Approximate and noisy realization of discrete-time dynamical systems (Q931082)

In this monograph new interesting results concerning the following two problems are presented. Approximate realization problem: For any given input/output map without noise, find a mathematical model such that its behavior is approximate equal to the input/output map and has lower dimension than minimal state space model. Noisy realization problem: For any given input/output map with noise, find a mathematical model which has the same input/output map. A new method called the constrained least square method is proposed to solve the problems. This monograph is a continuation and extension of the monograph by Matsuo and Hasegawa published in 2003. After two first chapters devoted to basic matters each chapter from 3 to 8 deals with the problems of one dynamical system: chapter 3 with linear systems, chapter 4 with so-called linear systems, chapter 5 with almost linear systems, chapter 6 with pseudo linear systems, chapter 7 with affine dynamical systems and chapter 8 with linear representation systems. This monograph can be recommended first of all to scientists and Phd students with good mathematical backgrounds.