systems. The book contains detailed examples to showcase the effectiveness of the presented method. The target audience comprises primarily research experts in the field of control theory, but the book may also be beneficial for graduate students alike.

Realization Theory of Continuous-Time Dynamical Systems

Realization Theory of Continuous-time Dynamical Systems

In this monograph, I shall present a basis of realization theory of dynamical system. Realization problem is to determine an intrinsic mathematical model (canonical dynamical system) from the input-output relations of a given causal black box, i.e., to understand fully the internal behavior of the black box from the experimental data of it. Moreover, if possible, we want to make the mathematical model real. Realization theory was mainly developed in the field of discrete-time linear systems as the algebraic system theory. On the other hand, it has been recognized that the highly developed automata theory has close relations with realization theory. However, there exist serious gaps between discrete-time linear systems and automata, for example, the way of action of inputs on states are quite different. In continuous-time linear system, the situation is worse. There is no established way to think what is the set of input functions which act on states.